Econ 104: Project Part 1
Anvita Chinthada 106287217| Kexin (Asteria) Xue 306293123| Khun Sint Nay Chi Tin Tun 206230876
2025-02-26
file_list <- list.files(path = "/Users/khunsint/Desktop", pattern = "*.csv", full.names = TRUE)
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## Loading required package: urcaall_columns <- unique(unlist(lapply(file_list, function(x) colnames(read.csv(x)))))
df_list <- lapply(file_list, function(file) {
data <- read.csv(file)
data[setdiff(all_columns, colnames(data))] <- NA
data[, all_columns]
})
df <- do.call(rbind, df_list)
head(df)## NULL infy_stock <- read.csv("~/Desktop/R Project/archive/infy_stock.csv")
attach(infy_stock)Introduction
This project focuses on modeling the National Stock Exchange Data from Indian IT companies in a time series analysis. We are modeling data on the INFY (Infosys is a technology company headquartered in India) stock recorded in 2015. Understanding the different measures of the stock market, it made more logical sense to use Close (Closing Price) and Turnover ( Stock turnover ratio) as response variables (y1 and y2) and Volume (total # of shares traded) and Open (current day opening point) as explanatory variables (independent variables x1 and x2). Using these four variable,s we will show and select different time series models that best fit the data to understand trends in the National Stock Exchange and to draw conclusions about the company.
Descriptive Analysis
Variables we are modeling: Close, Turnover, Volume, and Open
library(tidyverse)
attach(infy_stock)## The following objects are masked from infy_stock (pos = 3):
##
## Close, Date, Deliverable.Volume, High, Last, Low, Open, Prev.Close,
## Series, Symbol, Trades, Turnover, Volume, VWAP, X.DeliverbleStatistical Summaries
Close <- infy_stock$Close
fivenum(Close)## [1] 937.500 1085.825 1149.325 2126.425 2324.700summary(Close)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 937.5 1085.9 1149.3 1548.0 2125.3 2324.7Turnover <- infy_stock$Turnover
fivenum(Turnover)## [1] 3.923481e+13 2.843912e+14 3.624709e+14 4.916011e+14 2.285439e+15summary(Turnover)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.923e+13 2.847e+14 3.625e+14 4.234e+14 4.915e+14 2.285e+15Volume <- infy_stock$Volume
fivenum(Volume)## [1] 353652 1722570 2532474 3575393 19155056summary(Volume)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 353652 1722753 2532474 2982072 3567063 19155056Open <- infy_stock$Open
fivenum(Open)## [1] 941.000 1088.000 1150.000 2136.375 2328.500summary(Open)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 941 1088 1150 1551 2136 2328Histograms:
Histogram for Close is a bimodal distribution since there are two significant ranges with a split in the histogram. One of the clusters in centered around $1000 and another is centered around $2000. The histogram also shows the highest frequency of closing price (significantly higher) from around $1000-$1250.
hist(infy_stock$Close, breaks = "FD", col = "pink", main = "Normal Distr. of Close", xlab = "Close", probability = TRUE)
lines(density(infy_stock$Close))
Histogram for Turnover is a right-skewed distribution meaning that most of the values fall on the lower side. There are a few outlier values that seem to be extreme since they are not near the concentrated area of values. The majority of the observations fall from 0 to 5.0e+14.
hist(infy_stock$Turnover, breaks = "FD", col = "pink", main = "Normal Distr. of Turnover", xlab = "Turnover", probability = TRUE)
lines(density(infy_stock$Turnover))
The histogram for Volume is a right-skewed distribution and most of the values fall on the lower side. There are clearly a few outliers, a few of which are significantly higher than where the data is mostly concentrated around.
hist(infy_stock$Volume, breaks = "FD", col = "pink", main = "Normal Distr. of Volume", xlab = "Volume", probability = TRUE)
lines(density(infy_stock$Volume))
Histogram for Open is also a bimodal distribution where there are two significant clusters of values with a split in the histogram. These clusters are around $1000 and $2000. Between values $1200 to $1800 (approximately) there are no recorded values.
hist(infy_stock$Open, breaks = "FD", col = "pink", main = "Normal Distr. of Open", xlab = "Open", probability = TRUE)
lines(density(infy_stock$Open))
Scatterplots
Scatterplot got Close shows two different ranges in price. One from $1800 to $2400 and another one from $900 to $1100.
data <- infy_stock
plot(infy_stock$Close, col = "red")
title ('Scatter Plot of Close')
Scatterplot for Turnover shows that the values are concentrated around 5.0e+14. The values also seem to be consistently spread across a bounded range. However, there are a few outliers exceeding a lot above 5.0e+14.
data <- infy_stock
plot(infy_stock$Turnover, col = "red")
title ('Scatter Plot of Turnover')
Scatterplot for Volume shows values concentrated around a little less than 5.0e+06 shares and are consistently spread out for a majority of the values. There are a few outliers that exceed this range and the highest point seems to be at 1.5e+07 shares.
data <- infy_stock
plot(infy_stock$Volume, col = "red")
title ('Scatter Plot of Volume')
Scatterplot for Open shows two different ranges similar to the Closing price.
data <- infy_stock
plot(infy_stock$Open, col = "red")
title ('Scatter Plot of Open')
Quantile Plots
The Quantile Plot for close shows that the data doesn’t follow a normal distribution because of how deviated the data is from the reference line (red line). Since there are many deviations on the left side and on the right side, it indicates that there are both lower and higher than expected values.
qqnorm(infy_stock$Close, main = "Q-Q Plot of Close")
qqline(infy_stock$Close, col = "red")
The quantile plot for Turnover shows that the centered portion of the data aligns well with the reference line, exhibiting a more normal pattern.
qqnorm(infy_stock$Turnover, main = "Q-Q Plot of Turnover")
qqline(infy_stock$Turnover, col = "red")
Quantile plot for volume hat the centered portion of the data aligns well with the reference line, exhibiting a more normal pattern.
qqnorm(infy_stock$Volume, main = "Q-Q Plot of Volume")
qqline(infy_stock$Volume, col = "red")
Quantile Plot for Open shows that the data doesn’t follow a normal distribution because of how deviated the data is from the reference line (red line). Since there are many deviations on the left side and on the right side, it indicates that there are both lower and higher than expected values.
qqnorm(infy_stock$Open, main = "Q-Q Plot of Open")
qqline(infy_stock$Open, col = "red")
Box Plots
Box Plot for Close shows the median is in the lower quartile, and shows a large interquartile range. Therefore the prices (closing price) could be widely spread.
boxplot(infy_stock$Close, ylab="Close")
Box Plot for Turnover shows the interquartile range being significantly smaller than the range of the data meaning there isn’t a widespread consistency in the data but rather a concentration in one area. The Median line indicates that the data isn’t symmetrically distributed.
boxplot(infy_stock$Turnover, ylab="Turnover")
The box Plot for Volume shows many outlier values, and the interquartile range shows that many values are clustered around a certain value so it is not widely spread. Median line is towards the lower end of the p=Turnover values.
boxplot(infy_stock$Volume, ylab="Volume")
The Box Plot for Open shows a large interqaurtile range like Close and the median line is in the lower quartile which means that the data could be rightly skewed. There are no significant outliers.
boxplot(infy_stock$Open, ylab="Open")
Scatterplot Matrix
The scatter plot for close vs open shows a strong positive correlation, and the narrow band exhibits a smaller confidence interval. This means that as the opening price gets higher, the closing price also increases (The opening and closing price of a stock for a specific day will not have much variation).
scatterplot(Close~Open, data = infy_stock, col="red", main = "Scatter Plot for Close vs Open")
The Scatter Plot for Close vs. volume shows a negative relationship. This means that as volume (total number of shares traded) increases per day, closing prices tend to be lower. The band (confidence interval) shows that at lower volume the interval is tighter and at higher volumes the interval expands.
scatterplot(Close~Volume, data = infy_stock, col="red", main = "Scatter Plot for Close vs Volume")
The scatterplot for Turnover vs. Open shows neither a positive nor negative relationship but a non-linear correlation since the line is flat. This means the correlation is weak. The band shows a wide confidence interval between observations.
scatterplot(Turnover~Open, data = infy_stock, col="red", main = "Scatter Plot for Turnover vs Open")
The scatterplot for Turnover vs Volume shows a strong positive correlation, and the band for the confidence interval starts out narrow and continues to get wider as Volume increases.
scatterplot(Turnover~Volume, data = infy_stock, col="red", main = "Scatter Plot for Turnover vs Volume")
The tsdisplay plot for each variables
infy_stock.ts <- ts(infy_stock,
start=c(2015,1),
end=c(2015,365),
frequency=365)
Close.ts <- infy_stock.ts[,"Close"]
Turnover.ts <- infy_stock.ts[,"Turnover"]
Volume.ts <- infy_stock.ts[,"Volume"]
Open.ts <- infy_stock.ts[,"Open"]
tsdisplay(Close.ts)
tsdisplay(Turnover.ts)
tsdisplay(Volume.ts)
tsdisplay(Open.ts)
The variables Close and Open are not stationary as they don’t seem mean-reverting and therefore not stationary
Open.ts.diff <- diff(Open.ts)
tsdisplay(Open.ts.diff)
Close.ts.diff <- diff(Close.ts)
tsdisplay(Close.ts.diff)
Commenting on the stationarity, ACF and PACF results
Close Variable
According to the ACF and PACF of the Close variable, we can see that the variable is not stationary, since the distribution shows a strong disconnect from 2015.3 to 2015.7. Therefore, the variable is not mean-reverting. To transform this variable into a stationary variable, we take the difference of the Close (close price) by doing Close.ts.diff <- diff(Close.ts), and the result is shown in tsdisplay(Close.ts.diff). The transform Close.ts.diff seems mean-reverting and has constant variance with three outliers. Since the outliers are rare, we can conclude that the transformed variable is stationary enough for analysis. After transformation, the ACF shows no strong autocorrelation beyond lag 0. Most autocorrelations are within the blue significance bounds, meaning they are not statistically significant. The PACF also shows no significant spikes beyond lag 0. The few spikes that appear are not systematically cutting off at a specific lag, reinforcing that this is likely white noise.
Open Variable
According to the ACF and PACF of the Open variable, we can see that the variable is not stationary, since the distribution shows a strong disconnect from 2015.3 to 2015.7(same as the close variable). Therefore, the variable is not mean-reverting. To transform this variable into a stationary variable, we take the difference of Open (open price) by doing Open.ts.diff <- diff(Open.ts), and the result is shown in tsdisplay(Open.ts.diff). The transform Open.ts.diff seems mean-reverting and has constant variance, with three outliers. Since the outliers are rare, we can conclude that the transformed variable is stationary enough for analysis. After transformationThe ACF shows no strong autocorrelation beyond lag 0. Most autocorrelations are within the blue significance bounds, meaning they are not statistically significant. The PACF also shows no significant spikes beyond lag 0. The few spikes that appear are not systematically cutting off at a specific lag, reinforcing that this is likely white noise.
Volume Variable
The distribution seems mostly mean-reverting, with 8 outliers scattered. The variable also has constant variance. SInce we have more than 300 observations, we can conclude that the outliers are not significant and the variable is mostly stationary. The ACF does not remain high for many lags (which would indicate a unit root). Instead, it gradually declines, which can still work for AR modeling. A very slow decay (approaching 1 at high lags) would strongly suggest non-stationarity, but here the decay is moderate. The PACF cuts off after lag 1, which is a classic sign of an AR process. This suggests that an autoregressive (AR) model is appropriate.
Turnover Variable
The distribution seems mostly mean-reverting, with 8 outliers scattered. The variable also has constant variance. SInce we have more than 300 observations, we can conclude that the outliers are not significant and the variable is mostly stationary. The ACF does not remain high for many lags (which would indicate a unit root). Instead, it gradually declines, which can still work for AR modeling. A very slow decay (approaching 1 at high lags) would strongly suggest non-stationarity, but here the decay is moderate. The PACF cuts off after lag 1, which is a classic sign of an AR process. This suggests that an autoregressive (AR) model is appropriate.
AR Model for CLOSE (diff) (based on ACF and PACF graphs, the two lags models to use would be from 1-110 and only 110)
AR.Close.ts.diff.lag110 <- dynlm(Close.ts.diff~L(Close.ts.diff,110))
summary(AR.Close.ts.diff.lag110)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Close.ts.diff ~ L(Close.ts.diff, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -978.86 -12.09 4.97 19.11 872.23
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.72438 6.67589 -0.558 0.577
## L(Close.ts.diff, 110) -0.05206 0.07709 -0.675 0.500
##
## Residual standard error: 106.4 on 252 degrees of freedom
## Multiple R-squared: 0.001806, Adjusted R-squared: -0.002155
## F-statistic: 0.456 on 1 and 252 DF, p-value: 0.5001AR.Close.ts.diff.lag1.110 <- dynlm(Close.ts.diff~L(Close.ts.diff,1:110))
summary(AR.Close.ts.diff.lag1.110)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Close.ts.diff ~ L(Close.ts.diff, 1:110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -864.84 -19.97 5.33 27.12 852.50
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.2418672 8.3786908 -0.387 0.699
## L(Close.ts.diff, 1:110)1 0.0159777 0.0836037 0.191 0.849
## L(Close.ts.diff, 1:110)2 0.0226932 0.0835975 0.271 0.786
## L(Close.ts.diff, 1:110)3 -0.0338749 0.0836433 -0.405 0.686
## L(Close.ts.diff, 1:110)4 0.0223533 0.0836930 0.267 0.790
## L(Close.ts.diff, 1:110)5 -0.0092028 0.0837563 -0.110 0.913
## L(Close.ts.diff, 1:110)6 0.0884463 0.1010973 0.875 0.383
## L(Close.ts.diff, 1:110)7 0.0069257 0.1013506 0.068 0.946
## L(Close.ts.diff, 1:110)8 -0.0274712 0.1013067 -0.271 0.787
## L(Close.ts.diff, 1:110)9 0.0398144 0.1012823 0.393 0.695
## L(Close.ts.diff, 1:110)10 -0.0218935 0.1013141 -0.216 0.829
## L(Close.ts.diff, 1:110)11 0.0058744 0.1013472 0.058 0.954
## L(Close.ts.diff, 1:110)12 -0.0570005 0.1013255 -0.563 0.575
## L(Close.ts.diff, 1:110)13 0.0597780 0.1013998 0.590 0.556
## L(Close.ts.diff, 1:110)14 0.0357480 0.1014407 0.352 0.725
## L(Close.ts.diff, 1:110)15 0.0498519 0.1014621 0.491 0.624
## L(Close.ts.diff, 1:110)16 0.0038393 0.1015560 0.038 0.970
## L(Close.ts.diff, 1:110)17 -0.0294803 0.1013645 -0.291 0.772
## L(Close.ts.diff, 1:110)18 -0.0147365 0.1013580 -0.145 0.885
## L(Close.ts.diff, 1:110)19 -0.0206962 0.1013525 -0.204 0.838
## L(Close.ts.diff, 1:110)20 -0.0559949 0.1012260 -0.553 0.581
## L(Close.ts.diff, 1:110)21 -0.0430001 0.1013242 -0.424 0.672
## L(Close.ts.diff, 1:110)22 0.0055223 0.1013444 0.054 0.957
## L(Close.ts.diff, 1:110)23 0.0106073 0.1013348 0.105 0.917
## L(Close.ts.diff, 1:110)24 0.0648144 0.1010454 0.641 0.522
## L(Close.ts.diff, 1:110)25 -0.0139403 0.1011627 -0.138 0.891
## L(Close.ts.diff, 1:110)26 -0.0812167 0.1011572 -0.803 0.423
## L(Close.ts.diff, 1:110)27 0.0114422 0.1013671 0.113 0.910
## L(Close.ts.diff, 1:110)28 0.0440350 0.1013496 0.434 0.665
## L(Close.ts.diff, 1:110)29 0.0371217 0.1014123 0.366 0.715
## L(Close.ts.diff, 1:110)30 -0.0723102 0.1013736 -0.713 0.477
## L(Close.ts.diff, 1:110)31 0.0039553 0.1015621 0.039 0.969
## L(Close.ts.diff, 1:110)32 0.0056048 0.1015763 0.055 0.956
## L(Close.ts.diff, 1:110)33 0.0245252 0.1015922 0.241 0.810
## L(Close.ts.diff, 1:110)34 -0.0061197 0.1016102 -0.060 0.952
## L(Close.ts.diff, 1:110)35 0.0928452 0.1011359 0.918 0.360
## L(Close.ts.diff, 1:110)36 0.0424102 0.1013987 0.418 0.676
## L(Close.ts.diff, 1:110)37 0.0091770 0.1014057 0.090 0.928
## L(Close.ts.diff, 1:110)38 -0.0384362 0.1012522 -0.380 0.705
## L(Close.ts.diff, 1:110)39 0.0503154 0.1011587 0.497 0.620
## L(Close.ts.diff, 1:110)40 0.0399346 0.1012265 0.395 0.694
## L(Close.ts.diff, 1:110)41 -0.0189568 0.1014365 -0.187 0.852
## L(Close.ts.diff, 1:110)42 -0.0145250 0.1014390 -0.143 0.886
## L(Close.ts.diff, 1:110)43 -0.0352909 0.1014361 -0.348 0.728
## L(Close.ts.diff, 1:110)44 -0.0384279 0.1014462 -0.379 0.705
## L(Close.ts.diff, 1:110)45 -0.0173849 0.1014600 -0.171 0.864
## L(Close.ts.diff, 1:110)46 -0.0683404 0.1014104 -0.674 0.501
## L(Close.ts.diff, 1:110)47 0.0236919 0.1014716 0.233 0.816
## L(Close.ts.diff, 1:110)48 0.0401431 0.1014935 0.396 0.693
## L(Close.ts.diff, 1:110)49 0.0413050 0.1015298 0.407 0.685
## L(Close.ts.diff, 1:110)50 0.0649748 0.1015575 0.640 0.523
## L(Close.ts.diff, 1:110)51 -0.0312912 0.1016223 -0.308 0.759
## L(Close.ts.diff, 1:110)52 -0.0420572 0.1015429 -0.414 0.679
## L(Close.ts.diff, 1:110)53 0.0665238 0.1014135 0.656 0.513
## L(Close.ts.diff, 1:110)54 -0.0286601 0.1015852 -0.282 0.778
## L(Close.ts.diff, 1:110)55 -0.0024781 0.1015848 -0.024 0.981
## L(Close.ts.diff, 1:110)56 0.0317418 0.1015843 0.312 0.755
## L(Close.ts.diff, 1:110)57 -0.0246884 0.1015788 -0.243 0.808
## L(Close.ts.diff, 1:110)58 -0.0434951 0.1015490 -0.428 0.669
## L(Close.ts.diff, 1:110)59 0.0308901 0.1016062 0.304 0.762
## L(Close.ts.diff, 1:110)60 0.0488192 0.1016090 0.480 0.632
## L(Close.ts.diff, 1:110)61 -0.0421448 0.1015130 -0.415 0.679
## L(Close.ts.diff, 1:110)62 -0.0244018 0.1015429 -0.240 0.810
## L(Close.ts.diff, 1:110)63 -0.0375576 0.1014241 -0.370 0.712
## L(Close.ts.diff, 1:110)64 -0.0388429 0.1015070 -0.383 0.703
## L(Close.ts.diff, 1:110)65 0.0311338 0.1014450 0.307 0.759
## L(Close.ts.diff, 1:110)66 0.0567100 0.1014134 0.559 0.577
## L(Close.ts.diff, 1:110)67 0.0277998 0.1014939 0.274 0.785
## L(Close.ts.diff, 1:110)68 0.0257939 0.1014602 0.254 0.800
## L(Close.ts.diff, 1:110)69 -0.0086599 0.1014762 -0.085 0.932
## L(Close.ts.diff, 1:110)70 0.0072461 0.1014847 0.071 0.943
## L(Close.ts.diff, 1:110)71 -0.0432676 0.1013738 -0.427 0.670
## L(Close.ts.diff, 1:110)72 -0.0415484 0.1014075 -0.410 0.683
## L(Close.ts.diff, 1:110)73 0.0910813 0.1012589 0.899 0.370
## L(Close.ts.diff, 1:110)74 -0.0625441 0.1014783 -0.616 0.539
## L(Close.ts.diff, 1:110)75 -0.0294626 0.1015561 -0.290 0.772
## L(Close.ts.diff, 1:110)76 -0.0320286 0.1015134 -0.316 0.753
## L(Close.ts.diff, 1:110)77 0.0249377 0.1014821 0.246 0.806
## L(Close.ts.diff, 1:110)78 -0.0236800 0.1014784 -0.233 0.816
## L(Close.ts.diff, 1:110)79 -0.0226653 0.1014869 -0.223 0.824
## L(Close.ts.diff, 1:110)80 0.0305778 0.1014822 0.301 0.764
## L(Close.ts.diff, 1:110)81 0.0123753 0.1014071 0.122 0.903
## L(Close.ts.diff, 1:110)82 -0.0247163 0.1014219 -0.244 0.808
## L(Close.ts.diff, 1:110)83 0.0056352 0.1014384 0.056 0.956
## L(Close.ts.diff, 1:110)84 -0.0310366 0.1013726 -0.306 0.760
## L(Close.ts.diff, 1:110)85 -0.0020362 0.1011613 -0.020 0.984
## L(Close.ts.diff, 1:110)86 -0.0126342 0.1011472 -0.125 0.901
## L(Close.ts.diff, 1:110)87 -0.0918818 0.1010208 -0.910 0.365
## L(Close.ts.diff, 1:110)88 -0.0349886 0.1012829 -0.345 0.730
## L(Close.ts.diff, 1:110)89 -0.0156798 0.1013276 -0.155 0.877
## L(Close.ts.diff, 1:110)90 0.0041301 0.1012953 0.041 0.968
## L(Close.ts.diff, 1:110)91 0.0501664 0.1012378 0.496 0.621
## L(Close.ts.diff, 1:110)92 0.0161658 0.1013289 0.160 0.873
## L(Close.ts.diff, 1:110)93 0.0122805 0.1013494 0.121 0.904
## L(Close.ts.diff, 1:110)94 0.0971465 0.1011898 0.960 0.339
## L(Close.ts.diff, 1:110)95 -0.0175875 0.1015111 -0.173 0.863
## L(Close.ts.diff, 1:110)96 -0.0195728 0.1014529 -0.193 0.847
## L(Close.ts.diff, 1:110)97 -0.0590493 0.1013925 -0.582 0.561
## L(Close.ts.diff, 1:110)98 -0.0216744 0.1014251 -0.214 0.831
## L(Close.ts.diff, 1:110)99 0.0490977 0.1013339 0.485 0.629
## L(Close.ts.diff, 1:110)100 0.0125655 0.1014184 0.124 0.902
## L(Close.ts.diff, 1:110)101 -0.0137678 0.1014420 -0.136 0.892
## L(Close.ts.diff, 1:110)102 -0.0359516 0.1013823 -0.355 0.723
## L(Close.ts.diff, 1:110)103 0.0471292 0.1013844 0.465 0.643
## L(Close.ts.diff, 1:110)104 -0.0358237 0.1014073 -0.353 0.724
## L(Close.ts.diff, 1:110)105 -0.0950821 0.1008008 -0.943 0.347
## L(Close.ts.diff, 1:110)106 -0.0008114 0.1011113 -0.008 0.994
## L(Close.ts.diff, 1:110)107 -0.0105709 0.1010718 -0.105 0.917
## L(Close.ts.diff, 1:110)108 0.0129233 0.1009916 0.128 0.898
## L(Close.ts.diff, 1:110)109 -0.0157170 0.1009892 -0.156 0.877
## L(Close.ts.diff, 1:110)110 -0.0322934 0.1009697 -0.320 0.750
##
## Residual standard error: 133 on 143 degrees of freedom
## Multiple R-squared: 0.1144, Adjusted R-squared: -0.5669
## F-statistic: 0.1679 on 110 and 143 DF, p-value: 1AR model for Turnover (based on ACF and PACF graphs, the two lags models to use would be from 1-4 and only lags 2,61,70 and 117)
AR.Turnover.ts.lag1.4 <- dynlm(Turnover.ts~L(Turnover.ts,1:4))
summary(AR.Turnover.ts.lag1.4)##
## Time series regression with "ts" data:
## Start = 2015(5), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.822e+14 -1.147e+14 -5.190e+13 5.935e+13 1.771e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.487e+14 3.619e+13 6.872 2.85e-11 ***
## L(Turnover.ts, 1:4)1 3.297e-01 5.279e-02 6.245 1.21e-09 ***
## L(Turnover.ts, 1:4)2 1.731e-02 5.559e-02 0.311 0.7558
## L(Turnover.ts, 1:4)3 -1.393e-02 5.564e-02 -0.250 0.8025
## L(Turnover.ts, 1:4)4 9.132e-02 5.274e-02 1.732 0.0842 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.608e+14 on 356 degrees of freedom
## Multiple R-squared: 0.1235, Adjusted R-squared: 0.1136
## F-statistic: 12.54 on 4 and 356 DF, p-value: 1.491e-09AR.Turnover.ts.lag2n61n70n117 <- dynlm(Turnover.ts~L(Turnover.ts,2) + L(Turnover.ts,61) + L(Turnover.ts,70) + L(Turnover.ts, 117))
summary(AR.Turnover.ts.lag2n61n70n117)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 70) + L(Turnover.ts, 117))
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.092e+14 -1.365e+14 -1.708e+13 9.426e+13 1.448e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.793e+13 5.028e+13 0.357 0.72167
## L(Turnover.ts, 2) 1.670e-01 5.593e-02 2.985 0.00312 **
## L(Turnover.ts, 61) 2.776e-01 5.620e-02 4.940 1.46e-06 ***
## L(Turnover.ts, 70) 2.038e-01 5.620e-02 3.626 0.00035 ***
## L(Turnover.ts, 117) 3.092e-01 5.664e-02 5.460 1.18e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.377e+14 on 243 degrees of freedom
## Multiple R-squared: 0.2423, Adjusted R-squared: 0.2298
## F-statistic: 19.43 on 4 and 243 DF, p-value: 6.967e-14AR models for Volume (based on ACF and PACF graphs, the two lags models to use would be from 1-32, and 1-32 AND 91-122 together)
AR.Volume.ts.lag1.32 <- dynlm(Volume.ts~L(Volume.ts,1:32))
summary(AR.Volume.ts.lag1.32)##
## Time series regression with "ts" data:
## Start = 2015(33), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2560268 -738320 -215103 323411 16655993
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.598e+05 3.067e+05 1.499 0.1349
## L(Volume.ts, 1:32)1 3.378e-01 5.769e-02 5.856 1.25e-08 ***
## L(Volume.ts, 1:32)2 5.810e-02 6.088e-02 0.954 0.3406
## L(Volume.ts, 1:32)3 -4.009e-02 6.099e-02 -0.657 0.5115
## L(Volume.ts, 1:32)4 1.130e-01 6.073e-02 1.861 0.0637 .
## L(Volume.ts, 1:32)5 6.020e-03 6.088e-02 0.099 0.9213
## L(Volume.ts, 1:32)6 4.992e-02 6.087e-02 0.820 0.4127
## L(Volume.ts, 1:32)7 1.153e-01 6.090e-02 1.894 0.0592 .
## L(Volume.ts, 1:32)8 -1.452e-02 6.124e-02 -0.237 0.8128
## L(Volume.ts, 1:32)9 -8.593e-03 6.103e-02 -0.141 0.8881
## L(Volume.ts, 1:32)10 4.911e-02 6.103e-02 0.805 0.4216
## L(Volume.ts, 1:32)11 -6.167e-02 6.109e-02 -1.010 0.3135
## L(Volume.ts, 1:32)12 1.838e-02 6.117e-02 0.300 0.7641
## L(Volume.ts, 1:32)13 -3.072e-02 6.109e-02 -0.503 0.6154
## L(Volume.ts, 1:32)14 -3.234e-02 6.107e-02 -0.530 0.5968
## L(Volume.ts, 1:32)15 7.948e-02 6.091e-02 1.305 0.1930
## L(Volume.ts, 1:32)16 -3.868e-02 6.112e-02 -0.633 0.5273
## L(Volume.ts, 1:32)17 -2.775e-03 6.138e-02 -0.045 0.9640
## L(Volume.ts, 1:32)18 6.720e-02 6.125e-02 1.097 0.2735
## L(Volume.ts, 1:32)19 -3.024e-02 6.128e-02 -0.493 0.6221
## L(Volume.ts, 1:32)20 6.718e-03 6.125e-02 0.110 0.9127
## L(Volume.ts, 1:32)21 -3.728e-02 6.125e-02 -0.609 0.5432
## L(Volume.ts, 1:32)22 2.437e-02 6.119e-02 0.398 0.6908
## L(Volume.ts, 1:32)23 3.722e-03 6.114e-02 0.061 0.9515
## L(Volume.ts, 1:32)24 8.983e-02 6.118e-02 1.468 0.1431
## L(Volume.ts, 1:32)25 1.275e-02 6.135e-02 0.208 0.8355
## L(Volume.ts, 1:32)26 2.689e-02 5.834e-02 0.461 0.6451
## L(Volume.ts, 1:32)27 1.397e-02 5.831e-02 0.240 0.8108
## L(Volume.ts, 1:32)28 -7.804e-02 5.828e-02 -1.339 0.1816
## L(Volume.ts, 1:32)29 1.029e-01 5.817e-02 1.769 0.0779 .
## L(Volume.ts, 1:32)30 -3.212e-02 5.845e-02 -0.549 0.5831
## L(Volume.ts, 1:32)31 3.529e-02 5.844e-02 0.604 0.5464
## L(Volume.ts, 1:32)32 3.051e-02 5.529e-02 0.552 0.5814
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1702000 on 300 degrees of freedom
## Multiple R-squared: 0.2808, Adjusted R-squared: 0.204
## F-statistic: 3.66 on 32 and 300 DF, p-value: 1.741e-09AR.Volume.ts.lag1.32n90.122 <- dynlm(Volume.ts~L(Volume.ts,1:32) + L(Volume.ts,91:122))
summary(AR.Volume.ts.lag1.32n90.122)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3164619 -845564 -196953 515577 15844439
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.064e+06 9.492e+05 2.175 0.03099 *
## L(Volume.ts, 1:32)1 3.077e-01 7.471e-02 4.118 5.83e-05 ***
## L(Volume.ts, 1:32)2 8.579e-02 7.829e-02 1.096 0.27463
## L(Volume.ts, 1:32)3 -6.947e-02 7.932e-02 -0.876 0.38232
## L(Volume.ts, 1:32)4 4.361e-02 7.959e-02 0.548 0.58440
## L(Volume.ts, 1:32)5 2.659e-02 7.886e-02 0.337 0.73641
## L(Volume.ts, 1:32)6 4.105e-02 7.681e-02 0.534 0.59372
## L(Volume.ts, 1:32)7 9.857e-02 7.663e-02 1.286 0.19997
## L(Volume.ts, 1:32)8 -1.161e-02 7.667e-02 -0.151 0.87981
## L(Volume.ts, 1:32)9 6.843e-03 7.620e-02 0.090 0.92855
## L(Volume.ts, 1:32)10 5.843e-02 7.618e-02 0.767 0.44405
## L(Volume.ts, 1:32)11 -1.063e-01 7.655e-02 -1.389 0.16652
## L(Volume.ts, 1:32)12 3.302e-02 7.687e-02 0.429 0.66810
## L(Volume.ts, 1:32)13 -7.062e-02 7.702e-02 -0.917 0.36045
## L(Volume.ts, 1:32)14 -3.136e-02 7.714e-02 -0.407 0.68481
## L(Volume.ts, 1:32)15 5.747e-02 7.702e-02 0.746 0.45655
## L(Volume.ts, 1:32)16 -3.637e-02 7.736e-02 -0.470 0.63885
## L(Volume.ts, 1:32)17 -3.175e-02 7.756e-02 -0.409 0.68280
## L(Volume.ts, 1:32)18 1.843e-02 7.722e-02 0.239 0.81170
## L(Volume.ts, 1:32)19 5.873e-03 7.721e-02 0.076 0.93945
## L(Volume.ts, 1:32)20 1.127e-02 7.712e-02 0.146 0.88401
## L(Volume.ts, 1:32)21 -2.263e-02 7.748e-02 -0.292 0.77054
## L(Volume.ts, 1:32)22 1.163e-02 7.775e-02 0.150 0.88127
## L(Volume.ts, 1:32)23 3.839e-03 7.755e-02 0.050 0.96057
## L(Volume.ts, 1:32)24 5.412e-02 7.717e-02 0.701 0.48405
## L(Volume.ts, 1:32)25 3.788e-02 7.704e-02 0.492 0.62352
## L(Volume.ts, 1:32)26 3.157e-02 7.651e-02 0.413 0.68037
## L(Volume.ts, 1:32)27 3.416e-02 7.646e-02 0.447 0.65558
## L(Volume.ts, 1:32)28 -7.903e-02 7.629e-02 -1.036 0.30161
## L(Volume.ts, 1:32)29 6.674e-02 7.627e-02 0.875 0.38271
## L(Volume.ts, 1:32)30 3.846e-02 8.024e-02 0.479 0.63226
## L(Volume.ts, 1:32)31 -5.077e-03 8.045e-02 -0.063 0.94975
## L(Volume.ts, 1:32)32 5.654e-02 7.618e-02 0.742 0.45890
## L(Volume.ts, 91:122)91 -6.263e-02 7.620e-02 -0.822 0.41227
## L(Volume.ts, 91:122)92 4.249e-02 8.054e-02 0.528 0.59846
## L(Volume.ts, 91:122)93 -2.407e-02 8.048e-02 -0.299 0.76525
## L(Volume.ts, 91:122)94 8.727e-03 7.642e-02 0.114 0.90921
## L(Volume.ts, 91:122)95 -5.595e-02 7.639e-02 -0.732 0.46484
## L(Volume.ts, 91:122)96 -1.775e-02 7.651e-02 -0.232 0.81675
## L(Volume.ts, 91:122)97 -4.687e-02 7.657e-02 -0.612 0.54124
## L(Volume.ts, 91:122)98 -8.249e-02 7.719e-02 -1.069 0.28665
## L(Volume.ts, 91:122)99 9.428e-02 7.730e-02 1.220 0.22419
## L(Volume.ts, 91:122)100 -6.422e-02 7.788e-02 -0.825 0.41074
## L(Volume.ts, 91:122)101 3.421e-02 7.823e-02 0.437 0.66238
## L(Volume.ts, 91:122)102 1.586e-03 7.744e-02 0.020 0.98368
## L(Volume.ts, 91:122)103 -1.118e-02 7.695e-02 -0.145 0.88463
## L(Volume.ts, 91:122)104 1.170e-02 7.716e-02 0.152 0.87971
## L(Volume.ts, 91:122)105 2.485e-02 7.736e-02 0.321 0.74837
## L(Volume.ts, 91:122)106 -5.351e-02 7.745e-02 -0.691 0.49059
## L(Volume.ts, 91:122)107 4.020e-02 7.751e-02 0.519 0.60467
## L(Volume.ts, 91:122)108 -4.865e-02 7.724e-02 -0.630 0.52960
## L(Volume.ts, 91:122)109 -5.240e-02 7.723e-02 -0.679 0.49832
## L(Volume.ts, 91:122)110 3.850e-02 7.691e-02 0.501 0.61723
## L(Volume.ts, 91:122)111 -1.401e-01 8.108e-02 -1.727 0.08583 .
## L(Volume.ts, 91:122)112 1.512e-02 8.127e-02 0.186 0.85256
## L(Volume.ts, 91:122)113 9.254e-02 8.095e-02 1.143 0.25454
## L(Volume.ts, 91:122)114 -1.000e-01 8.111e-02 -1.233 0.21911
## L(Volume.ts, 91:122)115 -8.880e-02 8.156e-02 -1.089 0.27776
## L(Volume.ts, 91:122)116 6.094e-02 7.674e-02 0.794 0.42824
## L(Volume.ts, 91:122)117 2.543e-01 7.719e-02 3.295 0.00119 **
## L(Volume.ts, 91:122)118 -1.304e-01 7.928e-02 -1.645 0.10174
## L(Volume.ts, 91:122)119 -6.994e-02 7.984e-02 -0.876 0.38225
## L(Volume.ts, 91:122)120 5.097e-02 7.952e-02 0.641 0.52234
## L(Volume.ts, 91:122)121 -2.489e-02 7.845e-02 -0.317 0.75142
## L(Volume.ts, 91:122)122 -5.783e-02 7.478e-02 -0.773 0.44037
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1885000 on 178 degrees of freedom
## Multiple R-squared: 0.3863, Adjusted R-squared: 0.1656
## F-statistic: 1.75 on 64 and 178 DF, p-value: 0.002182AR models for Open (diff) (based on ACF and PACF graphs, the two lags models to use would be 110 only and 35 and 110 together)
AR.Open.ts.diff.lag110 <- dynlm(Open.ts.diff~L(Open.ts.diff,110))
summary(AR.Open.ts.diff.lag110)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Open.ts.diff ~ L(Open.ts.diff, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1024.16 -8.63 3.62 19.65 881.60
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.93811 6.88904 -0.572 0.568
## L(Open.ts.diff, 110) 0.01621 0.07788 0.208 0.835
##
## Residual standard error: 109.8 on 252 degrees of freedom
## Multiple R-squared: 0.0001718, Adjusted R-squared: -0.003796
## F-statistic: 0.0433 on 1 and 252 DF, p-value: 0.8353AR.Open.ts.diff.lag35n110 <- dynlm(Open.ts.diff ~ L(Open.ts.diff, 35) + L(Close.ts.diff, 110))
summary(AR.Open.ts.diff.lag35n110)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Open.ts.diff ~ L(Open.ts.diff, 35) + L(Close.ts.diff,
## 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1021.73 -8.74 3.90 18.31 882.11
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.911070 6.895541 -0.567 0.571
## L(Open.ts.diff, 35) 0.003046 0.077637 0.039 0.969
## L(Close.ts.diff, 110) -0.061089 0.079631 -0.767 0.444
##
## Residual standard error: 109.9 on 251 degrees of freedom
## Multiple R-squared: 0.002349, Adjusted R-squared: -0.0056
## F-statistic: 0.2955 on 2 and 251 DF, p-value: 0.7444
## Analyzing AR Residuals with ACF and PACF
``` r
library(dynlm)
library(forecast)
plot_acf_pacf <- function(model_residuals, model_name) {
par(mfrow = c(1, 2)) # Set up a 1x2 plotting area
acf(model_residuals, main = paste("ACF of Residuals:", model_name))
pacf(model_residuals, main = paste("PACF of Residuals:", model_name))
}Close AR Model
The ACF of the residuals shows that the first lag (0) has a strong autocorrelation (usual for all models). All other lags do not cross the blue line (within the confidence bounds) exhibiting that the residuals are uncorrelated. The PACF, though having a few spikes, is centered around 0, thus showing no significant partial autocorrelation.
AR.Close.ts.diff.lag110 <- dynlm(Close.ts.diff ~ L(Close.ts.diff, 110))
summary(AR.Close.ts.diff.lag110)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Close.ts.diff ~ L(Close.ts.diff, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -978.86 -12.09 4.97 19.11 872.23
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.72438 6.67589 -0.558 0.577
## L(Close.ts.diff, 110) -0.05206 0.07709 -0.675 0.500
##
## Residual standard error: 106.4 on 252 degrees of freedom
## Multiple R-squared: 0.001806, Adjusted R-squared: -0.002155
## F-statistic: 0.456 on 1 and 252 DF, p-value: 0.5001plot_acf_pacf(residuals(AR.Close.ts.diff.lag110), "AR.Close.ts.diff.lag110")
The ACF of the residuals shows that the first lag (0) has a strong autocorrelation (usual for all models). All other lags do not cross the blue line (within the confidence bounds) exhibiting that the residuals are uncorrelated. The PACF, though having a few spikes, is centered around 0, thus showing no significant partial autocorrelation.
AR.Close.ts.diff.lag1to110 <- dynlm(Close.ts.diff ~ L(Close.ts.diff, 1:110))
summary(AR.Close.ts.diff.lag1to110)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Close.ts.diff ~ L(Close.ts.diff, 1:110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -864.84 -19.97 5.33 27.12 852.50
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.2418672 8.3786908 -0.387 0.699
## L(Close.ts.diff, 1:110)1 0.0159777 0.0836037 0.191 0.849
## L(Close.ts.diff, 1:110)2 0.0226932 0.0835975 0.271 0.786
## L(Close.ts.diff, 1:110)3 -0.0338749 0.0836433 -0.405 0.686
## L(Close.ts.diff, 1:110)4 0.0223533 0.0836930 0.267 0.790
## L(Close.ts.diff, 1:110)5 -0.0092028 0.0837563 -0.110 0.913
## L(Close.ts.diff, 1:110)6 0.0884463 0.1010973 0.875 0.383
## L(Close.ts.diff, 1:110)7 0.0069257 0.1013506 0.068 0.946
## L(Close.ts.diff, 1:110)8 -0.0274712 0.1013067 -0.271 0.787
## L(Close.ts.diff, 1:110)9 0.0398144 0.1012823 0.393 0.695
## L(Close.ts.diff, 1:110)10 -0.0218935 0.1013141 -0.216 0.829
## L(Close.ts.diff, 1:110)11 0.0058744 0.1013472 0.058 0.954
## L(Close.ts.diff, 1:110)12 -0.0570005 0.1013255 -0.563 0.575
## L(Close.ts.diff, 1:110)13 0.0597780 0.1013998 0.590 0.556
## L(Close.ts.diff, 1:110)14 0.0357480 0.1014407 0.352 0.725
## L(Close.ts.diff, 1:110)15 0.0498519 0.1014621 0.491 0.624
## L(Close.ts.diff, 1:110)16 0.0038393 0.1015560 0.038 0.970
## L(Close.ts.diff, 1:110)17 -0.0294803 0.1013645 -0.291 0.772
## L(Close.ts.diff, 1:110)18 -0.0147365 0.1013580 -0.145 0.885
## L(Close.ts.diff, 1:110)19 -0.0206962 0.1013525 -0.204 0.838
## L(Close.ts.diff, 1:110)20 -0.0559949 0.1012260 -0.553 0.581
## L(Close.ts.diff, 1:110)21 -0.0430001 0.1013242 -0.424 0.672
## L(Close.ts.diff, 1:110)22 0.0055223 0.1013444 0.054 0.957
## L(Close.ts.diff, 1:110)23 0.0106073 0.1013348 0.105 0.917
## L(Close.ts.diff, 1:110)24 0.0648144 0.1010454 0.641 0.522
## L(Close.ts.diff, 1:110)25 -0.0139403 0.1011627 -0.138 0.891
## L(Close.ts.diff, 1:110)26 -0.0812167 0.1011572 -0.803 0.423
## L(Close.ts.diff, 1:110)27 0.0114422 0.1013671 0.113 0.910
## L(Close.ts.diff, 1:110)28 0.0440350 0.1013496 0.434 0.665
## L(Close.ts.diff, 1:110)29 0.0371217 0.1014123 0.366 0.715
## L(Close.ts.diff, 1:110)30 -0.0723102 0.1013736 -0.713 0.477
## L(Close.ts.diff, 1:110)31 0.0039553 0.1015621 0.039 0.969
## L(Close.ts.diff, 1:110)32 0.0056048 0.1015763 0.055 0.956
## L(Close.ts.diff, 1:110)33 0.0245252 0.1015922 0.241 0.810
## L(Close.ts.diff, 1:110)34 -0.0061197 0.1016102 -0.060 0.952
## L(Close.ts.diff, 1:110)35 0.0928452 0.1011359 0.918 0.360
## L(Close.ts.diff, 1:110)36 0.0424102 0.1013987 0.418 0.676
## L(Close.ts.diff, 1:110)37 0.0091770 0.1014057 0.090 0.928
## L(Close.ts.diff, 1:110)38 -0.0384362 0.1012522 -0.380 0.705
## L(Close.ts.diff, 1:110)39 0.0503154 0.1011587 0.497 0.620
## L(Close.ts.diff, 1:110)40 0.0399346 0.1012265 0.395 0.694
## L(Close.ts.diff, 1:110)41 -0.0189568 0.1014365 -0.187 0.852
## L(Close.ts.diff, 1:110)42 -0.0145250 0.1014390 -0.143 0.886
## L(Close.ts.diff, 1:110)43 -0.0352909 0.1014361 -0.348 0.728
## L(Close.ts.diff, 1:110)44 -0.0384279 0.1014462 -0.379 0.705
## L(Close.ts.diff, 1:110)45 -0.0173849 0.1014600 -0.171 0.864
## L(Close.ts.diff, 1:110)46 -0.0683404 0.1014104 -0.674 0.501
## L(Close.ts.diff, 1:110)47 0.0236919 0.1014716 0.233 0.816
## L(Close.ts.diff, 1:110)48 0.0401431 0.1014935 0.396 0.693
## L(Close.ts.diff, 1:110)49 0.0413050 0.1015298 0.407 0.685
## L(Close.ts.diff, 1:110)50 0.0649748 0.1015575 0.640 0.523
## L(Close.ts.diff, 1:110)51 -0.0312912 0.1016223 -0.308 0.759
## L(Close.ts.diff, 1:110)52 -0.0420572 0.1015429 -0.414 0.679
## L(Close.ts.diff, 1:110)53 0.0665238 0.1014135 0.656 0.513
## L(Close.ts.diff, 1:110)54 -0.0286601 0.1015852 -0.282 0.778
## L(Close.ts.diff, 1:110)55 -0.0024781 0.1015848 -0.024 0.981
## L(Close.ts.diff, 1:110)56 0.0317418 0.1015843 0.312 0.755
## L(Close.ts.diff, 1:110)57 -0.0246884 0.1015788 -0.243 0.808
## L(Close.ts.diff, 1:110)58 -0.0434951 0.1015490 -0.428 0.669
## L(Close.ts.diff, 1:110)59 0.0308901 0.1016062 0.304 0.762
## L(Close.ts.diff, 1:110)60 0.0488192 0.1016090 0.480 0.632
## L(Close.ts.diff, 1:110)61 -0.0421448 0.1015130 -0.415 0.679
## L(Close.ts.diff, 1:110)62 -0.0244018 0.1015429 -0.240 0.810
## L(Close.ts.diff, 1:110)63 -0.0375576 0.1014241 -0.370 0.712
## L(Close.ts.diff, 1:110)64 -0.0388429 0.1015070 -0.383 0.703
## L(Close.ts.diff, 1:110)65 0.0311338 0.1014450 0.307 0.759
## L(Close.ts.diff, 1:110)66 0.0567100 0.1014134 0.559 0.577
## L(Close.ts.diff, 1:110)67 0.0277998 0.1014939 0.274 0.785
## L(Close.ts.diff, 1:110)68 0.0257939 0.1014602 0.254 0.800
## L(Close.ts.diff, 1:110)69 -0.0086599 0.1014762 -0.085 0.932
## L(Close.ts.diff, 1:110)70 0.0072461 0.1014847 0.071 0.943
## L(Close.ts.diff, 1:110)71 -0.0432676 0.1013738 -0.427 0.670
## L(Close.ts.diff, 1:110)72 -0.0415484 0.1014075 -0.410 0.683
## L(Close.ts.diff, 1:110)73 0.0910813 0.1012589 0.899 0.370
## L(Close.ts.diff, 1:110)74 -0.0625441 0.1014783 -0.616 0.539
## L(Close.ts.diff, 1:110)75 -0.0294626 0.1015561 -0.290 0.772
## L(Close.ts.diff, 1:110)76 -0.0320286 0.1015134 -0.316 0.753
## L(Close.ts.diff, 1:110)77 0.0249377 0.1014821 0.246 0.806
## L(Close.ts.diff, 1:110)78 -0.0236800 0.1014784 -0.233 0.816
## L(Close.ts.diff, 1:110)79 -0.0226653 0.1014869 -0.223 0.824
## L(Close.ts.diff, 1:110)80 0.0305778 0.1014822 0.301 0.764
## L(Close.ts.diff, 1:110)81 0.0123753 0.1014071 0.122 0.903
## L(Close.ts.diff, 1:110)82 -0.0247163 0.1014219 -0.244 0.808
## L(Close.ts.diff, 1:110)83 0.0056352 0.1014384 0.056 0.956
## L(Close.ts.diff, 1:110)84 -0.0310366 0.1013726 -0.306 0.760
## L(Close.ts.diff, 1:110)85 -0.0020362 0.1011613 -0.020 0.984
## L(Close.ts.diff, 1:110)86 -0.0126342 0.1011472 -0.125 0.901
## L(Close.ts.diff, 1:110)87 -0.0918818 0.1010208 -0.910 0.365
## L(Close.ts.diff, 1:110)88 -0.0349886 0.1012829 -0.345 0.730
## L(Close.ts.diff, 1:110)89 -0.0156798 0.1013276 -0.155 0.877
## L(Close.ts.diff, 1:110)90 0.0041301 0.1012953 0.041 0.968
## L(Close.ts.diff, 1:110)91 0.0501664 0.1012378 0.496 0.621
## L(Close.ts.diff, 1:110)92 0.0161658 0.1013289 0.160 0.873
## L(Close.ts.diff, 1:110)93 0.0122805 0.1013494 0.121 0.904
## L(Close.ts.diff, 1:110)94 0.0971465 0.1011898 0.960 0.339
## L(Close.ts.diff, 1:110)95 -0.0175875 0.1015111 -0.173 0.863
## L(Close.ts.diff, 1:110)96 -0.0195728 0.1014529 -0.193 0.847
## L(Close.ts.diff, 1:110)97 -0.0590493 0.1013925 -0.582 0.561
## L(Close.ts.diff, 1:110)98 -0.0216744 0.1014251 -0.214 0.831
## L(Close.ts.diff, 1:110)99 0.0490977 0.1013339 0.485 0.629
## L(Close.ts.diff, 1:110)100 0.0125655 0.1014184 0.124 0.902
## L(Close.ts.diff, 1:110)101 -0.0137678 0.1014420 -0.136 0.892
## L(Close.ts.diff, 1:110)102 -0.0359516 0.1013823 -0.355 0.723
## L(Close.ts.diff, 1:110)103 0.0471292 0.1013844 0.465 0.643
## L(Close.ts.diff, 1:110)104 -0.0358237 0.1014073 -0.353 0.724
## L(Close.ts.diff, 1:110)105 -0.0950821 0.1008008 -0.943 0.347
## L(Close.ts.diff, 1:110)106 -0.0008114 0.1011113 -0.008 0.994
## L(Close.ts.diff, 1:110)107 -0.0105709 0.1010718 -0.105 0.917
## L(Close.ts.diff, 1:110)108 0.0129233 0.1009916 0.128 0.898
## L(Close.ts.diff, 1:110)109 -0.0157170 0.1009892 -0.156 0.877
## L(Close.ts.diff, 1:110)110 -0.0322934 0.1009697 -0.320 0.750
##
## Residual standard error: 133 on 143 degrees of freedom
## Multiple R-squared: 0.1144, Adjusted R-squared: -0.5669
## F-statistic: 0.1679 on 110 and 143 DF, p-value: 1plot_acf_pacf(residuals(AR.Close.ts.diff.lag1to110), "AR.Close.ts.diff.lag1to110")
BOTH MODELS FOR CLOSE, SHOW THAT THE RESIDUALS FOR ACF AND PACF ARE CENTERED AROUND 0, meaning that the models both properly capture the patterns in the data. Therefore no misspecification is present in the model. Open AR Model
The ACF of the residuals shows that the first lag (0) has a strong autocorrelation (usual for all models). All other lags do not cross the blue line (within the confidence bounds) exhibiting that the residuals are uncorrelated. The PACF, though having a few spikes, is centered around 0, thus showing no significant partial autocorrelation.
AR.Open.ts.diff.lag110 <- dynlm(Open.ts.diff ~ L(Open.ts.diff, 110))
summary(AR.Open.ts.diff.lag110)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Open.ts.diff ~ L(Open.ts.diff, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1024.16 -8.63 3.62 19.65 881.60
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.93811 6.88904 -0.572 0.568
## L(Open.ts.diff, 110) 0.01621 0.07788 0.208 0.835
##
## Residual standard error: 109.8 on 252 degrees of freedom
## Multiple R-squared: 0.0001718, Adjusted R-squared: -0.003796
## F-statistic: 0.0433 on 1 and 252 DF, p-value: 0.8353plot_acf_pacf(residuals(AR.Open.ts.diff.lag110), "AR.Open.ts.diff.lag110")
The ACF of the residuals shows that the first lag (0) has a strong autocorrelation (usual for all models). All other lags do not cross the blue line (within the confidence bounds) exhibiting that the residuals are uncorrelated. The PACF, though having a few spikes, is centered around 0, thus showing no significant partial autocorrelation.
AR.Open.ts.diff.lag35n110 <- dynlm(Open.ts.diff ~ L(Open.ts.diff, 35) + L(Open.ts.diff, 110))
summary(AR.Open.ts.diff.lag35n110)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Open.ts.diff ~ L(Open.ts.diff, 35) + L(Open.ts.diff,
## 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1024.12 -8.73 3.55 19.65 881.57
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.935308 6.902962 -0.570 0.569
## L(Open.ts.diff, 35) 0.003764 0.077716 0.048 0.961
## L(Open.ts.diff, 110) 0.016177 0.078032 0.207 0.836
##
## Residual standard error: 110 on 251 degrees of freedom
## Multiple R-squared: 0.0001811, Adjusted R-squared: -0.007786
## F-statistic: 0.02274 on 2 and 251 DF, p-value: 0.9775plot_acf_pacf(residuals(AR.Open.ts.diff.lag35n110), "AR.Open.ts.diff.lag35n110")
BOTH MODELS FOR CLOSE, SHOW THAT THE RESIDUALS FOR ACF AND PACF ARE CENTERED AROUND 0, meaning that the models both properly capture the patterns in the data. Therefore no misspecification is present in the model. Turnover AR Model
The ACF of the residuals shows autocorrelation at lag 0.05, and partial autocorrelation at lag 0.05. The spikes in the PACF graph, though within the confidence bounds, are significantly larger than the Open and Close AR Model’s. This suggests that there is some misspecification in the model.
AR.Turnover.ts.lag1.4 <- dynlm(Turnover.ts ~ L(Turnover.ts, 1:4))
summary(AR.Turnover.ts.lag1.4)##
## Time series regression with "ts" data:
## Start = 2015(5), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.822e+14 -1.147e+14 -5.190e+13 5.935e+13 1.771e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.487e+14 3.619e+13 6.872 2.85e-11 ***
## L(Turnover.ts, 1:4)1 3.297e-01 5.279e-02 6.245 1.21e-09 ***
## L(Turnover.ts, 1:4)2 1.731e-02 5.559e-02 0.311 0.7558
## L(Turnover.ts, 1:4)3 -1.393e-02 5.564e-02 -0.250 0.8025
## L(Turnover.ts, 1:4)4 9.132e-02 5.274e-02 1.732 0.0842 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.608e+14 on 356 degrees of freedom
## Multiple R-squared: 0.1235, Adjusted R-squared: 0.1136
## F-statistic: 12.54 on 4 and 356 DF, p-value: 1.491e-09plot_acf_pacf(residuals(AR.Turnover.ts.lag1.4), "AR.Turnover.ts.lag1.4")
The ACF and PACF of the residuals show autocorrelation and partial autocorrelation at lags 0.025, around 0.02, and around 0.04. This suggests that the model could be misspecified and the model is not white noise.
AR.Turnover.ts.lag2n61n70n117 <- dynlm(Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts, 61) + L(Turnover.ts, 70) + L(Turnover.ts, 117))
summary(AR.Turnover.ts.lag2n61n70n117)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 70) + L(Turnover.ts, 117))
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.092e+14 -1.365e+14 -1.708e+13 9.426e+13 1.448e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.793e+13 5.028e+13 0.357 0.72167
## L(Turnover.ts, 2) 1.670e-01 5.593e-02 2.985 0.00312 **
## L(Turnover.ts, 61) 2.776e-01 5.620e-02 4.940 1.46e-06 ***
## L(Turnover.ts, 70) 2.038e-01 5.620e-02 3.626 0.00035 ***
## L(Turnover.ts, 117) 3.092e-01 5.664e-02 5.460 1.18e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.377e+14 on 243 degrees of freedom
## Multiple R-squared: 0.2423, Adjusted R-squared: 0.2298
## F-statistic: 19.43 on 4 and 243 DF, p-value: 6.967e-14plot_acf_pacf(residuals(AR.Turnover.ts.lag2n61n70n117), "AR.Turnover.ts.lag2n61n70n117")
BOTH MODELS SHOW SOME AUTOCORRELATION AND PARTIAL AUTOCORRELATION. HOWEVER THE FIRST MOFEL FOR TURNOVER IS BETTER THAN THE SECOND.
Volume AR Model
The ACF of the residuals shows that the first lag (0) has a strong autocorrelation (usual for all models). All other lags do not cross the blue line (within the confidence bounds) exhibiting that the residuals are uncorrelated. The PACF, though having a few spikes, is centered around 0, thus showing no significant partial autocorrelation.
AR.Volume.ts.lag1.32 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32))
summary(AR.Volume.ts.lag1.32)##
## Time series regression with "ts" data:
## Start = 2015(33), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2560268 -738320 -215103 323411 16655993
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.598e+05 3.067e+05 1.499 0.1349
## L(Volume.ts, 1:32)1 3.378e-01 5.769e-02 5.856 1.25e-08 ***
## L(Volume.ts, 1:32)2 5.810e-02 6.088e-02 0.954 0.3406
## L(Volume.ts, 1:32)3 -4.009e-02 6.099e-02 -0.657 0.5115
## L(Volume.ts, 1:32)4 1.130e-01 6.073e-02 1.861 0.0637 .
## L(Volume.ts, 1:32)5 6.020e-03 6.088e-02 0.099 0.9213
## L(Volume.ts, 1:32)6 4.992e-02 6.087e-02 0.820 0.4127
## L(Volume.ts, 1:32)7 1.153e-01 6.090e-02 1.894 0.0592 .
## L(Volume.ts, 1:32)8 -1.452e-02 6.124e-02 -0.237 0.8128
## L(Volume.ts, 1:32)9 -8.593e-03 6.103e-02 -0.141 0.8881
## L(Volume.ts, 1:32)10 4.911e-02 6.103e-02 0.805 0.4216
## L(Volume.ts, 1:32)11 -6.167e-02 6.109e-02 -1.010 0.3135
## L(Volume.ts, 1:32)12 1.838e-02 6.117e-02 0.300 0.7641
## L(Volume.ts, 1:32)13 -3.072e-02 6.109e-02 -0.503 0.6154
## L(Volume.ts, 1:32)14 -3.234e-02 6.107e-02 -0.530 0.5968
## L(Volume.ts, 1:32)15 7.948e-02 6.091e-02 1.305 0.1930
## L(Volume.ts, 1:32)16 -3.868e-02 6.112e-02 -0.633 0.5273
## L(Volume.ts, 1:32)17 -2.775e-03 6.138e-02 -0.045 0.9640
## L(Volume.ts, 1:32)18 6.720e-02 6.125e-02 1.097 0.2735
## L(Volume.ts, 1:32)19 -3.024e-02 6.128e-02 -0.493 0.6221
## L(Volume.ts, 1:32)20 6.718e-03 6.125e-02 0.110 0.9127
## L(Volume.ts, 1:32)21 -3.728e-02 6.125e-02 -0.609 0.5432
## L(Volume.ts, 1:32)22 2.437e-02 6.119e-02 0.398 0.6908
## L(Volume.ts, 1:32)23 3.722e-03 6.114e-02 0.061 0.9515
## L(Volume.ts, 1:32)24 8.983e-02 6.118e-02 1.468 0.1431
## L(Volume.ts, 1:32)25 1.275e-02 6.135e-02 0.208 0.8355
## L(Volume.ts, 1:32)26 2.689e-02 5.834e-02 0.461 0.6451
## L(Volume.ts, 1:32)27 1.397e-02 5.831e-02 0.240 0.8108
## L(Volume.ts, 1:32)28 -7.804e-02 5.828e-02 -1.339 0.1816
## L(Volume.ts, 1:32)29 1.029e-01 5.817e-02 1.769 0.0779 .
## L(Volume.ts, 1:32)30 -3.212e-02 5.845e-02 -0.549 0.5831
## L(Volume.ts, 1:32)31 3.529e-02 5.844e-02 0.604 0.5464
## L(Volume.ts, 1:32)32 3.051e-02 5.529e-02 0.552 0.5814
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1702000 on 300 degrees of freedom
## Multiple R-squared: 0.2808, Adjusted R-squared: 0.204
## F-statistic: 3.66 on 32 and 300 DF, p-value: 1.741e-09plot_acf_pacf(residuals(AR.Volume.ts.lag1.32), "AR.Volume.ts.lag1.32")
The ACF of the residuals shows that the first lag (0) has a strong autocorrelation (usual for all models). All other lags do not cross the blue line (within the confidence bounds) exhibiting that the residuals are uncorrelated. The PACF has spikes that are significaly longer than the previous model, but are stil within the confidence bounds.
AR.Volume.ts.lag1.32n90.122 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts, 91:122))
summary(AR.Volume.ts.lag1.32n90.122)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3164619 -845564 -196953 515577 15844439
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.064e+06 9.492e+05 2.175 0.03099 *
## L(Volume.ts, 1:32)1 3.077e-01 7.471e-02 4.118 5.83e-05 ***
## L(Volume.ts, 1:32)2 8.579e-02 7.829e-02 1.096 0.27463
## L(Volume.ts, 1:32)3 -6.947e-02 7.932e-02 -0.876 0.38232
## L(Volume.ts, 1:32)4 4.361e-02 7.959e-02 0.548 0.58440
## L(Volume.ts, 1:32)5 2.659e-02 7.886e-02 0.337 0.73641
## L(Volume.ts, 1:32)6 4.105e-02 7.681e-02 0.534 0.59372
## L(Volume.ts, 1:32)7 9.857e-02 7.663e-02 1.286 0.19997
## L(Volume.ts, 1:32)8 -1.161e-02 7.667e-02 -0.151 0.87981
## L(Volume.ts, 1:32)9 6.843e-03 7.620e-02 0.090 0.92855
## L(Volume.ts, 1:32)10 5.843e-02 7.618e-02 0.767 0.44405
## L(Volume.ts, 1:32)11 -1.063e-01 7.655e-02 -1.389 0.16652
## L(Volume.ts, 1:32)12 3.302e-02 7.687e-02 0.429 0.66810
## L(Volume.ts, 1:32)13 -7.062e-02 7.702e-02 -0.917 0.36045
## L(Volume.ts, 1:32)14 -3.136e-02 7.714e-02 -0.407 0.68481
## L(Volume.ts, 1:32)15 5.747e-02 7.702e-02 0.746 0.45655
## L(Volume.ts, 1:32)16 -3.637e-02 7.736e-02 -0.470 0.63885
## L(Volume.ts, 1:32)17 -3.175e-02 7.756e-02 -0.409 0.68280
## L(Volume.ts, 1:32)18 1.843e-02 7.722e-02 0.239 0.81170
## L(Volume.ts, 1:32)19 5.873e-03 7.721e-02 0.076 0.93945
## L(Volume.ts, 1:32)20 1.127e-02 7.712e-02 0.146 0.88401
## L(Volume.ts, 1:32)21 -2.263e-02 7.748e-02 -0.292 0.77054
## L(Volume.ts, 1:32)22 1.163e-02 7.775e-02 0.150 0.88127
## L(Volume.ts, 1:32)23 3.839e-03 7.755e-02 0.050 0.96057
## L(Volume.ts, 1:32)24 5.412e-02 7.717e-02 0.701 0.48405
## L(Volume.ts, 1:32)25 3.788e-02 7.704e-02 0.492 0.62352
## L(Volume.ts, 1:32)26 3.157e-02 7.651e-02 0.413 0.68037
## L(Volume.ts, 1:32)27 3.416e-02 7.646e-02 0.447 0.65558
## L(Volume.ts, 1:32)28 -7.903e-02 7.629e-02 -1.036 0.30161
## L(Volume.ts, 1:32)29 6.674e-02 7.627e-02 0.875 0.38271
## L(Volume.ts, 1:32)30 3.846e-02 8.024e-02 0.479 0.63226
## L(Volume.ts, 1:32)31 -5.077e-03 8.045e-02 -0.063 0.94975
## L(Volume.ts, 1:32)32 5.654e-02 7.618e-02 0.742 0.45890
## L(Volume.ts, 91:122)91 -6.263e-02 7.620e-02 -0.822 0.41227
## L(Volume.ts, 91:122)92 4.249e-02 8.054e-02 0.528 0.59846
## L(Volume.ts, 91:122)93 -2.407e-02 8.048e-02 -0.299 0.76525
## L(Volume.ts, 91:122)94 8.727e-03 7.642e-02 0.114 0.90921
## L(Volume.ts, 91:122)95 -5.595e-02 7.639e-02 -0.732 0.46484
## L(Volume.ts, 91:122)96 -1.775e-02 7.651e-02 -0.232 0.81675
## L(Volume.ts, 91:122)97 -4.687e-02 7.657e-02 -0.612 0.54124
## L(Volume.ts, 91:122)98 -8.249e-02 7.719e-02 -1.069 0.28665
## L(Volume.ts, 91:122)99 9.428e-02 7.730e-02 1.220 0.22419
## L(Volume.ts, 91:122)100 -6.422e-02 7.788e-02 -0.825 0.41074
## L(Volume.ts, 91:122)101 3.421e-02 7.823e-02 0.437 0.66238
## L(Volume.ts, 91:122)102 1.586e-03 7.744e-02 0.020 0.98368
## L(Volume.ts, 91:122)103 -1.118e-02 7.695e-02 -0.145 0.88463
## L(Volume.ts, 91:122)104 1.170e-02 7.716e-02 0.152 0.87971
## L(Volume.ts, 91:122)105 2.485e-02 7.736e-02 0.321 0.74837
## L(Volume.ts, 91:122)106 -5.351e-02 7.745e-02 -0.691 0.49059
## L(Volume.ts, 91:122)107 4.020e-02 7.751e-02 0.519 0.60467
## L(Volume.ts, 91:122)108 -4.865e-02 7.724e-02 -0.630 0.52960
## L(Volume.ts, 91:122)109 -5.240e-02 7.723e-02 -0.679 0.49832
## L(Volume.ts, 91:122)110 3.850e-02 7.691e-02 0.501 0.61723
## L(Volume.ts, 91:122)111 -1.401e-01 8.108e-02 -1.727 0.08583 .
## L(Volume.ts, 91:122)112 1.512e-02 8.127e-02 0.186 0.85256
## L(Volume.ts, 91:122)113 9.254e-02 8.095e-02 1.143 0.25454
## L(Volume.ts, 91:122)114 -1.000e-01 8.111e-02 -1.233 0.21911
## L(Volume.ts, 91:122)115 -8.880e-02 8.156e-02 -1.089 0.27776
## L(Volume.ts, 91:122)116 6.094e-02 7.674e-02 0.794 0.42824
## L(Volume.ts, 91:122)117 2.543e-01 7.719e-02 3.295 0.00119 **
## L(Volume.ts, 91:122)118 -1.304e-01 7.928e-02 -1.645 0.10174
## L(Volume.ts, 91:122)119 -6.994e-02 7.984e-02 -0.876 0.38225
## L(Volume.ts, 91:122)120 5.097e-02 7.952e-02 0.641 0.52234
## L(Volume.ts, 91:122)121 -2.489e-02 7.845e-02 -0.317 0.75142
## L(Volume.ts, 91:122)122 -5.783e-02 7.478e-02 -0.773 0.44037
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1885000 on 178 degrees of freedom
## Multiple R-squared: 0.3863, Adjusted R-squared: 0.1656
## F-statistic: 1.75 on 64 and 178 DF, p-value: 0.002182plot_acf_pacf(residuals(AR.Volume.ts.lag1.32n90.122), "AR.Volume.ts.lag1.32n90.122")
BOTH MODELS FOR CLOSE, SHOW THAT THE RESIDUALS FOR ACF AND PACF ARE CENTERED AROUND 0, meaning that the models both properly capture the patterns in the data. Therefore no misspecification is present in the model. However Model 1 is a better representation for Volume since the ACF ANF PACF graphs show residuals with very short spikes.
Testing AR Models
Open Diff with 35th and 110th lags training & testing
train_size.Open.diff <- floor(2/3 * length(Open.ts.diff))
train_data.Open.diff <- Open.ts.diff[1:train_size.Open.diff]
train_data.Open.diff = ts(train_data.Open.diff,
start=c(2015,1),
end=c(2015,365),
frequency=365)
test_data.Open.diff <- Open.ts.diff[(train_size.Open.diff + 1):length(Open.ts.diff)]
test_data.Open.diff = ts(test_data.Open.diff,
start=c(2015,1),
end=c(2015,365),
frequency=365)
length(train_data.Open.diff) ## [1] 365length(test_data.Open.diff) ## [1] 365Open.diff.training.AR35n110 <- dynlm(train_data.Open.diff ~ L(train_data.Open.diff, 35) + L(train_data.Open.diff, 110))
summary(Open.diff.training.AR35n110) ##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Open.diff ~ L(train_data.Open.diff,
## 35) + L(train_data.Open.diff, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1020.50 -5.62 6.87 22.59 119.40
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.336809 5.941263 -1.235 0.218
## L(train_data.Open.diff, 35) 0.016812 0.085120 0.198 0.844
## L(train_data.Open.diff, 110) 0.001373 0.085385 0.016 0.987
##
## Residual standard error: 94.62 on 252 degrees of freedom
## Multiple R-squared: 0.0001555, Adjusted R-squared: -0.00778
## F-statistic: 0.0196 on 2 and 252 DF, p-value: 0.9806Open.diff.testing.AR35n110 <- predict(object=Open.diff.training.AR35n110, n.ahead = length(test_data.Open.diff))
fitted_training.Open.AR35n110 <- fitted(Open.diff.training.AR35n110)
Open.diff.35n110.training.mse_value <- mse(train_data.Open.diff, fitted_training.Open.AR35n110)
Open.diff.35n110.training.rmse_value <- rmse(train_data.Open.diff, fitted_training.Open.AR35n110)
Open.diff.35n110.testing.mse_value <- mse(test_data.Open.diff, Open.diff.testing.AR35n110)
Open.diff.35n110.testing.rmse_value <- rmse(test_data.Open.diff, Open.diff.testing.AR35n110)
cat("Training Model MSE:", Open.diff.35n110.training.mse_value, "\n Training Model RMSE:", Open.diff.35n110.training.rmse_value , "\n Testing Model MSE:", Open.diff.35n110.testing.mse_value, "\n Testing Model RMSE:", Open.diff.35n110.testing.rmse_value , "\n")## Training Model MSE: 8847.17
## Training Model RMSE: 94.0594
## Testing Model MSE: 15974.65
## Testing Model RMSE: 126.3909cat("AIC:", AIC(Open.diff.training.AR35n110), "\nBIC:", BIC(Open.diff.training.AR35n110), "\n")## AIC: 3049.061
## BIC: 3063.226The AR(35,110) model of variable Open.diff is not a good fit. To start with, the training model has a R^2 of 0.0001555, suggesting that the model can not well explain the relation between the lags and the response variable. The MSE and RMSE can also confirm this as we obtain a large number for both the MSE (8847.17) and RMSE (94.0594) for the training model. Upon testing the model using the last ⅓ of the dataset, we obtain a MSE and RMSE of 15974.65 and 126.3909 for the testing results, which are also large values.
Open Diff with 110th lags training & testing
train_size.Open.diff <- floor(2/3 * length(Open.ts.diff))
train_data.Open.diff <- Open.ts.diff[1:train_size.Open.diff]
train_data.Open.diff = ts(train_data.Open.diff,
start=c(2015,1),
end=c(2015,365),
frequency=365)
test_data.Open.diff <- Open.ts.diff[(train_size.Open.diff + 1):length(Open.ts.diff)]
test_data.Open.diff = ts(test_data.Open.diff,
start=c(2015,1),
end=c(2015,365),
frequency=365)
length(train_data.Open.diff) ## [1] 365length(test_data.Open.diff) ## [1] 365Open.diff.training.AR110 <- dynlm(train_data.Open.diff ~ L(train_data.Open.diff, 110))
summary(Open.diff.training.AR110) ##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Open.diff ~ L(train_data.Open.diff,
## 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -1020.65 -5.49 6.90 22.57 119.31
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.408048 5.919032 -1.252 0.212
## L(train_data.Open.diff, 110) 0.001152 0.085216 0.014 0.989
##
## Residual standard error: 94.44 on 253 degrees of freedom
## Multiple R-squared: 7.224e-07, Adjusted R-squared: -0.003952
## F-statistic: 0.0001828 on 1 and 253 DF, p-value: 0.9892Open.diff.testing.AR110 <- predict(object=Open.diff.training.AR110, n.ahead = length(test_data.Open.diff))
fitted_training.Open.AR110 <- fitted(Open.diff.training.AR110)
Open.diff.110.training.mse_value <- mse(train_data.Open.diff, fitted_training.Open.AR110)
Open.diff.110.training.rmse_value <- rmse(train_data.Open.diff, fitted_training.Open.AR110)
Open.diff.110.testing.mse_value <- mse(test_data.Open.diff, Open.diff.testing.AR110)
Open.diff.110.testing.rmse_value <- rmse(test_data.Open.diff, Open.diff.testing.AR110)
cat("Training Model MSE:", Open.diff.110.training.mse_value, "\n Training Model RMSE:", Open.diff.110.training.rmse_value , "\n Testing Model MSE:", Open.diff.110.testing.mse_value, "\n Testing Model RMSE:", Open.diff.110.testing.rmse_value , "\n")## Training Model MSE: 8848.54
## Training Model RMSE: 94.06668
## Testing Model MSE: 15960.31
## Testing Model RMSE: 126.3341cat("AIC:", AIC(Open.diff.training.AR110), "\nBIC:", BIC(Open.diff.training.AR110), "\n")## AIC: 3047.101
## BIC: 3057.724The AR(35,110) model of variable Open.diff is not a good fit. To start with, the training model has a R^2 close to 0, suggesting that the model can not explain the relation between the lags and the response variable. The MSE and RMSE can also confirm this as we obtain a large number for both the MSE (8848.54) and RMSE (94.06668) for the training model. Upon testing the model using the last ⅓ of the dataset, we obtain a MSE and RMSE of 15960.31 and 126.3341 for the testing results, which are also large values.
Comparing the MSE and RMSE of the testing results of the two AR models for Open.diff. We can conclude that the second AR mode AR(110) is slightly better by a small margin as it has smaller MSE and RMSE. Based on the AIC and BIC results, AR(35,110) has a bigger AIC and BIC than AR(110), which is consistent with the conclusion we draw from comparing MSE and RMSE. However, none of the AR models are good fit, so we conclude that although one is slightly better than the other, we wouldn’t use them as they don’t capture serial correlation. This is consistent with the ACF and PACF we did for Open.diff, which exhibits what seems to be white noise and no serial correlation. The conclusion is that we won’t use AR models for Open.diff.
Close Diff with 110th lags training & testing
train_size.Close.diff <- floor(2/3 * length(Close.ts.diff))
train_data.Close.diff <- Close.ts.diff[1:train_size.Close.diff]
train_data.Close.diff = ts(train_data.Close.diff,
start=c(2015,1),
end=c(2015,365),
frequency=365)
test_data.Close.diff <- Close.ts.diff[(train_size.Close.diff + 1):length(Close.ts.diff)]
test_data.Close.diff = ts(test_data.Close.diff,
start=c(2015,1),
end=c(2015,365),
frequency=365)
length(train_data.Close.diff) ## [1] 365length(test_data.Close.diff) ## [1] 365Close.diff.training.AR110 <- dynlm(train_data.Close.diff ~ L(train_data.Close.diff, 110))
summary(Close.diff.training.AR110) ##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Close.diff ~ L(train_data.Close.diff,
## 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -974.45 -8.48 8.22 22.66 120.90
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.45689 5.69355 -1.310 0.191
## L(train_data.Close.diff, 110) -0.06951 0.08464 -0.821 0.412
##
## Residual standard error: 90.84 on 253 degrees of freedom
## Multiple R-squared: 0.002659, Adjusted R-squared: -0.001283
## F-statistic: 0.6744 on 1 and 253 DF, p-value: 0.4123Close.diff.testing.AR110 <- predict(object=Close.diff.training.AR110, n.ahead = length(test_data.Close.diff))
fitted_training.Close.AR110 <- fitted(Close.diff.training.AR110)
Close.diff.110.training.mse_value <- mse(train_data.Close.diff, fitted_training.Close.AR110)
Close.diff.110.training.rmse_value <- rmse(train_data.Close.diff, fitted_training.Close.AR110)
Close.diff.110.testing.mse_value <- mse(test_data.Close.diff, Close.diff.testing.AR110)
Close.diff.110.testing.rmse_value <- rmse(test_data.Close.diff, Close.diff.testing.AR110)
cat("Training Model MSE:", Close.diff.110.training.mse_value, "\n Training Model RMSE:", Close.diff.110.training.rmse_value , "\n Testing Model MSE:", Close.diff.110.testing.mse_value, "\n Testing Model RMSE:", Close.diff.110.testing.rmse_value , "\n")## Training Model MSE: 8186.789
## Training Model RMSE: 90.48088
## Testing Model MSE: 15231.04
## Testing Model RMSE: 123.4141cat("AIC:", AIC(Close.diff.training.AR110), "\nBIC:", BIC(Close.diff.training.AR110), "\n")## AIC: 3027.279
## BIC: 3037.903The AR(110) model of variable Close.diff is not a good fit. To start with, the training model has a R^2 of 0.002659, suggesting that the model can not explain the relation between the lags and the response variable (only 0.02%) of it. The MSE and RMSE can also confirm this as we obtain a large number for both the MSE (8186.789) and RMSE (90.48088) for the training model. Upon testing the model using the last ⅓ of the dataset, we obtain a MSE and RMSE of 15231.04 and 123.4141 for the testing results, which are also large values.
Close Diff with 1st to 110th lags training & testing
train_size.Close.diff <- floor(2/3 * length(Close.ts.diff))
train_data.Close.diff <- Close.ts.diff[1:train_size.Close.diff]
train_data.Close.diff = ts(train_data.Close.diff,
start=c(2015,1),
end=c(2015,365),
frequency=365)
test_data.Close.diff <- Close.ts.diff[(train_size.Close.diff + 1):length(Close.ts.diff)]
test_data.Close.diff = ts(test_data.Close.diff,
start=c(2015,1),
end=c(2015,365),
frequency=365)
length(train_data.Close.diff) ## [1] 365length(test_data.Close.diff) ## [1] 365Close.diff.AR1to110.formula <- paste("train_data.Close.diff ~",
paste(sprintf("L(train_data.Close.diff, %d)", 1:110),
collapse = " + "))
Close.diff.training.AR1to110 <- dynlm(as.formula(Close.diff.AR1to110.formula))
summary(Close.diff.training.AR1to110) ##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = as.formula(Close.diff.AR1to110.formula))
##
## Residuals:
## Min 1Q Median 3Q Max
## -803.56 -19.06 10.62 30.51 177.54
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -10.511347 8.377472 -1.255 0.2116
## L(train_data.Close.diff, 1) -0.007501 0.083379 -0.090 0.9284
## L(train_data.Close.diff, 2) 0.041188 0.083362 0.494 0.6220
## L(train_data.Close.diff, 3) -0.038139 0.083439 -0.457 0.6483
## L(train_data.Close.diff, 4) 0.001852 0.083549 0.022 0.9823
## L(train_data.Close.diff, 5) -0.025632 0.083539 -0.307 0.7594
## L(train_data.Close.diff, 6) 0.019272 0.082908 0.232 0.8165
## L(train_data.Close.diff, 7) -0.026477 0.082778 -0.320 0.7495
## L(train_data.Close.diff, 8) -0.002266 0.082722 -0.027 0.9782
## L(train_data.Close.diff, 9) 0.023295 0.082665 0.282 0.7785
## L(train_data.Close.diff, 10) -0.011063 0.082703 -0.134 0.8938
## L(train_data.Close.diff, 11) -0.007062 0.082719 -0.085 0.9321
## L(train_data.Close.diff, 12) -0.061292 0.082629 -0.742 0.4594
## L(train_data.Close.diff, 13) 0.091695 0.109141 0.840 0.4022
## L(train_data.Close.diff, 14) 0.005108 0.109276 0.047 0.9628
## L(train_data.Close.diff, 15) 0.042573 0.109253 0.390 0.6974
## L(train_data.Close.diff, 16) -0.007293 0.109234 -0.067 0.9469
## L(train_data.Close.diff, 17) -0.006878 0.109006 -0.063 0.9498
## L(train_data.Close.diff, 18) -0.041088 0.108939 -0.377 0.7066
## L(train_data.Close.diff, 19) -0.039715 0.108957 -0.365 0.7160
## L(train_data.Close.diff, 20) -0.094406 0.108884 -0.867 0.3874
## L(train_data.Close.diff, 21) -0.075505 0.109107 -0.692 0.4900
## L(train_data.Close.diff, 22) 0.015008 0.109274 0.137 0.8910
## L(train_data.Close.diff, 23) -0.010918 0.109067 -0.100 0.9204
## L(train_data.Close.diff, 24) 0.044268 0.108938 0.406 0.6851
## L(train_data.Close.diff, 25) -0.065667 0.108894 -0.603 0.5474
## L(train_data.Close.diff, 26) -0.171040 0.108968 -1.570 0.1187
## L(train_data.Close.diff, 27) -0.004296 0.109795 -0.039 0.9688
## L(train_data.Close.diff, 28) 0.076590 0.109712 0.698 0.4862
## L(train_data.Close.diff, 29) 0.059980 0.109853 0.546 0.5859
## L(train_data.Close.diff, 30) -0.092376 0.109696 -0.842 0.4011
## L(train_data.Close.diff, 31) 0.016926 0.109933 0.154 0.8779
## L(train_data.Close.diff, 32) -0.010943 0.109941 -0.100 0.9209
## L(train_data.Close.diff, 33) 0.026137 0.109939 0.238 0.8124
## L(train_data.Close.diff, 34) 0.035286 0.109953 0.321 0.7487
## L(train_data.Close.diff, 35) 0.188784 0.109371 1.726 0.0865 .
## L(train_data.Close.diff, 36) 0.046130 0.110366 0.418 0.6766
## L(train_data.Close.diff, 37) -0.066054 0.110219 -0.599 0.5499
## L(train_data.Close.diff, 38) -0.021304 0.110028 -0.194 0.8467
## L(train_data.Close.diff, 39) 0.078617 0.110061 0.714 0.4762
## L(train_data.Close.diff, 40) 0.030304 0.110203 0.275 0.7837
## L(train_data.Close.diff, 41) -0.008997 0.110226 -0.082 0.9351
## L(train_data.Close.diff, 42) -0.015400 0.110197 -0.140 0.8891
## L(train_data.Close.diff, 43) -0.033732 0.110213 -0.306 0.7600
## L(train_data.Close.diff, 44) -0.057258 0.110169 -0.520 0.6041
## L(train_data.Close.diff, 45) -0.016206 0.110126 -0.147 0.8832
## L(train_data.Close.diff, 46) -0.099905 0.110076 -0.908 0.3656
## L(train_data.Close.diff, 47) 0.030797 0.110310 0.279 0.7805
## L(train_data.Close.diff, 48) 0.012219 0.110141 0.111 0.9118
## L(train_data.Close.diff, 49) 0.035732 0.109965 0.325 0.7457
## L(train_data.Close.diff, 50) 0.060164 0.109993 0.547 0.5852
## L(train_data.Close.diff, 51) -0.055228 0.109948 -0.502 0.6162
## L(train_data.Close.diff, 52) -0.079832 0.109837 -0.727 0.4685
## L(train_data.Close.diff, 53) 0.103177 0.109835 0.939 0.3491
## L(train_data.Close.diff, 54) -0.012070 0.110107 -0.110 0.9129
## L(train_data.Close.diff, 55) 0.066254 0.110084 0.602 0.5482
## L(train_data.Close.diff, 56) 0.035761 0.110107 0.325 0.7458
## L(train_data.Close.diff, 57) -0.049543 0.110107 -0.450 0.6534
## L(train_data.Close.diff, 58) -0.037715 0.110020 -0.343 0.7322
## L(train_data.Close.diff, 59) 0.043490 0.109989 0.395 0.6931
## L(train_data.Close.diff, 60) 0.067036 0.109988 0.609 0.5432
## L(train_data.Close.diff, 61) -0.038189 0.109991 -0.347 0.7289
## L(train_data.Close.diff, 62) -0.067399 0.110027 -0.613 0.5411
## L(train_data.Close.diff, 63) -0.101175 0.110072 -0.919 0.3595
## L(train_data.Close.diff, 64) -0.033343 0.110385 -0.302 0.7630
## L(train_data.Close.diff, 65) 0.016964 0.110171 0.154 0.8778
## L(train_data.Close.diff, 66) 0.084395 0.110096 0.767 0.4446
## L(train_data.Close.diff, 67) 0.023364 0.110291 0.212 0.8325
## L(train_data.Close.diff, 68) 0.010519 0.110261 0.095 0.9241
## L(train_data.Close.diff, 69) -0.024029 0.110230 -0.218 0.8277
## L(train_data.Close.diff, 70) -0.006278 0.110248 -0.057 0.9547
## L(train_data.Close.diff, 71) -0.066001 0.110153 -0.599 0.5500
## L(train_data.Close.diff, 72) -0.046245 0.110240 -0.419 0.6755
## L(train_data.Close.diff, 73) 0.126722 0.110122 1.151 0.2517
## L(train_data.Close.diff, 74) -0.097027 0.110378 -0.879 0.3808
## L(train_data.Close.diff, 75) -0.062845 0.110623 -0.568 0.5709
## L(train_data.Close.diff, 76) 0.032824 0.110186 0.298 0.7662
## L(train_data.Close.diff, 77) 0.033901 0.110147 0.308 0.7587
## L(train_data.Close.diff, 78) -0.031865 0.110110 -0.289 0.7727
## L(train_data.Close.diff, 79) -0.024364 0.110095 -0.221 0.8252
## L(train_data.Close.diff, 80) 0.059515 0.110067 0.541 0.5895
## L(train_data.Close.diff, 81) -0.036162 0.110085 -0.328 0.7430
## L(train_data.Close.diff, 82) -0.037144 0.110001 -0.338 0.7361
## L(train_data.Close.diff, 83) -0.008532 0.109908 -0.078 0.9382
## L(train_data.Close.diff, 84) -0.074600 0.109811 -0.679 0.4980
## L(train_data.Close.diff, 85) -0.006336 0.108910 -0.058 0.9537
## L(train_data.Close.diff, 86) -0.053183 0.108802 -0.489 0.6257
## L(train_data.Close.diff, 87) -0.068343 0.108813 -0.628 0.5309
## L(train_data.Close.diff, 88) -0.095134 0.108889 -0.874 0.3838
## L(train_data.Close.diff, 89) -0.012948 0.109180 -0.119 0.9058
## L(train_data.Close.diff, 90) -0.028815 0.109056 -0.264 0.7920
## L(train_data.Close.diff, 91) 0.013711 0.108933 0.126 0.9000
## L(train_data.Close.diff, 92) 0.022516 0.108926 0.207 0.8365
## L(train_data.Close.diff, 93) -0.012920 0.108940 -0.119 0.9058
## L(train_data.Close.diff, 94) 0.107412 0.108855 0.987 0.3254
## L(train_data.Close.diff, 95) -0.072731 0.109184 -0.666 0.5064
## L(train_data.Close.diff, 96) -0.022746 0.109329 -0.208 0.8355
## L(train_data.Close.diff, 97) -0.078072 0.109283 -0.714 0.4761
## L(train_data.Close.diff, 98) -0.017354 0.109254 -0.159 0.8740
## L(train_data.Close.diff, 99) 0.059257 0.109026 0.544 0.5876
## L(train_data.Close.diff, 100) -0.023475 0.109138 -0.215 0.8300
## L(train_data.Close.diff, 101) -0.033646 0.109120 -0.308 0.7583
## L(train_data.Close.diff, 102) -0.047813 0.109021 -0.439 0.6616
## L(train_data.Close.diff, 103) 0.061128 0.109048 0.561 0.5760
## L(train_data.Close.diff, 104) -0.069370 0.109057 -0.636 0.5257
## L(train_data.Close.diff, 105) -0.164604 0.108596 -1.516 0.1318
## L(train_data.Close.diff, 106) 0.022748 0.109424 0.208 0.8356
## L(train_data.Close.diff, 107) -0.021125 0.109398 -0.193 0.8472
## L(train_data.Close.diff, 108) -0.029624 0.109313 -0.271 0.7868
## L(train_data.Close.diff, 109) 0.001705 0.109251 0.016 0.9876
## L(train_data.Close.diff, 110) -0.020012 0.109243 -0.183 0.8549
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 109 on 144 degrees of freedom
## Multiple R-squared: 0.1832, Adjusted R-squared: -0.4407
## F-statistic: 0.2937 on 110 and 144 DF, p-value: 1Close.diff.testing.AR1to110 <- predict(object=Close.diff.training.AR1to110, n.ahead = length(test_data.Close.diff))
fitted_training.Close.AR1to110 <- fitted(Close.diff.training.AR1to110)
Close.diff.1to110.training.mse_value <- mse(train_data.Close.diff, fitted_training.Close.AR1to110)
Close.diff.1to110.training.rmse_value <- rmse(train_data.Close.diff, fitted_training.Close.AR1to110)
Close.diff.1to110.testing.mse_value <- mse(test_data.Close.diff, Close.diff.testing.AR1to110)
Close.diff.1to110.testing.rmse_value <- rmse(test_data.Close.diff, Close.diff.testing.AR1to110)
cat("Training Model MSE:", Close.diff.1to110.training.mse_value, "\n Training Model RMSE:", Close.diff.1to110.training.rmse_value , "\n Testing Model MSE:", Close.diff.1to110.testing.mse_value, "\n Testing Model RMSE:", Close.diff.1to110.testing.rmse_value, "\n")## Training Model MSE: 6704.575
## Training Model RMSE: 81.88147
## Testing Model MSE: 17704.15
## Testing Model RMSE: 133.0569cat(" Training Model AIC:", AIC(Close.diff.training.AR1to110), "\n Training Model BIC:", BIC(Close.diff.training.AR1to110), "\n")## Training Model AIC: 3194.348
## Training Model BIC: 3590.969The AR(1:110) model of variable Close.diff is not a good fit. To start with, the training model has a R^2 of 0.1832, suggesting that the model can not well explain the relation between the lags and the response variable (only 18%) of it. The MSE and RMSE can also confirm this as we obtain a large number for both the MSE (6704.575) and RMSE (81.88147) for the training model. Upon testing the model using the last ⅓ of the dataset, we obtain a MSE and RMSE of 17704.15 and 133.0569 for the testing results, which are also large values.
Comparing the MSE and RMSE of the testing results of the two AR models for Close.diff. We can conclude that the second AR mode AR(1:110) is slightly better than AR(110) by a small margin as it has smaller MSE and RMSE. Based on the AIC and BIC results, AR(110) has a smaller AIC 3027.279, BIC: 3037.903 than AR(1:110): 3194.348, BIC: 3590.969, which is consistent with the conclusion we draw from comparing MSE and RMSE of the tests results. While the MSE and RMSE of the training set suggests that we should choose AR(1:110) over AR(110), the testing sets suggest otherwise. In this case, we would choose AR(110) since we want the model to more accurately predict future value (that is, to have better test results), so we go with the MSE and RMS for test results. And this result is also consistent with AIC and BIC results. However, none of the AR models are good fit, so we conclude that although one is slightly better than the other, we wouldn’t use them as they don’t have good fit. This is consistent with the ACF and PACF we did for Close.diff, which exhibits what seems to be white noise and no serial correlation. The conclusion is that we won’t use AR models for Close.diff.
Turnover with 1st to 4th lags training & testing
train_size.Turnover <- floor(2/3 * length(Turnover.ts))
train_data.Turnover <- Turnover.ts[1:train_size.Turnover]
train_data.Turnover = ts(train_data.Turnover,
start=c(2015,1),
end=c(2015,365),
frequency=365)
test_data.Turnover <- Turnover.ts[(train_size.Turnover + 1):length(Turnover.ts)]
test_data.Turnover = ts(test_data.Turnover,
start=c(2015,1),
end=c(2015,365),
frequency=365)
length(train_data.Turnover) ## [1] 365length(test_data.Turnover) ## [1] 365Turnover.training.AR1to4 <- dynlm(train_data.Turnover ~ L(train_data.Turnover, 1) + L(train_data.Turnover, 2) + L(train_data.Turnover, 3) + L(train_data.Turnover, 4))
summary(Turnover.training.AR1to4) ##
## Time series regression with "ts" data:
## Start = 2015(5), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover ~ L(train_data.Turnover,
## 1) + L(train_data.Turnover, 2) + L(train_data.Turnover, 3) +
## L(train_data.Turnover, 4))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.861e+14 -1.157e+14 -4.990e+13 5.611e+13 1.770e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.513e+14 3.629e+13 6.926 2.04e-11 ***
## L(train_data.Turnover, 1) 3.315e-01 5.278e-02 6.281 9.82e-10 ***
## L(train_data.Turnover, 2) 1.511e-02 5.562e-02 0.272 0.7861
## L(train_data.Turnover, 3) -1.913e-02 5.563e-02 -0.344 0.7311
## L(train_data.Turnover, 4) 9.199e-02 5.269e-02 1.746 0.0817 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.6e+14 on 356 degrees of freedom
## Multiple R-squared: 0.1233, Adjusted R-squared: 0.1134
## F-statistic: 12.51 on 4 and 356 DF, p-value: 1.556e-09Turnover.testing.AR1to4 <- predict(object=Turnover.training.AR1to4, n.ahead = length(test_data.Turnover))
fitted_training.Turnover.AR1to4 <- fitted(Turnover.training.AR1to4)
Turnover.AR1to4.training.mse_value <- mse(train_data.Turnover, fitted_training.Turnover.AR1to4)
Turnover.AR1to4.training.rmse_value <- rmse(train_data.Turnover, fitted_training.Turnover.AR1to4)
Turnover.AR1to4.testing.mse_value <- mse(test_data.Turnover, Turnover.testing.AR1to4)
Turnover.AR1to4.testing.rmse_value <- rmse(test_data.Turnover, Turnover.testing.AR1to4)
cat("Training Model MSE:", Turnover.AR1to4.training.mse_value, "\n Training Model RMSE:", Turnover.AR1to4.training.rmse_value, "\n Testing Model MSE:", Turnover.AR1to4.testing.mse_value, "\n Testing Model RMSE:", Turnover.AR1to4.testing.rmse_value, "\n")## Training Model MSE: 6.667361e+28
## Training Model RMSE: 2.582123e+14
## Testing Model MSE: 9.427846e+28
## Testing Model RMSE: 3.07048e+14cat(" Training Model AIC:", AIC(Turnover.training.AR1to4), "\n Training Model BIC:", BIC(Turnover.training.AR1to4), "\n")## Training Model AIC: 24995.9
## Training Model BIC: 25019.23The AR(1:4) model of variable Turnover is not a good fit. To start with, the training model has a R^2 of 0.1233, suggesting that the model can not explain the relation between the lags and the response variable (only 12%) of it. The MSE and RMSE can also confirm this as we obtain a large number for both the MSE (6.667361e+28) and RMSE (2.582123e+14) for the training model. Upon testing the model using the last ⅓ of the dataset, we obtain a MSE and RMSE of 9.427846e+28 and 3.07048e+14 for the testing results, which are also large values.
Turnover with 2nd, 61st, 75th, and 117th lags training & testing
train_size.Turnover <- floor(2/3 * length(Turnover.ts))
train_data.Turnover <- Turnover.ts[1:train_size.Turnover]
train_data.Turnover = ts(train_data.Turnover,
start=c(2015,1),
end=c(2015,365),
frequency=365)
test_data.Turnover <- Turnover.ts[(train_size.Turnover + 1):length(Turnover.ts)]
test_data.Turnover = ts(test_data.Turnover,
start=c(2015,1),
end=c(2015,365),
frequency=365)
length(train_data.Turnover) ## [1] 365length(test_data.Turnover) ## [1] 365Turnover.training.AR2n61n75n117 <- dynlm(train_data.Turnover ~ L(train_data.Turnover, 2) + L(train_data.Turnover, 61) + L(train_data.Turnover, 75) + L(train_data.Turnover, 117))
summary(Turnover.training.AR2n61n75n117 ) ##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover ~ L(train_data.Turnover,
## 2) + L(train_data.Turnover, 61) + L(train_data.Turnover,
## 75) + L(train_data.Turnover, 117))
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.276e+14 -1.330e+14 -4.577e+13 7.619e+13 1.888e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.591e+14 5.480e+13 4.728 3.84e-06 ***
## L(train_data.Turnover, 2) 1.458e-01 6.243e-02 2.336 0.0203 *
## L(train_data.Turnover, 61) 1.462e-01 6.440e-02 2.270 0.0241 *
## L(train_data.Turnover, 75) 1.223e-02 6.252e-02 0.196 0.8451
## L(train_data.Turnover, 117) 8.440e-02 6.466e-02 1.305 0.1930
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.641e+14 on 243 degrees of freedom
## Multiple R-squared: 0.05643, Adjusted R-squared: 0.04089
## F-statistic: 3.633 on 4 and 243 DF, p-value: 0.006769Turnover.testing.AR2n61n75n117 <- predict(object=Turnover.training.AR2n61n75n117, n.ahead = length(test_data.Turnover))
fitted_training.Turnover.AR2n61n75n117 <- fitted(Turnover.training.AR2n61n75n117)
Turnover.AR2n61n75n117.training.mse_value <- mse(train_data.Turnover, fitted_training.Turnover.AR2n61n75n117)
Turnover.AR2n61n75n117.training.rmse_value <- rmse(train_data.Turnover, fitted_training.Turnover.AR2n61n75n117)
Turnover.AR2n61n75n117.testing.mse_value <- mse(test_data.Turnover, Turnover.testing.AR2n61n75n117)
Turnover.AR2n61n75n117.testing.rmse_value <- rmse(test_data.Turnover, Turnover.testing.AR2n61n75n117)
cat("Training Model MSE:", Turnover.AR2n61n75n117.training.mse_value, "\n Training Model RMSE:", Turnover.AR2n61n75n117.training.rmse_value, "\n Testing Model MSE:", Turnover.AR2n61n75n117.testing.mse_value, "\n Testing Model RMSE:", Turnover.AR2n61n75n117.testing.rmse_value, "\n")## Training Model MSE: 6.832895e+28
## Training Model RMSE: 2.613981e+14
## Testing Model MSE: 7.537423e+28
## Testing Model RMSE: 2.745437e+14cat(" Training Model AIC:", AIC(Turnover.training.AR2n61n75n117), "\n Training Model BIC:", BIC(Turnover.training.AR2n61n75n117), "\n")## Training Model AIC: 17181.54
## Training Model BIC: 17202.62The AR(2,6,75,117) model of variable Turnover is not a good fit. To start with, the training model has a R^2 of 0.05643, suggesting that the model can not explain the relation between the lags and the response variable . The MSE and RMSE can also confirm this as we obtain a large number for both the MSE (6.832895e+28) and RMSE (2.613981e+14) for the training model. Upon testing the model using the last ⅓ of the dataset, we obtain a MSE and RMSE of 7.537423e+28 and 2.745437e+14 for the testing results, which are also large values.
Comparing the MSE and RMSE of the testing results of the two AR models for Turnover. We can conclude that the first AR mode AR(1:4) is slightly better than AR(2,6,75,117) by a small margin as it has smaller MSE and RMSE, especially for the testing results. Based on the AIC and BIC results, AR(1:4) has a bigger AIC 24995.9, BIC: 25019.23 than AR(2,6,75,117): 17181.54, BIC: 17202.62, which is consistent with the conclusion we draw from comparing MSE and RMSE of the tests results. While the MSE and RMSE of the training set suggests that we should choose AR(1:4) over AR(2,6,75,117), the testing sets and AIC suggest otherwise. In this case, we would choose AR(2,6,75,117) since we want the model to more accurately predict future value (that is, to have better test results), so we go with the MSE and RMS for test results. And this result is also consistent with AIC and BIC results. However, none of the AR models are good fit, so we conclude that although one is slightly better than the other, we wouldn’t use them as they don’t have good fit.
Volume with 1st to 32th lags
train_size.Volume <- floor(2/3 * length(Volume.ts))
train_data.Volume <- Volume.ts [1:train_size.Volume]
train_data.Volume = ts(train_data.Volume,
start=c(2015,1),
end=c(2015,365),
frequency=365)
test_data.Volume <- Volume.ts[(train_size.Volume + 1):length(Volume.ts)]
test_data.Volume = ts(test_data.Volume,
start=c(2015,1),
end=c(2015,365),
frequency=365)
length(train_data.Volume) ## [1] 365length(test_data.Volume)## [1] 365Volume.AR1to32.formula <- paste("train_data.Volume ~",
paste(sprintf("L(train_data.Volume, %d)", 1:32),
collapse = " + "))
Volume.training.AR1to32 <- dynlm(as.formula(Volume.AR1to32.formula))
summary(Volume.training.AR1to32) ##
## Time series regression with "ts" data:
## Start = 2015(33), End = 2015(365)
##
## Call:
## dynlm(formula = as.formula(Volume.AR1to32.formula))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2352306 -794523 -208019 319236 16681306
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.800e+05 3.027e+05 1.586 0.1139
## L(train_data.Volume, 1) 3.399e-01 5.767e-02 5.895 1.01e-08 ***
## L(train_data.Volume, 2) 6.409e-02 6.082e-02 1.054 0.2929
## L(train_data.Volume, 3) -4.166e-02 6.095e-02 -0.684 0.4948
## L(train_data.Volume, 4) 1.250e-01 6.089e-02 2.053 0.0410 *
## L(train_data.Volume, 5) 4.791e-03 6.101e-02 0.079 0.9375
## L(train_data.Volume, 6) 4.156e-02 6.099e-02 0.681 0.4962
## L(train_data.Volume, 7) 9.116e-02 6.100e-02 1.495 0.1361
## L(train_data.Volume, 8) -1.608e-02 6.119e-02 -0.263 0.7929
## L(train_data.Volume, 9) -1.512e-03 6.061e-02 -0.025 0.9801
## L(train_data.Volume, 10) 5.109e-02 6.058e-02 0.843 0.3997
## L(train_data.Volume, 11) -3.909e-02 6.065e-02 -0.645 0.5197
## L(train_data.Volume, 12) 1.765e-02 6.065e-02 0.291 0.7713
## L(train_data.Volume, 13) -2.898e-02 6.056e-02 -0.479 0.6326
## L(train_data.Volume, 14) -2.699e-02 6.053e-02 -0.446 0.6560
## L(train_data.Volume, 15) 5.817e-02 6.043e-02 0.963 0.3365
## L(train_data.Volume, 16) -3.923e-02 6.053e-02 -0.648 0.5174
## L(train_data.Volume, 17) 4.118e-03 6.053e-02 0.068 0.9458
## L(train_data.Volume, 18) 4.640e-02 6.046e-02 0.767 0.4434
## L(train_data.Volume, 19) -3.791e-02 6.046e-02 -0.627 0.5311
## L(train_data.Volume, 20) 2.620e-02 6.045e-02 0.433 0.6650
## L(train_data.Volume, 21) -4.637e-02 6.050e-02 -0.766 0.4440
## L(train_data.Volume, 22) 8.681e-03 6.080e-02 0.143 0.8866
## L(train_data.Volume, 23) 2.787e-02 6.071e-02 0.459 0.6466
## L(train_data.Volume, 24) 1.564e-01 6.071e-02 2.576 0.0105 *
## L(train_data.Volume, 25) -3.498e-02 6.130e-02 -0.571 0.5687
## L(train_data.Volume, 26) 4.326e-02 5.841e-02 0.741 0.4595
## L(train_data.Volume, 27) 1.127e-02 5.841e-02 0.193 0.8471
## L(train_data.Volume, 28) -1.014e-01 5.839e-02 -1.737 0.0835 .
## L(train_data.Volume, 29) 5.428e-02 5.838e-02 0.930 0.3532
## L(train_data.Volume, 30) 2.273e-03 5.845e-02 0.039 0.9690
## L(train_data.Volume, 31) 2.278e-02 5.838e-02 0.390 0.6967
## L(train_data.Volume, 32) 4.790e-02 5.520e-02 0.868 0.3863
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1688000 on 300 degrees of freedom
## Multiple R-squared: 0.2892, Adjusted R-squared: 0.2134
## F-statistic: 3.814 on 32 and 300 DF, p-value: 4.581e-10Volume.testing.AR1to32 <- predict(object=Volume.training.AR1to32, n.ahead = length(test_data.Volume))
fitted_training.Volume.AR1to32 <- fitted(Volume.training.AR1to32)
Volume.1to32.training.mse_value <- mse(train_data.Volume, fitted_training.Volume.AR1to32)
Volume.1to32.training.rmse_value <- rmse(train_data.Volume, fitted_training.Volume.AR1to32)
Volume.1to32.testing.mse_value <- mse(test_data.Volume, Volume.testing.AR1to32)
Volume.1to32.testing.rmse_value <- rmse(test_data.Volume, Volume.testing.AR1to32)
cat("Training Model MSE:", Volume.1to32.training.mse_value, "\n Training Model RMSE:", Volume.1to32.training.rmse_value , "\n Testing Model MSE:", Volume.1to32.testing.mse_value, "\n Testing Model RMSE:", Volume.1to32.testing.rmse_value, "\n")## Training Model MSE: 2.566267e+12
## Training Model RMSE: 1601957
## Testing Model MSE: 3.385563e+12
## Testing Model RMSE: 1839990cat(" Training Model AIC:", AIC(Volume.training.AR1to32), "\n Training Model BIC:", BIC(Volume.training.AR1to32), "\n")## Training Model AIC: 10527.98
## Training Model BIC: 10657.46The AR(1:32) model of variable Volume is not a good fit. To start with, the training model has a R^2 of 0.2892, suggesting that the model can not well explain the relation between the lags and the response variable . We obtained MSE (2.566267e+12) and RMSE (1601957) for the training model. Upon testing the model using the last ⅓ of the dataset, we obtain a MSE and RMSE of 3.385563e+12 and 1839990 for the testing results, which are also large values.
Volume with 1st to 32th lags and 91th to 122th lags
train_size.Volume <- floor(2/3 * length(Volume.ts))
train_data.Volume <- Volume.ts[1:train_size.Volume]
train_data.Volume = ts(train_data.Volume,
start=c(2015,1),
end=c(2015,365),
frequency=365)
test_data.Volume <- Volume.ts[(train_size.Volume + 1):length(Volume.ts)]
test_data.Volume = ts(test_data.Volume,
start=c(2015,1),
end=c(2015,365),
frequency=365)
length(train_data.Volume) ## [1] 365length(test_data.Volume)## [1] 365Volume.AR1to32and91to122.formula <- paste("train_data.Volume ~",
paste(c(sprintf("L(train_data.Volume, %d)", 1:32),
sprintf("L(train_data.Volume, %d)", 91:122)),
collapse = " + "))
Volume.training.AR1to32and91to122 <- dynlm(as.formula(Volume.AR1to32and91to122.formula))
summary(Volume.training.AR1to32and91to122) ##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = as.formula(Volume.AR1to32and91to122.formula))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2747977 -852049 -152678 513522 16174356
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.496e+06 1.019e+06 2.451 0.0152 *
## L(train_data.Volume, 1) 3.026e-01 7.483e-02 4.045 7.8e-05 ***
## L(train_data.Volume, 2) 4.140e-02 7.812e-02 0.530 0.5968
## L(train_data.Volume, 3) -3.732e-02 7.888e-02 -0.473 0.6367
## L(train_data.Volume, 4) 6.439e-02 7.871e-02 0.818 0.4144
## L(train_data.Volume, 5) -1.632e-02 7.873e-02 -0.207 0.8361
## L(train_data.Volume, 6) 2.431e-02 7.851e-02 0.310 0.7572
## L(train_data.Volume, 7) 1.087e-01 7.844e-02 1.386 0.1675
## L(train_data.Volume, 8) -3.515e-02 7.897e-02 -0.445 0.6568
## L(train_data.Volume, 9) -1.787e-03 7.854e-02 -0.023 0.9819
## L(train_data.Volume, 10) 5.795e-02 7.844e-02 0.739 0.4610
## L(train_data.Volume, 11) -7.501e-02 7.791e-02 -0.963 0.3370
## L(train_data.Volume, 12) 4.898e-02 7.817e-02 0.627 0.5318
## L(train_data.Volume, 13) -9.087e-02 7.831e-02 -1.160 0.2474
## L(train_data.Volume, 14) -2.186e-03 7.876e-02 -0.028 0.9779
## L(train_data.Volume, 15) 1.175e-02 7.875e-02 0.149 0.8815
## L(train_data.Volume, 16) -4.150e-02 7.866e-02 -0.528 0.5985
## L(train_data.Volume, 17) -7.238e-03 7.842e-02 -0.092 0.9266
## L(train_data.Volume, 18) -3.403e-03 7.843e-02 -0.043 0.9654
## L(train_data.Volume, 19) -2.458e-02 7.834e-02 -0.314 0.7541
## L(train_data.Volume, 20) 2.886e-02 7.823e-02 0.369 0.7126
## L(train_data.Volume, 21) -3.565e-02 7.884e-02 -0.452 0.6517
## L(train_data.Volume, 22) 4.727e-03 7.951e-02 0.059 0.9527
## L(train_data.Volume, 23) 3.427e-02 7.930e-02 0.432 0.6661
## L(train_data.Volume, 24) 9.331e-02 7.921e-02 1.178 0.2404
## L(train_data.Volume, 25) 3.548e-02 7.953e-02 0.446 0.6560
## L(train_data.Volume, 26) 1.835e-02 7.926e-02 0.232 0.8172
## L(train_data.Volume, 27) 3.886e-02 7.925e-02 0.490 0.6245
## L(train_data.Volume, 28) -1.143e-01 7.923e-02 -1.442 0.1510
## L(train_data.Volume, 29) 3.922e-02 7.916e-02 0.495 0.6209
## L(train_data.Volume, 30) 5.443e-02 7.979e-02 0.682 0.4961
## L(train_data.Volume, 31) 8.862e-03 8.012e-02 0.111 0.9120
## L(train_data.Volume, 32) 7.218e-02 7.536e-02 0.958 0.3394
## L(train_data.Volume, 91) -7.935e-02 7.536e-02 -1.053 0.2938
## L(train_data.Volume, 92) 1.477e-02 8.012e-02 0.184 0.8539
## L(train_data.Volume, 93) -1.156e-01 7.979e-02 -1.448 0.1493
## L(train_data.Volume, 94) 8.855e-02 7.916e-02 1.119 0.2648
## L(train_data.Volume, 95) -5.780e-02 7.923e-02 -0.729 0.4667
## L(train_data.Volume, 96) 1.655e-02 7.925e-02 0.209 0.8349
## L(train_data.Volume, 97) -3.889e-02 7.926e-02 -0.491 0.6243
## L(train_data.Volume, 98) -2.589e-02 7.953e-02 -0.326 0.7452
## L(train_data.Volume, 99) 5.621e-02 7.921e-02 0.710 0.4789
## L(train_data.Volume, 100) -5.450e-02 7.930e-02 -0.687 0.4928
## L(train_data.Volume, 101) 1.154e-02 7.951e-02 0.145 0.8847
## L(train_data.Volume, 102) -2.835e-03 7.884e-02 -0.036 0.9714
## L(train_data.Volume, 103) 9.399e-03 7.823e-02 0.120 0.9045
## L(train_data.Volume, 104) -5.236e-02 7.834e-02 -0.668 0.5048
## L(train_data.Volume, 105) -1.545e-02 7.843e-02 -0.197 0.8441
## L(train_data.Volume, 106) -9.298e-02 7.842e-02 -1.186 0.2373
## L(train_data.Volume, 107) 5.782e-02 7.866e-02 0.735 0.4632
## L(train_data.Volume, 108) -3.582e-02 7.875e-02 -0.455 0.6498
## L(train_data.Volume, 109) -3.773e-02 7.876e-02 -0.479 0.6325
## L(train_data.Volume, 110) -4.380e-02 7.831e-02 -0.559 0.5766
## L(train_data.Volume, 111) -2.899e-02 7.817e-02 -0.371 0.7112
## L(train_data.Volume, 112) 1.577e-01 7.791e-02 2.024 0.0445 *
## L(train_data.Volume, 113) -7.961e-02 7.844e-02 -1.015 0.3115
## L(train_data.Volume, 114) -5.643e-02 7.854e-02 -0.718 0.4735
## L(train_data.Volume, 115) -5.065e-03 7.897e-02 -0.064 0.9489
## L(train_data.Volume, 116) 1.731e-02 7.844e-02 0.221 0.8256
## L(train_data.Volume, 117) 8.516e-02 7.851e-02 1.085 0.2795
## L(train_data.Volume, 118) -3.027e-02 7.873e-02 -0.384 0.7011
## L(train_data.Volume, 119) -1.051e-01 7.871e-02 -1.336 0.1833
## L(train_data.Volume, 120) 6.780e-02 7.888e-02 0.860 0.3912
## L(train_data.Volume, 121) -4.937e-02 7.812e-02 -0.632 0.5282
## L(train_data.Volume, 122) -1.172e-02 7.483e-02 -0.157 0.8757
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1928000 on 178 degrees of freedom
## Multiple R-squared: 0.3531, Adjusted R-squared: 0.1204
## F-statistic: 1.518 on 64 and 178 DF, p-value: 0.01726Volume.testing.AR1to32and91to122 <- predict(object=Volume.training.AR1to32and91to122, n.ahead = length(test_data.Volume))
fitted_training.Volume.AR1to32and91to122 <- fitted(Volume.training.AR1to32and91to122)
Volume.1to32and91to122.training.mse_value <- mse(train_data.Volume, fitted_training.Volume.AR1to32and91to122)
Volume.1to32and91to122.training.rmse_value <- rmse(train_data.Volume, fitted_training.Volume.AR1to32and91to122)
Volume.1to32and91to122.testing.mse_value <- mse(test_data.Volume, Volume.testing.AR1to32and91to122)
Volume.1to32and91to122.testing.rmse_value <- rmse(test_data.Volume, Volume.testing.AR1to32and91to122)
cat("Training Model MSE:", Volume.1to32and91to122.training.mse_value, "\n Training Model RMSE:", Volume.1to32and91to122.training.rmse_value, "\n Testing Model MSE:", Volume.1to32and91to122.testing.mse_value, "\n Testing Model RMSE:", Volume.1to32and91to122.testing.rmse_value, "\n")## Training Model MSE: 2.723629e+12
## Training Model RMSE: 1650342
## Testing Model MSE: 4.663293e+12
## Testing Model RMSE: 2159466cat(" Training Model AIC:", AIC(Volume.training.AR1to32and91to122), "\n Training Model BIC:", BIC(Volume.training.AR1to32and91to122), "\n")## Training Model AIC: 7779.42
## Training Model BIC: 8009.962The AR(1:32,91:122) model of variable Volume is not a good fit. To start with, the training model has a R^2 of 0.3531, and adjusted R^2 0.1204, suggesting that the model can not well explain the relation between the lags and the response variable . We obtained MSE (2.723629e+12) and RMSE (1650342) for the training model. Upon testing the model using the last ⅓ of the dataset, we obtain a MSE and RMSE of 4.663293e+12 and 2159466 for the testing results, which are also large values.
Comparing the MSE and RMSE of the testing results of the two AR models for Volume. We can conclude that the first AR mode AR(1:32) is slightly better than AR(1:32,91:122) as it has smaller MSE and RMSE for the testing results. However, the latter has a bigger MSE and RMSE for the training set. Based on the AIC and BIC results, AR(1:32,91:122) has a smaller AIC 7779.42, BIC: 8009.962 than AR(1:32): 10527.98, BIC:10657.46, which is NOT consistent with the conclusion we draw from comparing MSE and RMSE of the tests results. While the MSE and RMSE of the testing set suggest that we should choose AR(1:32) over AR(1:32,91:122), the training sets MSE and RMSE, as well as AIC and BIC, suggest otherwise. In this case, we would choose AR(1:32) since we want the model to more accurately predict future value (that is, to have better test results) and therefore perform better with small testing result MSE and RMSE, so we go with the MSE and RMS for test results. This result is not consistent with AIC and BIC results. However, none of the AR models are good fit, so we conclude that although one is slightly better than the other, we wouldn’t use them as none of them have good fit.
AR Models Forecasting
Computation and Plot of 10 steps ahead forecast for Open.ts.diff with lag 35 and 110
Open.forecast.AR35n110 <- predict(AR.Open.ts.diff.lag35n110, n.ahead = 10)
Open.forecast.AR35n110 <- ts(Open.forecast.AR35n110, start = end(Open.ts.diff)[1] + 1, frequency = frequency(Open.ts.diff))
ts.plot(Open.ts.diff, Open.forecast.AR35n110, col = c("black", "red"), lty = c(1, 2), xlab = "Time", ylab = "Open.ts.diff")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Open.forecast.AR35n110)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117)
## -3.9341445 -3.8336935 -4.4867623 -4.2573869 -3.6054409 -4.0261658
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## -1.9726189 -3.7738016 -4.2852429 -3.2060978 -3.7018901 -4.2804409
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## -4.3033205 -3.5079096 -3.3289227 -3.3959020 -3.5304675 -4.8855487
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## -3.9826967 -3.6868237 -4.2343912 -4.1253310 -3.9348972 -3.8786652
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## -2.9468936 -3.9109951 -3.1820922 -3.4411947 -3.8504509 -3.6667630
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## -4.2851708 -3.8306524 -3.9312492 -3.2042377 -4.5128560 -8.1444765
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## -3.7096604 -3.5717398 -4.4830166 -3.9200445 -3.4986210 -4.0699608
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## -3.8111726 -4.5278229 -4.0662890 -4.9656790 -3.9887261 -4.1833509
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## -3.1535084 -4.2104742 -3.0390468 -4.1318637 -4.2798218 -3.9126958
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## -3.7765595 -4.2548427 -4.0767429 -4.1198936 -4.5804938 -3.2499069
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## -3.2587738 -4.5546209 -3.9937680 -4.0039698 -3.8455940 -3.5003383
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## -4.0239761 -3.4648747 -3.8993523 -4.2129769 -4.6160207 -4.0008266
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## -4.4484975 -3.7655233 -4.0279011 -4.0727475 -6.1308075 -4.1655269
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## -4.1562078 -3.8821182 -3.9998548 -3.2801228 -4.2644661 -4.8341135
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## -3.4210472 -3.9385579 -3.5092757 -4.6515331 -3.8086194 -4.2885548
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## -3.2439501 -3.8242482 -3.0526475 -3.7455981 -4.0414891 -3.8980927
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## -4.5150999 -4.0511414 -4.4580303 -3.4306181 -3.4551086 -3.6862881
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## -4.3866435 -3.7301119 -3.9797217 -4.0406242 -4.2266082 -4.1349761
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## -3.0924017 -4.5788378 -20.4445487 -3.5202038 -3.6542862 -3.9697838
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## -3.9761423 -4.0964379 -3.6116476 -3.8599586 -4.5354932 -3.9987654
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## -4.0976324 -3.8901633 -3.9401939 -3.7321314 -4.0680932 -3.9206074
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## -3.8893889 -4.0474280 -4.3038237 -4.0550065 -4.0806550 -3.7652823
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## -3.6798497 -3.5861113 -3.9088343 -3.8421521 -3.4030386 -2.7746602
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## -3.9880511 -4.1391361 -4.1365937 -4.2467106 -3.9931231 -3.7169310
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## -4.0537308 -3.9366779 -3.9353081 -4.2282097 -3.3534569 -4.1247142
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## -3.5682763 -3.9526653 -3.7445593 -3.4627973 -3.6204023 -4.2165489
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## -3.9430240 -3.6358486 -4.0477684 -4.2450567 -4.3466072 -4.0580701
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## -4.0378375 -3.9516303 -3.8146613 -3.3204380 -4.6698984 -3.7795417
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## -3.7841071 -4.0086331 -4.2278750 -4.3477941 -0.2215693 -3.9594186
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## -3.6850778 -3.9273260 -3.9852951 -3.7186467 -3.8945352 -3.7050249
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## -3.6331778 -4.0924515 -3.6993008 -3.4592380 -4.6546292 -3.4600902
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## -3.2687952 -3.7221827 -3.6131660 -4.3585756 -4.5196199 -3.9605984
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## -2.8540273 -5.4916276 -4.2116487 -3.7871292 -3.9088416 -3.6827743
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## -3.7761759 -3.5793329 -3.5223826 -3.7285340 -3.9375376 -4.0969265
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## -3.7576027 -4.0533598 -4.0481159 -3.9875751 -3.7441865 -4.0137143
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## -4.1880396 -4.1065424 -3.8145421 -3.9826643 -4.2762407 -4.1613613
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## -4.1183750 -4.5965263 -4.3384347 -3.6632145 -3.9597876 -3.7621702
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## -4.1361015 -3.4483303 -3.7869101 -3.7190156 -4.0414475 -4.1967037
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## -4.1975630 -3.8785568 -4.1572082 -4.1340819 -3.8822667 -3.5055248
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## -4.1816207 -3.6259955 -3.7861628 -3.6385340 -3.7715291 -4.3669084
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## -3.4998445 -3.9797797 -3.8766423 -4.2881401 -3.7685558 -4.0431230
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## -4.1009710 10.2725577 -3.9341445 -3.8336935 -4.4867623 -4.2573869
## 2015(364) 2015(365)
## -3.6054409 -4.0261658Computation and Plot of 10 steps ahead forecast for Open.ts.diff with lag 110
Open.forecast.AR110 <- predict(AR.Open.ts.diff.lag110, n.ahead = 10)
Open.forecast.AR110 <- ts(Open.forecast.AR110, start = end(Open.ts.diff)[1] + 1, frequency = frequency(Open.ts.diff))
ts.plot(Open.ts.diff, Open.forecast.AR110, col = c("black", "red"), lty = c(1, 2), xlab = "Time", ylab = "Open.ts.diff")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Open.forecast.AR110)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117) 2015(118)
## -3.888687 -3.323938 -4.422646 -4.181190 -3.604287 -4.027241 -2.124759
## 2015(119) 2015(120) 2015(121) 2015(122) 2015(123) 2015(124) 2015(125)
## -3.682072 -4.088821 -3.343385 -3.730687 -4.391857 -4.148780 -3.541087
## 2015(126) 2015(127) 2015(128) 2015(129) 2015(130) 2015(131) 2015(132)
## -3.236431 -3.529744 -3.597805 -5.088677 -4.019139 -3.670728 -4.262216
## 2015(133) 2015(134) 2015(135) 2015(136) 2015(137) 2015(138) 2015(139)
## -4.013467 -3.888687 -3.761477 -3.059795 -4.019139 -3.241292 -3.330421
## 2015(140) 2015(141) 2015(142) 2015(143) 2015(144) 2015(145) 2015(146)
## -3.897600 -3.669108 -4.250872 -3.772010 -3.882205 -3.379036 -4.399959
## 2015(147) 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## -4.278421 -3.777682 -3.636697 -4.466400 -3.940544 -3.480318 -4.148780
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159) 2015(160)
## -3.776062 -4.472072 -4.068564 -4.925005 -4.002933 -4.182810 -3.192677
## 2015(161) 2015(162) 2015(163) 2015(164) 2015(165) 2015(166) 2015(167)
## -4.172277 -3.029005 -4.135005 -4.260595 -3.834400 -3.743651 -4.231426
## 2015(168) 2015(169) 2015(170) 2015(171) 2015(172) 2015(173) 2015(174)
## -4.132575 -4.179569 -4.651139 -3.263979 -3.299631 -4.685170 -4.260595
## 2015(175) 2015(176) 2015(177) 2015(178) 2015(179) 2015(180) 2015(181)
## -4.002933 -3.816574 -3.469785 -3.957559 -3.487610 -3.962421 -4.173087
## 2015(182) 2015(183) 2015(184) 2015(185) 2015(186) 2015(187) 2015(188)
## -4.617918 -4.003744 -4.391857 -3.888687 -3.976195 -4.145539 -6.140390
## 2015(189) 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## -4.229805 -4.280041 -3.952698 -3.946216 -3.281805 -4.343241 -4.796985
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201) 2015(202)
## -3.354728 -3.824677 -3.473836 -4.617108 -3.804421 -4.343241 -3.370933
## 2015(203) 2015(204) 2015(205) 2015(206) 2015(207) 2015(208) 2015(209)
## -3.657764 -3.084103 -3.793887 -4.017518 -3.832780 -4.432369 -4.148780
## 2015(210) 2015(211) 2015(212) 2015(213) 2015(214) 2015(215) 2015(216)
## -4.453436 -3.457631 -3.485180 -3.690174 -4.422646 -3.746892 -3.938113
## 2015(217) 2015(218) 2015(219) 2015(220) 2015(221) 2015(222) 2015(223)
## -4.100164 -4.201446 -4.160934 -3.193487 -4.439662 -20.597798 -3.656144
## 2015(224) 2015(225) 2015(226) 2015(227) 2015(228) 2015(229) 2015(230)
## -3.668298 -4.025621 -3.861949 -4.025621 -3.612390 -4.100164 -4.194154
## 2015(231) 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## -3.941354 -4.132575 -3.889498 -3.954318 -3.776062 -4.116369 -3.986728
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243) 2015(244)
## -3.938113 -4.035344 -4.286523 -4.090441 -4.053169 -3.711241 -3.695036
## 2015(245) 2015(246) 2015(247) 2015(248) 2015(249) 2015(250) 2015(251)
## -3.651282 -3.884636 -3.769580 -3.393621 -2.803754 -3.955128 -4.074236
## 2015(252) 2015(253) 2015(254) 2015(255) 2015(256) 2015(257) 2015(258)
## -4.078287 -4.236287 -3.848985 -3.678831 -4.123662 -3.947026 -3.938113
## 2015(259) 2015(260) 2015(261) 2015(262) 2015(263) 2015(264) 2015(265)
## -4.197395 -3.419549 -4.173087 -3.638318 -3.925149 -3.675590 -3.419549
## 2015(266) 2015(267) 2015(268) 2015(269) 2015(270) 2015(271) 2015(272)
## -3.646421 -4.181190 -3.938113 -3.614010 -4.116369 -4.231426 -4.439662
## 2015(273) 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## -4.099354 -4.103405 -3.967282 -3.717723 -3.399292 -4.664913 -3.808472
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285) 2015(286)
## -3.741221 -4.053980 -4.230616 -4.310021 -3.531364 -3.973764 -3.830349
## 2015(287) 2015(288) 2015(289) 2015(290) 2015(291) 2015(292) 2015(293)
## -3.817385 -3.931631 -3.798749 -3.876533 -4.129333 -3.695036 -4.060462
## 2015(294) 2015(295) 2015(296) 2015(297) 2015(298) 2015(299) 2015(300)
## -3.840072 -3.509487 -4.553098 -3.413067 -3.362831 -3.887877 -3.710431
## 2015(301) 2015(302) 2015(303) 2015(304) 2015(305) 2015(306) 2015(307)
## -4.441282 -4.255734 -3.944595 -2.917190 -5.421693 -4.197395 -3.801180
## 2015(308) 2015(309) 2015(310) 2015(311) 2015(312) 2015(313) 2015(314)
## -3.952698 -3.889498 -3.759856 -3.743651 -3.665867 -3.740410 -4.002933
## 2015(315) 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## -4.027241 -3.798749 -4.069375 -4.181190 -3.883015 -3.667487 -4.053980
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327) 2015(328)
## -4.261405 -3.986728 -3.816574 -4.092062 -4.230616 -4.202257 -3.997262
## 2015(329) 2015(330) 2015(331) 2015(332) 2015(333) 2015(334) 2015(335)
## -4.570113 -4.112318 -3.650472 -3.905703 -3.938113 -4.084769 -3.661815
## 2015(336) 2015(337) 2015(338) 2015(339) 2015(340) 2015(341) 2015(342)
## -3.743651 -3.646421 -4.068564 -4.245200 -4.132575 -3.836021 -4.104216
## 2015(343) 2015(344) 2015(345) 2015(346) 2015(347) 2015(348) 2015(349)
## -3.971333 -4.041826 -3.656144 -4.011036 -3.553241 -3.773631 -3.669108
## 2015(350) 2015(351) 2015(352) 2015(353) 2015(354) 2015(355) 2015(356)
## -3.883015 -4.365928 -3.606718 -3.977005 -3.824677 -4.133385 -3.755805
## 2015(357) 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## -3.940544 -4.115559 10.302957 -3.888687 -3.323938 -4.422646 -4.181190
## 2015(364) 2015(365)
## -3.604287 -4.027241Computation and Plot of 10 steps ahead forecast for Close.ts.diff with lag 110
Close.forecast.AR110 <- predict(AR.Close.ts.diff.lag110, n.ahead = 10)
Close.forecast.AR110 <- ts(Close.forecast.AR110, start = end(Close.ts.diff)[1] + 1, frequency = frequency(Close.ts.diff))
ts.plot(Close.ts.diff, Close.forecast.AR110, col = c("black", "red"), lty = c(1, 2), xlab = "Time", ylab = "Close.ts.diff")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Close.forecast.AR110)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117)
## -5.74419933 -2.82378561 -1.55358784 -4.21111227 -4.23974378 -8.98216249
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## -5.88475400 -2.31622707 -5.79365375 -4.01589745 -2.89406294 -2.90187154
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## -4.85401975 -6.10339460 -5.10649758 -4.69264216 0.36472314 -4.14343780
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## -3.77383107 -3.53697042 -3.46148736 -2.89406294 -4.86703407 -6.37669535
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## -5.63487903 -4.68223070 -5.25486084 -4.06535187 -5.09608612 -2.93831164
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## -2.82118274 -4.64839347 -5.19239210 -1.55879357 -2.81337415 -4.09918910
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## -6.05654304 -0.62696815 -4.12261488 -5.32253532 -3.47710454 -4.04452895
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## -2.51664762 -2.31622707 -0.72847986 -4.13823207 -2.90187154 -5.60364466
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## -3.83369695 -6.13202611 -2.36307863 -3.15174651 -3.77383107 -5.12992336
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## -2.47500179 -2.57911636 -4.12261488 0.06279088 -6.62917319 -5.07005748
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## -3.22202384 -1.41303317 -3.94562011 -2.75090541 -5.86132822 -4.47660443
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## -4.71086221 -3.97685448 -2.41773878 -2.73268536 -2.92269445 -1.27247850
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## -4.26837528 -3.46929595 -2.90707726 2.87648717 -3.17517228 -2.48801611
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## -3.73739097 -2.74049395 -6.37148962 -2.14443803 -1.60564512 -4.86703407
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## -4.45057578 -5.58282174 -1.30111000 -4.22412659 -2.58432209 -5.12732050
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## -5.35376969 -5.24965512 -5.02320592 -3.78424253 -3.62026208 -2.18087813
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## -3.22983243 -1.70455397 -6.22833209 -4.06535187 -5.00758874 -1.68633392
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## -4.36207840 -4.09658624 -2.87063716 -3.12051213 -3.31052123 -5.51514727
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## -2.22252396 -2.54788199 47.53122677 -4.18768649 -3.53436756 -4.04973468
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## -3.38079856 -5.20800929 -2.50363330 -3.44847303 -3.48231027 -4.49482447
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## -2.93831164 -3.42244439 -4.40372423 -3.23503816 -3.84410840 -3.35997565
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## -3.57861625 -2.52705908 -2.70925958 -3.69834801 -4.38290131 -4.82278537
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## -4.38810704 -3.98726594 -4.39070990 -3.69314228 -9.52355827 -3.22983243
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## -3.45628163 -3.18298088 -2.56349918 -3.59683630 -4.89826844 -2.92269445
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## -4.09138051 -3.82328549 -2.59473355 -5.23924366 -3.75561102 -4.17467217
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## -3.22462671 -4.92950281 -5.55939597 -4.43235573 -3.26887540 -3.35476992
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## -4.88004839 -4.30741825 -1.59002794 -4.52345598 -0.71286268 -3.39121002
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## -2.62857079 -4.67181925 -5.19499497 -2.85762284 -3.44326731 -4.26837528
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## -3.71917092 -2.40212159 -2.93310591 -3.72697951 -5.28088949 -3.29490404
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## -4.26056669 -4.19289222 -3.69574514 -3.85191700 -3.87013705 -3.73478811
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## -3.87013705 -4.18248076 -4.98936869 -1.90237165 -4.57291040 -5.81187380
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## -4.30221252 -4.17727503 -2.31102134 -2.61035074 -3.66971650 -5.55939597
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## -1.40782744 -2.50103044 -3.63067353 -3.71136233 -3.59683630 -4.61195337
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## -4.45317865 -4.37248985 -4.32303543 -3.84150554 -3.58121911 -3.92219433
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## -3.30010977 -3.22462671 -3.50313318 -4.46879583 -3.27147826 -3.00078038
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## -4.52605885 -3.53176469 -2.12361512 -3.91959147 -3.37038711 -2.65199656
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## -2.75090541 -1.56399930 -5.17156919 -3.96384016 -3.79205112 -3.07105771
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## -4.31002111 -4.45057578 -4.84621115 -3.26106681 -2.77172832 -3.57080766
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## -3.27147826 -3.57861625 -3.62807067 -2.88104862 -4.72127367 -4.00808885
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## -4.59373332 -4.14343780 -4.67702497 -4.31002111 -2.47760466 -4.78113955
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## -2.69884812 -4.61455623 -3.49011886 -4.16165785 -3.72177378 -2.76652259
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## -4.71867080 -48.96215784 -5.74419933 -2.82378561 -1.55358784 -4.21111227
## 2015(364) 2015(365)
## -4.23974378 -8.98216249Computation and Plot of 10 steps ahead forecast for Close.ts.diff with lags 1 to 110
Close.forecast.AR1to110 <- predict(AR.Close.ts.diff.lag1to110, n.ahead = 10)
Close.forecast.AR1to110 <- ts(Close.forecast.AR1to110, start = end(Close.ts.diff)[1] + 1, frequency = frequency(Close.ts.diff))
ts.plot(Close.ts.diff, Close.forecast.AR1to110, col = c("black", "red"), lty = c(1, 2), xlab = "Time", ylab = "Close.ts.diff")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Close.forecast.AR1to110)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## -119.75580844 -34.33421570 -14.63715766 47.10859309 -27.83906279
## 2015(117) 2015(118) 2015(119) 2015(120) 2015(121)
## 2.24071865 -81.37420041 -10.50944205 33.05919185 -46.10908511
## 2015(122) 2015(123) 2015(124) 2015(125) 2015(126)
## 31.32269232 -4.52721425 55.19809930 -83.49929277 -46.33796439
## 2015(127) 2015(128) 2015(129) 2015(130) 2015(131)
## -52.30084756 13.41684331 23.15837461 -5.58802356 18.23840048
## 2015(132) 2015(133) 2015(134) 2015(135) 2015(136)
## 51.61529851 46.91581776 -4.32132558 -9.70071455 -81.02986881
## 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 9.03543417 50.38784010 -22.00664918 -31.43541408 -10.84682694
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146)
## 72.15007521 -25.24360438 3.25501770 -27.94898571 -7.46706289
## 2015(147) 2015(148) 2015(149) 2015(150) 2015(151)
## -96.60231428 -38.40904290 5.28964543 23.13399642 -35.75696269
## 2015(152) 2015(153) 2015(154) 2015(155) 2015(156)
## -29.40303725 15.50191552 4.51664306 38.98791433 21.56992968
## 2015(157) 2015(158) 2015(159) 2015(160) 2015(161)
## 8.61265052 55.55528998 -15.75407122 -13.70948269 -41.78839059
## 2015(162) 2015(163) 2015(164) 2015(165) 2015(166)
## -55.05448015 18.04693893 36.33573800 -70.08177519 22.79951342
## 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 11.16558379 -33.73896983 15.06336189 33.53141280 -47.75902163
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176)
## -47.49490847 53.16677320 33.38813541 36.39144800 15.43057058
## 2015(177) 2015(178) 2015(179) 2015(180) 2015(181)
## -32.63196370 -62.50338717 -38.55389795 -35.94399660 17.27478945
## 2015(182) 2015(183) 2015(184) 2015(185) 2015(186)
## 7.17751839 47.21735384 25.64721844 -74.74346271 77.51073945
## 2015(187) 2015(188) 2015(189) 2015(190) 2015(191)
## 23.98135258 43.15691450 -30.11316082 26.74657149 7.49680725
## 2015(192) 2015(193) 2015(194) 2015(195) 2015(196)
## -35.67953268 1.57002225 44.25047134 -27.67995669 3.42790249
## 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## -5.72177514 10.41958754 78.07364248 26.45798733 11.22464226
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206)
## -7.34134084 -40.58852034 -16.96422481 -14.01070722 -90.39894482
## 2015(207) 2015(208) 2015(209) 2015(210) 2015(211)
## 6.76899598 25.36472640 46.98506024 1.92976743 -34.64342694
## 2015(212) 2015(213) 2015(214) 2015(215) 2015(216)
## -27.47068929 5.96273668 33.01414459 -35.84795312 40.89933873
## 2015(217) 2015(218) 2015(219) 2015(220) 2015(221)
## 91.72712617 -6.58883296 3.25602563 -24.77490413 8.69594629
## 2015(222) 2015(223) 2015(224) 2015(225) 2015(226)
## 24.50691029 -6.47767031 3.65715705 -20.01109850 3.25302427
## 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 0.97795137 -6.56936646 -6.20658609 -14.50252430 -1.08686989
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236)
## 7.34828208 -11.01752370 3.58301469 -5.89348704 6.21251875
## 2015(237) 2015(238) 2015(239) 2015(240) 2015(241)
## 2.37715061 -2.86807109 -2.42810764 -0.08656215 -8.77602682
## 2015(242) 2015(243) 2015(244) 2015(245) 2015(246)
## -12.84284772 -10.87715196 -5.04467107 -8.53698676 -7.01307242
## 2015(247) 2015(248) 2015(249) 2015(250) 2015(251)
## 4.19478734 -3.72408198 16.50271591 7.52658247 4.20380997
## 2015(252) 2015(253) 2015(254) 2015(255) 2015(256)
## -21.12953647 10.95827754 -17.08439784 69.13198608 -5.09492002
## 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## -16.11929674 15.06586064 -11.56590435 10.19521365 -50.01093144
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266)
## 48.46682876 12.02700598 43.30843365 7.33613406 -33.86478226
## 2015(267) 2015(268) 2015(269) 2015(270) 2015(271)
## -28.47869130 -13.31408326 -28.50027153 -39.97285776 -2.83139780
## 2015(272) 2015(273) 2015(274) 2015(275) 2015(276)
## 8.01404463 61.32313600 -13.91965694 -93.80565739 -0.82006837
## 2015(277) 2015(278) 2015(279) 2015(280) 2015(281)
## 45.98196818 51.18778625 -66.47215042 -2.20635678 -8.91349672
## 2015(282) 2015(283) 2015(284) 2015(285) 2015(286)
## 28.45917582 -4.08931823 61.29767169 24.04026070 10.89386747
## 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## -21.88864702 35.78233056 20.79883170 -7.96746440 1.76150495
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296)
## -24.55853107 -46.81053028 -26.80009015 -50.59567001 14.15220924
## 2015(297) 2015(298) 2015(299) 2015(300) 2015(301)
## 32.99031647 29.19675976 50.89271301 -38.51076680 -48.03151763
## 2015(302) 2015(303) 2015(304) 2015(305) 2015(306)
## 46.65706875 -8.11161218 12.18647767 31.36882649 -28.04251579
## 2015(307) 2015(308) 2015(309) 2015(310) 2015(311)
## -60.23375724 22.12240094 42.61717880 -35.06530497 -26.22304628
## 2015(312) 2015(313) 2015(314) 2015(315) 2015(316)
## -22.90938884 -38.54126913 40.96602760 55.68762655 10.58279435
## 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 12.51335619 -15.85158396 -17.55988855 -49.30435918 -21.19635518
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326)
## 68.83825126 -36.20553465 -21.80161284 -39.56228329 9.56414771
## 2015(327) 2015(328) 2015(329) 2015(330) 2015(331)
## -38.11111812 -5.31592699 14.81729951 9.44106934 -34.38462433
## 2015(332) 2015(333) 2015(334) 2015(335) 2015(336)
## 1.78362045 -37.40856240 -27.11864399 -16.65054321 -85.58754510
## 2015(337) 2015(338) 2015(339) 2015(340) 2015(341)
## -22.34094757 -16.34573746 1.66238616 22.46974695 20.82592788
## 2015(342) 2015(343) 2015(344) 2015(345) 2015(346)
## -8.00840157 65.21741292 -7.86221560 -13.37697619 -55.20023582
## 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## -25.64894616 56.44677233 13.08759342 -15.21812342 -38.11503738
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356)
## 26.30498644 -44.53909484 -80.38067796 7.93799246 -14.05860128
## 2015(357) 2015(358) 2015(359) 2015(360) 2015(361)
## 16.08879258 -6.36611388 -28.07210689 -119.75580844 -34.33421570
## 2015(362) 2015(363) 2015(364) 2015(365)
## -14.63715766 47.10859309 -27.83906279 2.24071865Computation and Plot of 10 steps ahead forecast for Turnover.ts with lag 1 to 4
Turnover.forecast.AR1to4 <- predict(AR.Turnover.ts.lag1.4, n.ahead = 10)
Turnover.forecast.AR1to4 <- ts(Turnover.forecast.AR1to4, start = end(Turnover.ts)[1] + 1, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.forecast.AR1to4, col = c("black", "red"), lty = c(1, 2), xlab = "Time", ylab = "Turnover.ts")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.forecast.AR1to4)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 361)
## Frequency = 365
## 2015(5) 2015(6) 2015(7) 2015(8) 2015(9) 2015(10)
## 4.173194e+14 3.981731e+14 5.142750e+14 1.051896e+15 5.321496e+14 4.410827e+14
## 2015(11) 2015(12) 2015(13) 2015(14) 2015(15) 2015(16)
## 6.286097e+14 4.594398e+14 4.082961e+14 3.673217e+14 4.069317e+14 4.347932e+14
## 2015(17) 2015(18) 2015(19) 2015(20) 2015(21) 2015(22)
## 4.511817e+14 4.562459e+14 5.348038e+14 5.361617e+14 5.694032e+14 5.119074e+14
## 2015(23) 2015(24) 2015(25) 2015(26) 2015(27) 2015(28)
## 4.652462e+14 4.157098e+14 3.911681e+14 5.064567e+14 4.184888e+14 3.926568e+14
## 2015(29) 2015(30) 2015(31) 2015(32) 2015(33) 2015(34)
## 4.679810e+14 3.987982e+14 4.003290e+14 4.019037e+14 3.969224e+14 4.453610e+14
## 2015(35) 2015(36) 2015(37) 2015(38) 2015(39) 2015(40)
## 4.671062e+14 4.161296e+14 3.885392e+14 4.204360e+14 4.029707e+14 3.968468e+14
## 2015(41) 2015(42) 2015(43) 2015(44) 2015(45) 2015(46)
## 4.295118e+14 3.433033e+14 4.119763e+14 3.862262e+14 3.470047e+14 3.916580e+14
## 2015(47) 2015(48) 2015(49) 2015(50) 2015(51) 2015(52)
## 4.212833e+14 3.892615e+14 4.011978e+14 3.940081e+14 3.933924e+14 4.111771e+14
## 2015(53) 2015(54) 2015(55) 2015(56) 2015(57) 2015(58)
## 3.817288e+14 3.704150e+14 4.109733e+14 3.994101e+14 3.686132e+14 4.071537e+14
## 2015(59) 2015(60) 2015(61) 2015(62) 2015(63) 2015(64)
## 3.969114e+14 5.552088e+14 4.757532e+14 3.621194e+14 4.696944e+14 4.240583e+14
## 2015(65) 2015(66) 2015(67) 2015(68) 2015(69) 2015(70)
## 4.107290e+14 4.436468e+14 4.681624e+14 4.823926e+14 4.240415e+14 3.881558e+14
## 2015(71) 2015(72) 2015(73) 2015(74) 2015(75) 2015(76)
## 4.148947e+14 4.492178e+14 3.929730e+14 5.046671e+14 4.569504e+14 4.958035e+14
## 2015(77) 2015(78) 2015(79) 2015(80) 2015(81) 2015(82)
## 5.240687e+14 1.037160e+15 6.611219e+14 4.599882e+14 5.833230e+14 5.482288e+14
## 2015(83) 2015(84) 2015(85) 2015(86) 2015(87) 2015(88)
## 5.176829e+14 4.409808e+14 4.730770e+14 4.196774e+14 3.827915e+14 3.734347e+14
## 2015(89) 2015(90) 2015(91) 2015(92) 2015(93) 2015(94)
## 4.123784e+14 3.922169e+14 3.697831e+14 3.695227e+14 3.861327e+14 4.488565e+14
## 2015(95) 2015(96) 2015(97) 2015(98) 2015(99) 2015(100)
## 3.754652e+14 4.456212e+14 4.166666e+14 3.532640e+14 3.607403e+14 4.180083e+14
## 2015(101) 2015(102) 2015(103) 2015(104) 2015(105) 2015(106)
## 4.557635e+14 5.875367e+14 3.922530e+14 3.682388e+14 4.279331e+14 4.026615e+14
## 2015(107) 2015(108) 2015(109) 2015(110) 2015(111) 2015(112)
## 3.749621e+14 3.752839e+14 4.086740e+14 3.850617e+14 4.299834e+14 4.483267e+14
## 2015(113) 2015(114) 2015(115) 2015(116) 2015(117) 2015(118)
## 3.654885e+14 3.743866e+14 4.002548e+14 3.316428e+14 3.807700e+14 3.765508e+14
## 2015(119) 2015(120) 2015(121) 2015(122) 2015(123) 2015(124)
## 3.799998e+14 3.979392e+14 3.929084e+14 3.699422e+14 3.735931e+14 3.831551e+14
## 2015(125) 2015(126) 2015(127) 2015(128) 2015(129) 2015(130)
## 3.873476e+14 3.414070e+14 3.192845e+14 3.491194e+14 3.253507e+14 3.723208e+14
## 2015(131) 2015(132) 2015(133) 2015(134) 2015(135) 2015(136)
## 4.048445e+14 3.816720e+14 3.817797e+14 3.711642e+14 3.474271e+14 3.333072e+14
## 2015(137) 2015(138) 2015(139) 2015(140) 2015(141) 2015(142)
## 3.290577e+14 3.398155e+14 9.601262e+14 5.275713e+14 3.919599e+14 5.192401e+14
## 2015(143) 2015(144) 2015(145) 2015(146) 2015(147) 2015(148)
## 4.300701e+14 4.395074e+14 3.999505e+14 4.944364e+14 4.358458e+14 4.235039e+14
## 2015(149) 2015(150) 2015(151) 2015(152) 2015(153) 2015(154)
## 4.681800e+14 3.745310e+14 4.155205e+14 3.861014e+14 3.433659e+14 4.226628e+14
## 2015(155) 2015(156) 2015(157) 2015(158) 2015(159) 2015(160)
## 4.684273e+14 4.592118e+14 3.861455e+14 3.569082e+14 3.790954e+14 4.106119e+14
## 2015(161) 2015(162) 2015(163) 2015(164) 2015(165) 2015(166)
## 4.256844e+14 4.777309e+14 5.474152e+14 5.428157e+14 5.114369e+14 5.950591e+14
## 2015(167) 2015(168) 2015(169) 2015(170) 2015(171) 2015(172)
## 4.549774e+14 4.800796e+14 4.930346e+14 4.894300e+14 4.579924e+14 4.240300e+14
## 2015(173) 2015(174) 2015(175) 2015(176) 2015(177) 2015(178)
## 3.961119e+14 3.867967e+14 4.500884e+14 4.273109e+14 4.544738e+14 4.156135e+14
## 2015(179) 2015(180) 2015(181) 2015(182) 2015(183) 2015(184)
## 3.843745e+14 4.340657e+14 4.962105e+14 3.596498e+14 4.597646e+14 4.006532e+14
## 2015(185) 2015(186) 2015(187) 2015(188) 2015(189) 2015(190)
## 5.190374e+14 4.873453e+14 4.322591e+14 4.993339e+14 5.123678e+14 4.301067e+14
## 2015(191) 2015(192) 2015(193) 2015(194) 2015(195) 2015(196)
## 4.633607e+14 4.839284e+14 4.577830e+14 5.206215e+14 8.753695e+14 5.936228e+14
## 2015(197) 2015(198) 2015(199) 2015(200) 2015(201) 2015(202)
## 4.624301e+14 5.536127e+14 4.423030e+14 4.274812e+14 4.546627e+14 4.201165e+14
## 2015(203) 2015(204) 2015(205) 2015(206) 2015(207) 2015(208)
## 3.996847e+14 3.544997e+14 3.846207e+14 3.821552e+14 3.774403e+14 3.535947e+14
## 2015(209) 2015(210) 2015(211) 2015(212) 2015(213) 2015(214)
## 3.411381e+14 3.478164e+14 3.308127e+14 3.109522e+14 3.240490e+14 3.803832e+14
## 2015(215) 2015(216) 2015(217) 2015(218) 2015(219) 2015(220)
## 3.503322e+14 2.770178e+14 3.409421e+14 3.966108e+14 3.816307e+14 4.393143e+14
## 2015(221) 2015(222) 2015(223) 2015(224) 2015(225) 2015(226)
## 4.321607e+14 3.895784e+14 3.931042e+14 3.642137e+14 4.485592e+14 3.714463e+14
## 2015(227) 2015(228) 2015(229) 2015(230) 2015(231) 2015(232)
## 5.901294e+14 4.144034e+14 3.776583e+14 4.355655e+14 4.227008e+14 3.612676e+14
## 2015(233) 2015(234) 2015(235) 2015(236) 2015(237) 2015(238)
## 3.724627e+14 4.070872e+14 3.680171e+14 3.698144e+14 3.664429e+14 3.716324e+14
## 2015(239) 2015(240) 2015(241) 2015(242) 2015(243) 2015(244)
## 3.750379e+14 3.631556e+14 4.051249e+14 3.572995e+14 3.457528e+14 3.369777e+14
## 2015(245) 2015(246) 2015(247) 2015(248) 2015(249) 2015(250)
## 2.921648e+14 3.687236e+14 3.282741e+14 3.467371e+14 4.231838e+14 3.017109e+14
## 2015(251) 2015(252) 2015(253) 2015(254) 2015(255) 2015(256)
## 3.819425e+14 4.573130e+14 4.173194e+14 3.981731e+14 5.142750e+14 1.051896e+15
## 2015(257) 2015(258) 2015(259) 2015(260) 2015(261) 2015(262)
## 5.321496e+14 4.410827e+14 6.286097e+14 4.594398e+14 4.082961e+14 3.673217e+14
## 2015(263) 2015(264) 2015(265) 2015(266) 2015(267) 2015(268)
## 4.069317e+14 4.347932e+14 4.511817e+14 4.562459e+14 5.348038e+14 5.361617e+14
## 2015(269) 2015(270) 2015(271) 2015(272) 2015(273) 2015(274)
## 5.694032e+14 5.119074e+14 4.652462e+14 4.157098e+14 3.911681e+14 5.064567e+14
## 2015(275) 2015(276) 2015(277) 2015(278) 2015(279) 2015(280)
## 4.184888e+14 3.926568e+14 4.679810e+14 3.987982e+14 4.003290e+14 4.019037e+14
## 2015(281) 2015(282) 2015(283) 2015(284) 2015(285) 2015(286)
## 3.969224e+14 4.453610e+14 4.671062e+14 4.161296e+14 3.885392e+14 4.204360e+14
## 2015(287) 2015(288) 2015(289) 2015(290) 2015(291) 2015(292)
## 4.029707e+14 3.968468e+14 4.295118e+14 3.433033e+14 4.119763e+14 3.862262e+14
## 2015(293) 2015(294) 2015(295) 2015(296) 2015(297) 2015(298)
## 3.470047e+14 3.916580e+14 4.212833e+14 3.892615e+14 4.011978e+14 3.940081e+14
## 2015(299) 2015(300) 2015(301) 2015(302) 2015(303) 2015(304)
## 3.933924e+14 4.111771e+14 3.817288e+14 3.704150e+14 4.109733e+14 3.994101e+14
## 2015(305) 2015(306) 2015(307) 2015(308) 2015(309) 2015(310)
## 3.686132e+14 4.071537e+14 3.969114e+14 5.552088e+14 4.757532e+14 3.621194e+14
## 2015(311) 2015(312) 2015(313) 2015(314) 2015(315) 2015(316)
## 4.696944e+14 4.240583e+14 4.107290e+14 4.436468e+14 4.681624e+14 4.823926e+14
## 2015(317) 2015(318) 2015(319) 2015(320) 2015(321) 2015(322)
## 4.240415e+14 3.881558e+14 4.148947e+14 4.492178e+14 3.929730e+14 5.046671e+14
## 2015(323) 2015(324) 2015(325) 2015(326) 2015(327) 2015(328)
## 4.569504e+14 4.958035e+14 5.240687e+14 1.037160e+15 6.611219e+14 4.599882e+14
## 2015(329) 2015(330) 2015(331) 2015(332) 2015(333) 2015(334)
## 5.833230e+14 5.482288e+14 5.176829e+14 4.409808e+14 4.730770e+14 4.196774e+14
## 2015(335) 2015(336) 2015(337) 2015(338) 2015(339) 2015(340)
## 3.827915e+14 3.734347e+14 4.123784e+14 3.922169e+14 3.697831e+14 3.695227e+14
## 2015(341) 2015(342) 2015(343) 2015(344) 2015(345) 2015(346)
## 3.861327e+14 4.488565e+14 3.754652e+14 4.456212e+14 4.166666e+14 3.532640e+14
## 2015(347) 2015(348) 2015(349) 2015(350) 2015(351) 2015(352)
## 3.607403e+14 4.180083e+14 4.557635e+14 5.875367e+14 3.922530e+14 3.682388e+14
## 2015(353) 2015(354) 2015(355) 2015(356) 2015(357) 2015(358)
## 4.279331e+14 4.026615e+14 3.749621e+14 3.752839e+14 4.086740e+14 3.850617e+14
## 2015(359) 2015(360) 2015(361) 2015(362) 2015(363) 2015(364)
## 4.299834e+14 4.483267e+14 3.654885e+14 3.743866e+14 4.002548e+14 3.316428e+14
## 2015(365)
## 3.807700e+14Computation and Plot of 10 steps ahead forecast for Turnover.ts with lag 2, 61, 70, and 117
Turnover.forecast.AR2n61n70n117 <- predict(AR.Turnover.ts.lag2n61n70n117, n.ahead = 10)
Turnover.forecast.AR2n61n70n117 <- ts(Turnover.forecast.AR2n61n70n117, start = end(Turnover.ts)[1] + 1, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.forecast.AR2n61n70n117, col = c("black", "red"), lty = c(1, 2), xlab = "Time", ylab = "Turnover.ts")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.forecast.AR2n61n70n117)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 248)
## Frequency = 365
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 2.843328e+14 3.300140e+14 5.355669e+14 4.556652e+14 3.214857e+14 4.490779e+14
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## 9.516066e+14 4.667516e+14 4.034747e+14 4.442095e+14 4.094747e+14 4.464079e+14
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 3.019085e+14 3.338873e+14 4.538866e+14 4.170239e+14 5.057920e+14 5.148106e+14
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 5.654224e+14 5.951847e+14 9.331840e+14 5.255144e+14 6.678249e+14 4.324794e+14
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## 5.388959e+14 5.092309e+14 4.169909e+14 5.175807e+14 4.042004e+14 7.753734e+14
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## 4.546934e+14 4.161430e+14 4.291345e+14 4.480293e+14 4.121090e+14 3.369849e+14
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 4.151113e+14 3.467545e+14 4.281638e+14 3.951658e+14 2.720864e+14 2.980391e+14
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## 3.220605e+14 3.667963e+14 5.290260e+14 4.442216e+14 3.828011e+14 4.400103e+14
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 3.960856e+14 3.970777e+14 3.299462e+14 3.942927e+14 3.872102e+14 5.644025e+14
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## 4.049325e+14 2.920580e+14 3.085694e+14 3.389439e+14 4.749459e+14 4.200219e+14
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 3.444982e+14 3.779961e+14 3.725111e+14 4.149036e+14 3.949697e+14 3.617282e+14
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## 4.389876e+14 3.154934e+14 3.524328e+14 3.116666e+14 3.811239e+14 3.378156e+14
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## 5.021257e+14 3.992006e+14 4.595697e+14 4.494703e+14 9.427325e+14 5.304186e+14
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## 5.411520e+14 3.743827e+14 3.928009e+14 9.507512e+14 4.959646e+14 4.323781e+14
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 3.328825e+14 3.276474e+14 3.154810e+14 3.150607e+14 3.893042e+14 3.237797e+14
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## 7.009195e+14 4.315094e+14 3.695596e+14 3.047088e+14 3.574160e+14 3.016987e+14
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## 3.143000e+14 4.291799e+14 4.336294e+14 3.638782e+14 4.948797e+14 2.896416e+14
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## 3.470376e+14 3.787814e+14 4.264731e+14 4.695653e+14 4.870306e+14 4.592880e+14
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 4.953680e+14 3.545042e+14 5.339300e+14 3.722555e+14 4.233579e+14 4.234395e+14
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## 4.139849e+14 3.889398e+14 3.643027e+14 4.929222e+14 3.833262e+14 4.359203e+14
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## 3.449376e+14 3.598114e+14 3.737231e+14 4.280743e+14 2.675985e+14 3.080393e+14
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## 2.955669e+14 4.012537e+14 3.954396e+14 4.025355e+14 3.675916e+14 4.224834e+14
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 4.140690e+14 2.863004e+14 3.840506e+14 3.514829e+14 5.086482e+14 1.323220e+15
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## 6.778920e+14 7.787334e+14 4.615196e+14 3.868358e+14 4.613334e+14 4.549539e+14
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## 4.965889e+14 4.194295e+14 6.167449e+14 4.988020e+14 3.719835e+14 4.124119e+14
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## 3.609068e+14 3.413978e+14 4.426893e+14 4.289439e+14 3.777151e+14 2.412377e+14
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 2.762512e+14 3.352129e+14 2.917540e+14 3.269703e+14 4.331010e+14 4.628899e+14
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## 4.905795e+14 4.140495e+14 4.591343e+14 3.768019e+14 3.958798e+14 3.909487e+14
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## 3.720448e+14 5.727803e+14 3.648690e+14 3.649271e+14 3.526866e+14 3.894666e+14
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## 3.508676e+14 3.618410e+14 3.744305e+14 2.976690e+14 4.975067e+14 4.108855e+14
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 3.047479e+14 3.802333e+14 3.220665e+14 4.751214e+14 3.657259e+14 3.483276e+14
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## 3.541376e+14 3.531430e+14 3.278895e+14 3.474210e+14 3.773616e+14 4.962947e+14
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## 4.282547e+14 7.417403e+14 5.360157e+14 3.936315e+14 3.405282e+14 4.516534e+14
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 9.092587e+14 5.110785e+14 4.291414e+14 3.353485e+14 3.254087e+14 3.938276e+14
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 3.257680e+14 4.086541e+14 4.311773e+14 8.064996e+14 4.683300e+14 7.494843e+14
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## 5.244571e+14 4.756420e+14 4.260932e+14 3.783793e+14 2.908468e+14 3.248177e+14
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## 5.082419e+14 4.122501e+14 4.778605e+14 4.723741e+14 4.440983e+14 3.860174e+14
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## 3.234109e+14 3.762396e+14 3.486128e+14 6.961057e+14 3.627582e+14 3.644528e+14
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 3.671018e+14 3.577159e+14 2.998050e+14 3.697022e+14 3.421104e+14 4.804235e+14
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## 3.471694e+14 2.877822e+14 3.026069e+14 3.712919e+14 3.218256e+14 3.690115e+14
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## 3.316116e+14 2.726681e+14 3.330638e+14 2.643042e+14 2.828703e+14 2.905869e+14
## 2015(364) 2015(365)
## 3.490093e+14 3.323483e+14Computation and Plot of 10 steps ahead forecast for Volume.ts with lag 1 to 32
Volume.forecast.AR1to32 <- predict(AR.Volume.ts.lag1.32, n.ahead = 10)
Volume.forecast.AR1to32 <- ts(Volume.forecast.AR1to32, start = end(Volume.ts)[1] + 1, frequency = frequency(Volume.ts))
ts.plot(Volume.ts, Volume.forecast.AR1to32, col = c("black", "red"), lty = c(1, 2), xlab = "Time", ylab = "Volume.ts")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.forecast.AR1to32)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 333)
## Frequency = 365
## 2015(33) 2015(34) 2015(35) 2015(36) 2015(37) 2015(38) 2015(39) 2015(40)
## 2141368 2187982 1857078 2717486 1627725 2249563 2106873 2165372
## 2015(41) 2015(42) 2015(43) 2015(44) 2015(45) 2015(46) 2015(47) 2015(48)
## 2069275 1694266 2141183 1978126 1686048 1769824 2002108 1683801
## 2015(49) 2015(50) 2015(51) 2015(52) 2015(53) 2015(54) 2015(55) 2015(56)
## 2117899 1886843 1858595 2135476 1609631 1766688 1839265 1713597
## 2015(57) 2015(58) 2015(59) 2015(60) 2015(61) 2015(62) 2015(63) 2015(64)
## 1859779 1890789 1714786 2541614 2231724 1541390 2128925 2105058
## 2015(65) 2015(66) 2015(67) 2015(68) 2015(69) 2015(70) 2015(71) 2015(72)
## 1889398 2429666 2104744 2037250 2215016 1570860 1928542 2178751
## 2015(73) 2015(74) 2015(75) 2015(76) 2015(77) 2015(78) 2015(79) 2015(80)
## 1757528 2547754 2166061 2070267 2740759 5016010 3567635 2273653
## 2015(81) 2015(82) 2015(83) 2015(84) 2015(85) 2015(86) 2015(87) 2015(88)
## 3114630 3032273 3495149 3390423 2675059 2156224 1967321 1903709
## 2015(89) 2015(90) 2015(91) 2015(92) 2015(93) 2015(94) 2015(95) 2015(96)
## 2252823 1841157 1923654 2258913 1683538 1993496 2351338 2125646
## 2015(97) 2015(98) 2015(99) 2015(100) 2015(101) 2015(102) 2015(103) 2015(104)
## 2226299 1398776 2130706 2445211 2946146 3536124 2275779 1869783
## 2015(105) 2015(106) 2015(107) 2015(108) 2015(109) 2015(110) 2015(111) 2015(112)
## 1726949 2906804 2218789 2622330 2105722 2017607 2272247 1998523
## 2015(113) 2015(114) 2015(115) 2015(116) 2015(117) 2015(118) 2015(119) 2015(120)
## 2371179 2207862 2544626 2143917 2646757 2685130 2897466 2843011
## 2015(121) 2015(122) 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128)
## 2681520 2438530 2696178 2972810 3129574 2585702 1994094 2372637
## 2015(129) 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135) 2015(136)
## 2013485 2841143 3053897 2765406 2568509 2767007 2305862 2521092
## 2015(137) 2015(138) 2015(139) 2015(140) 2015(141) 2015(142) 2015(143) 2015(144)
## 2544150 2499063 8219702 4729049 2370538 4269293 3264044 4091589
## 2015(145) 2015(146) 2015(147) 2015(148) 2015(149) 2015(150) 2015(151) 2015(152)
## 5268958 4073609 3597811 4124595 3150496 3034059 2670597 2612250
## 2015(153) 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159) 2015(160)
## 3870635 3058188 3894454 4465677 2532386 2411270 1675881 3687455
## 2015(161) 2015(162) 2015(163) 2015(164) 2015(165) 2015(166) 2015(167) 2015(168)
## 3528140 5417119 5148974 4718616 4524208 3704656 5296890 4100980
## 2015(169) 2015(170) 2015(171) 2015(172) 2015(173) 2015(174) 2015(175) 2015(176)
## 5685641 5236663 4520989 4257667 2978891 3413150 3676313 3375662
## 2015(177) 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183) 2015(184)
## 4356815 3365489 3337644 3808502 3917379 2844422 3790803 3460415
## 2015(185) 2015(186) 2015(187) 2015(188) 2015(189) 2015(190) 2015(191) 2015(192)
## 4434478 4794683 4090361 4159916 4810178 3519575 4437071 4754434
## 2015(193) 2015(194) 2015(195) 2015(196) 2015(197) 2015(198) 2015(199) 2015(200)
## 3848105 5599867 7705601 5513383 3973219 5158296 4161834 4804612
## 2015(201) 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207) 2015(208)
## 5077298 4008921 3332865 3272673 2487744 3411511 2564144 2606946
## 2015(209) 2015(210) 2015(211) 2015(212) 2015(213) 2015(214) 2015(215) 2015(216)
## 3634982 2223091 2920426 2786769 2445953 2876344 2387704 2170209
## 2015(217) 2015(218) 2015(219) 2015(220) 2015(221) 2015(222) 2015(223) 2015(224)
## 2926684 3959044 3685325 4157883 3617789 2255504 4102658 3273507
## 2015(225) 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231) 2015(232)
## 4154179 3873171 4924011 3601188 2788453 3332347 3635048 2853922
## 2015(233) 2015(234) 2015(235) 2015(236) 2015(237) 2015(238) 2015(239) 2015(240)
## 3139123 3104116 2536553 3042628 2469944 2569119 2502955 2201711
## 2015(241) 2015(242) 2015(243) 2015(244) 2015(245) 2015(246) 2015(247) 2015(248)
## 3152874 2643982 2556164 2787335 1810364 2628416 1928325 2840425
## 2015(249) 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255) 2015(256)
## 3060959 2512393 2136868 2928584 2614524 1784933 3861491 5102143
## 2015(257) 2015(258) 2015(259) 2015(260) 2015(261) 2015(262) 2015(263) 2015(264)
## 3596575 2492474 3382596 2678229 2623104 3145869 2360347 2231362
## 2015(265) 2015(266) 2015(267) 2015(268) 2015(269) 2015(270) 2015(271) 2015(272)
## 2795624 1941512 2518060 2056460 2754970 3314584 2196153 2527783
## 2015(273) 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279) 2015(280)
## 2489335 2695720 2150232 1562524 2687167 1858164 2651631 2294573
## 2015(281) 2015(282) 2015(283) 2015(284) 2015(285) 2015(286) 2015(287) 2015(288)
## 2141368 2187982 1857078 2717486 1627725 2249563 2106873 2165372
## 2015(289) 2015(290) 2015(291) 2015(292) 2015(293) 2015(294) 2015(295) 2015(296)
## 2069275 1694266 2141183 1978126 1686048 1769824 2002108 1683801
## 2015(297) 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303) 2015(304)
## 2117899 1886843 1858595 2135476 1609631 1766688 1839265 1713597
## 2015(305) 2015(306) 2015(307) 2015(308) 2015(309) 2015(310) 2015(311) 2015(312)
## 1859779 1890789 1714786 2541614 2231724 1541390 2128925 2105058
## 2015(313) 2015(314) 2015(315) 2015(316) 2015(317) 2015(318) 2015(319) 2015(320)
## 1889398 2429666 2104744 2037250 2215016 1570860 1928542 2178751
## 2015(321) 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327) 2015(328)
## 1757528 2547754 2166061 2070267 2740759 5016010 3567635 2273653
## 2015(329) 2015(330) 2015(331) 2015(332) 2015(333) 2015(334) 2015(335) 2015(336)
## 3114630 3032273 3495149 3390423 2675059 2156224 1967321 1903709
## 2015(337) 2015(338) 2015(339) 2015(340) 2015(341) 2015(342) 2015(343) 2015(344)
## 2252823 1841157 1923654 2258913 1683538 1993496 2351338 2125646
## 2015(345) 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351) 2015(352)
## 2226299 1398776 2130706 2445211 2946146 3536124 2275779 1869783
## 2015(353) 2015(354) 2015(355) 2015(356) 2015(357) 2015(358) 2015(359) 2015(360)
## 1726949 2906804 2218789 2622330 2105722 2017607 2272247 1998523
## 2015(361) 2015(362) 2015(363) 2015(364) 2015(365)
## 2371179 2207862 2544626 2143917 2646757Computation and Plot of 10 steps ahead forecast for Volume with 1 to 32 lags and 91 to 122 lags
Volume.forecast.AR1to32and91to122 <- predict(AR.Volume.ts.lag1.32n90.122, n.ahead = 10)
Volume.forecast.AR1to32and91to122 <- ts(Volume.forecast.AR1to32and91to122,
start = end(train_data.Volume)[1] + 1,
frequency = frequency(Volume.ts))
time_series_plot <- ts.plot(Volume.ts, Volume.forecast.AR1to32and91to122, col = c("black", "red"), lty = c(1, 2), xlab = "Time", ylab = "Volume")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.forecast.AR1to32and91to122)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 243)
## Frequency = 365
## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129) 2015(130)
## 3954532.3 5700605.9 2379593.7 2397080.7 2953199.1 2414288.9 1598006.6 2775501.6
## 2015(131) 2015(132) 2015(133) 2015(134) 2015(135) 2015(136) 2015(137) 2015(138)
## 3392655.4 3340282.2 2999364.8 2948646.1 3031476.1 2879275.6 3203254.3 3310617.5
## 2015(139) 2015(140) 2015(141) 2015(142) 2015(143) 2015(144) 2015(145) 2015(146)
## 8254408.1 5217615.4 2559225.4 3723928.0 3617469.9 4402678.5 5608309.2 4407231.6
## 2015(147) 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153) 2015(154)
## 4280590.6 4535112.6 2801812.4 3973312.7 2604181.1 3088551.4 3935324.6 3352888.0
## 2015(155) 2015(156) 2015(157) 2015(158) 2015(159) 2015(160) 2015(161) 2015(162)
## 3828508.2 3897746.8 3070565.3 2726785.0 2524209.7 3802202.0 3707475.0 5103421.2
## 2015(163) 2015(164) 2015(165) 2015(166) 2015(167) 2015(168) 2015(169) 2015(170)
## 5859738.6 5242868.8 4971544.1 3614305.5 5045804.4 4337561.0 5409714.8 5526310.7
## 2015(171) 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177) 2015(178)
## 4510301.5 4212377.1 2342005.4 2927933.0 3347477.5 4457621.3 3909257.6 3046130.8
## 2015(179) 2015(180) 2015(181) 2015(182) 2015(183) 2015(184) 2015(185) 2015(186)
## 3268596.5 3889687.5 3924016.9 3143752.9 3825132.0 3913458.2 4166797.7 4117491.4
## 2015(187) 2015(188) 2015(189) 2015(190) 2015(191) 2015(192) 2015(193) 2015(194)
## 4272454.4 3180800.4 4721080.7 4688219.5 3656472.0 4022948.9 4287813.2 8318420.7
## 2015(195) 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201) 2015(202)
## 7343597.8 4791656.9 3867325.9 4448074.3 3808932.3 4996852.0 5189307.0 4106231.8
## 2015(203) 2015(204) 2015(205) 2015(206) 2015(207) 2015(208) 2015(209) 2015(210)
## 3442202.2 3294891.6 2541481.2 3786523.1 2227641.9 2514316.2 3596444.8 2454013.6
## 2015(211) 2015(212) 2015(213) 2015(214) 2015(215) 2015(216) 2015(217) 2015(218)
## 2451945.3 2765987.6 2955712.0 3382079.6 2521255.6 2494182.1 3549777.6 4810145.1
## 2015(219) 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225) 2015(226)
## 3816752.0 4355365.7 4465890.6 2471494.9 4010631.2 4071418.8 4149060.8 4528511.9
## 2015(227) 2015(228) 2015(229) 2015(230) 2015(231) 2015(232) 2015(233) 2015(234)
## 4954754.9 3763392.4 1990858.3 3529126.2 3633114.9 3059139.1 2428290.1 2756721.0
## 2015(235) 2015(236) 2015(237) 2015(238) 2015(239) 2015(240) 2015(241) 2015(242)
## 1668316.9 1761798.0 3542577.9 1432489.0 2716101.9 2329350.3 2353077.0 2387487.4
## 2015(243) 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249) 2015(250)
## 2352233.3 1879016.0 2169135.5 2370394.6 2127544.8 3065162.4 1366106.6 2312081.2
## 2015(251) 2015(252) 2015(253) 2015(254) 2015(255) 2015(256) 2015(257) 2015(258)
## 3112400.8 1453063.9 698797.0 2279330.5 8153410.0 3584976.3 2050649.5 2298611.0
## 2015(259) 2015(260) 2015(261) 2015(262) 2015(263) 2015(264) 2015(265) 2015(266)
## 1855506.1 1721805.1 2064609.4 3132456.1 2107590.2 2499891.6 2417879.8 1412277.7
## 2015(267) 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273) 2015(274)
## 2826532.8 1743872.3 1817557.5 3164472.6 1926295.4 2266484.2 947475.5 2101331.5
## 2015(275) 2015(276) 2015(277) 2015(278) 2015(279) 2015(280) 2015(281) 2015(282)
## 2034436.5 986150.7 1962614.1 2248404.1 2418202.3 2061805.6 2419365.7 2156529.4
## 2015(283) 2015(284) 2015(285) 2015(286) 2015(287) 2015(288) 2015(289) 2015(290)
## 1092818.9 1861116.0 1167888.6 1990299.3 2189878.3 1462903.6 1411004.5 704762.6
## 2015(291) 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297) 2015(298)
## 1059535.5 1532790.6 2404662.2 1121510.3 1672057.7 1982582.9 2557682.8 1419402.4
## 2015(299) 2015(300) 2015(301) 2015(302) 2015(303) 2015(304) 2015(305) 2015(306)
## 1975880.7 1936388.6 2832545.3 1083402.6 1227263.9 2212160.3 1029032.8 1514478.8
## 2015(307) 2015(308) 2015(309) 2015(310) 2015(311) 2015(312) 2015(313) 2015(314)
## 2956761.7 1933676.2 1348533.3 2307997.9 4849240.9 1945157.2 1352242.7 2688710.6
## 2015(315) 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321) 2015(322)
## 1586457.4 1566279.2 2019181.4 2294504.0 1738287.2 2294095.8 1832083.5 2698523.7
## 2015(323) 2015(324) 2015(325) 2015(326) 2015(327) 2015(328) 2015(329) 2015(330)
## 2552109.5 1555552.3 3239167.3 5049484.9 3912203.3 1375463.4 2972372.6 3383797.9
## 2015(331) 2015(332) 2015(333) 2015(334) 2015(335) 2015(336) 2015(337) 2015(338)
## 3605519.8 2616977.0 3060376.8 2710306.1 1865558.2 2190438.7 2401556.4 1354773.4
## 2015(339) 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345) 2015(346)
## 2462680.5 2038267.9 1703896.6 2173656.9 3449234.8 1999302.2 1969544.4 1754942.2
## 2015(347) 2015(348) 2015(349) 2015(350) 2015(351) 2015(352) 2015(353) 2015(354)
## 3009724.9 1639761.9 3171904.4 3971804.7 2463823.0 1933559.9 1640211.7 3573329.7
## 2015(355) 2015(356) 2015(357) 2015(358) 2015(359) 2015(360) 2015(361) 2015(362)
## 3135003.7 2985453.8 3253281.5 2764967.3 2512492.3 2535217.1 2286100.6 2765279.0
## 2015(363) 2015(364) 2015(365)
## 2240505.0 2302526.3 3497956.7ARDL Models
Open.ts.diff <- diff(Open.ts)
tsdisplay(Open.ts.diff)
Close.ts.diff <- diff(Close.ts)
tsdisplay(Close.ts.diff)
Turnover.ts <- infy_stock.ts[,"Turnover"]
Volume.ts <- infy_stock.ts[,"Volume"]
tsdisplay(Turnover.ts)
tsdisplay(Volume.ts)
ARDL of Turnover and Close
ardl.turnover.close.1 <- dynlm(Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.close.1)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.759e+14 -1.190e+14 -4.453e+13 5.802e+13 1.781e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.379e+14 4.188e+13 5.679 3.78e-08 ***
## L(Turnover.ts, 1:4)1 3.277e-01 6.329e-02 5.178 4.65e-07 ***
## L(Turnover.ts, 1:4)2 3.515e-02 6.661e-02 0.528 0.598
## L(Turnover.ts, 1:4)3 -1.813e-02 6.671e-02 -0.272 0.786
## L(Turnover.ts, 1:4)4 8.763e-02 6.337e-02 1.383 0.168
## L(Close.ts.diff, 110) 4.385e+10 1.844e+11 0.238 0.812
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.537e+14 on 248 degrees of freedom
## Multiple R-squared: 0.1263, Adjusted R-squared: 0.1087
## F-statistic: 7.172 on 5 and 248 DF, p-value: 2.743e-06ardl.turnover.close.2 <- dynlm(Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff, 1:110), data = infy_stock)
summary(ardl.turnover.close.2)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff,
## 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.735e+14 -9.649e+13 -3.265e+13 4.919e+13 1.050e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.329e+14 5.284e+13 4.407 2.08e-05 ***
## L(Turnover.ts, 1:4)1 3.394e-01 8.448e-02 4.017 9.60e-05 ***
## L(Turnover.ts, 1:4)2 7.559e-02 8.914e-02 0.848 0.397897
## L(Turnover.ts, 1:4)3 -5.991e-02 8.919e-02 -0.672 0.502864
## L(Turnover.ts, 1:4)4 9.371e-02 8.434e-02 1.111 0.268478
## L(Close.ts.diff, 1:110)1 7.339e+10 1.611e+11 0.456 0.649388
## L(Close.ts.diff, 1:110)2 1.657e+11 1.612e+11 1.028 0.305817
## L(Close.ts.diff, 1:110)3 4.332e+10 1.617e+11 0.268 0.789204
## L(Close.ts.diff, 1:110)4 -8.638e+10 1.618e+11 -0.534 0.594402
## L(Close.ts.diff, 1:110)5 1.430e+11 1.620e+11 0.883 0.378722
## L(Close.ts.diff, 1:110)6 8.402e+11 1.957e+11 4.293 3.29e-05 ***
## L(Close.ts.diff, 1:110)7 -2.172e+11 2.088e+11 -1.040 0.299955
## L(Close.ts.diff, 1:110)8 -1.052e+11 2.092e+11 -0.503 0.615890
## L(Close.ts.diff, 1:110)9 1.464e+11 2.088e+11 0.701 0.484299
## L(Close.ts.diff, 1:110)10 -9.255e+10 2.086e+11 -0.444 0.657961
## L(Close.ts.diff, 1:110)11 -1.621e+10 1.954e+11 -0.083 0.934008
## L(Close.ts.diff, 1:110)12 -6.319e+10 1.951e+11 -0.324 0.746579
## L(Close.ts.diff, 1:110)13 1.828e+11 1.953e+11 0.936 0.350926
## L(Close.ts.diff, 1:110)14 1.700e+11 1.959e+11 0.868 0.387061
## L(Close.ts.diff, 1:110)15 7.128e+10 1.965e+11 0.363 0.717289
## L(Close.ts.diff, 1:110)16 1.206e+11 1.968e+11 0.613 0.540998
## L(Close.ts.diff, 1:110)17 2.457e+11 1.962e+11 1.252 0.212560
## L(Close.ts.diff, 1:110)18 3.434e+10 1.972e+11 0.174 0.861992
## L(Close.ts.diff, 1:110)19 1.181e+11 1.968e+11 0.600 0.549307
## L(Close.ts.diff, 1:110)20 3.291e+09 1.966e+11 0.017 0.986670
## L(Close.ts.diff, 1:110)21 -1.867e+10 1.967e+11 -0.095 0.924545
## L(Close.ts.diff, 1:110)22 4.037e+10 1.957e+11 0.206 0.836893
## L(Close.ts.diff, 1:110)23 -6.412e+10 1.956e+11 -0.328 0.743565
## L(Close.ts.diff, 1:110)24 1.775e+11 1.946e+11 0.912 0.363203
## L(Close.ts.diff, 1:110)25 9.822e+10 1.954e+11 0.503 0.615977
## L(Close.ts.diff, 1:110)26 -9.431e+11 1.955e+11 -4.823 3.67e-06 ***
## L(Close.ts.diff, 1:110)27 1.977e+11 2.113e+11 0.935 0.351197
## L(Close.ts.diff, 1:110)28 3.297e+10 2.116e+11 0.156 0.876418
## L(Close.ts.diff, 1:110)29 7.482e+10 2.110e+11 0.355 0.723470
## L(Close.ts.diff, 1:110)30 -1.721e+10 2.076e+11 -0.083 0.934058
## L(Close.ts.diff, 1:110)31 -1.372e+11 1.961e+11 -0.700 0.485290
## L(Close.ts.diff, 1:110)32 1.895e+11 1.964e+11 0.965 0.336298
## L(Close.ts.diff, 1:110)33 -6.174e+10 1.968e+11 -0.314 0.754153
## L(Close.ts.diff, 1:110)34 -8.987e+10 1.964e+11 -0.458 0.647906
## L(Close.ts.diff, 1:110)35 4.004e+09 1.957e+11 0.020 0.983701
## L(Close.ts.diff, 1:110)36 -5.505e+10 1.955e+11 -0.282 0.778705
## L(Close.ts.diff, 1:110)37 8.448e+10 1.952e+11 0.433 0.665822
## L(Close.ts.diff, 1:110)38 -1.034e+11 1.951e+11 -0.530 0.596762
## L(Close.ts.diff, 1:110)39 1.527e+11 1.950e+11 0.783 0.435093
## L(Close.ts.diff, 1:110)40 3.860e+10 1.956e+11 0.197 0.843839
## L(Close.ts.diff, 1:110)41 -1.435e+11 1.959e+11 -0.733 0.465072
## L(Close.ts.diff, 1:110)42 -1.637e+11 1.961e+11 -0.835 0.405096
## L(Close.ts.diff, 1:110)43 -8.991e+10 1.962e+11 -0.458 0.647521
## L(Close.ts.diff, 1:110)44 1.694e+11 1.962e+11 0.863 0.389466
## L(Close.ts.diff, 1:110)45 9.928e+10 1.967e+11 0.505 0.614490
## L(Close.ts.diff, 1:110)46 8.374e+10 1.968e+11 0.426 0.671100
## L(Close.ts.diff, 1:110)47 1.267e+10 1.964e+11 0.065 0.948629
## L(Close.ts.diff, 1:110)48 -7.329e+10 1.956e+11 -0.375 0.708483
## L(Close.ts.diff, 1:110)49 -2.369e+10 1.957e+11 -0.121 0.903837
## L(Close.ts.diff, 1:110)50 -7.656e+10 1.957e+11 -0.391 0.696191
## L(Close.ts.diff, 1:110)51 -6.874e+10 1.956e+11 -0.351 0.725829
## L(Close.ts.diff, 1:110)52 -1.316e+11 1.955e+11 -0.673 0.502071
## L(Close.ts.diff, 1:110)53 -1.302e+11 1.956e+11 -0.666 0.506643
## L(Close.ts.diff, 1:110)54 4.434e+10 1.962e+11 0.226 0.821527
## L(Close.ts.diff, 1:110)55 -6.630e+10 1.962e+11 -0.338 0.735944
## L(Close.ts.diff, 1:110)56 5.868e+10 1.962e+11 0.299 0.765380
## L(Close.ts.diff, 1:110)57 -7.955e+10 1.960e+11 -0.406 0.685506
## L(Close.ts.diff, 1:110)58 3.189e+11 1.957e+11 1.630 0.105448
## L(Close.ts.diff, 1:110)59 -6.487e+09 1.976e+11 -0.033 0.973855
## L(Close.ts.diff, 1:110)60 -6.811e+10 1.974e+11 -0.345 0.730630
## L(Close.ts.diff, 1:110)61 5.678e+09 1.972e+11 0.029 0.977077
## L(Close.ts.diff, 1:110)62 -1.244e+11 1.965e+11 -0.633 0.527797
## L(Close.ts.diff, 1:110)63 2.182e+10 1.953e+11 0.112 0.911218
## L(Close.ts.diff, 1:110)64 -1.290e+11 1.954e+11 -0.660 0.510300
## L(Close.ts.diff, 1:110)65 -4.913e+10 1.956e+11 -0.251 0.802104
## L(Close.ts.diff, 1:110)66 1.716e+11 1.956e+11 0.877 0.381862
## L(Close.ts.diff, 1:110)67 3.261e+10 1.961e+11 0.166 0.868160
## L(Close.ts.diff, 1:110)68 -1.529e+11 1.959e+11 -0.780 0.436597
## L(Close.ts.diff, 1:110)69 1.901e+11 1.963e+11 0.969 0.334410
## L(Close.ts.diff, 1:110)70 -1.062e+10 1.965e+11 -0.054 0.956999
## L(Close.ts.diff, 1:110)71 7.715e+10 1.961e+11 0.394 0.694545
## L(Close.ts.diff, 1:110)72 -1.286e+11 1.960e+11 -0.656 0.512991
## L(Close.ts.diff, 1:110)73 -2.963e+10 1.956e+11 -0.151 0.879828
## L(Close.ts.diff, 1:110)74 1.183e+11 1.959e+11 0.604 0.546719
## L(Close.ts.diff, 1:110)75 1.475e+10 1.963e+11 0.075 0.940220
## L(Close.ts.diff, 1:110)76 8.400e+11 1.958e+11 4.291 3.32e-05 ***
## L(Close.ts.diff, 1:110)77 3.778e+10 2.075e+11 0.182 0.855775
## L(Close.ts.diff, 1:110)78 -8.592e+10 2.074e+11 -0.414 0.679314
## L(Close.ts.diff, 1:110)79 -9.532e+10 2.074e+11 -0.460 0.646531
## L(Close.ts.diff, 1:110)80 6.725e+10 2.065e+11 0.326 0.745186
## L(Close.ts.diff, 1:110)81 -2.137e+10 1.975e+11 -0.108 0.913998
## L(Close.ts.diff, 1:110)82 -7.124e+11 1.958e+11 -3.638 0.000386 ***
## L(Close.ts.diff, 1:110)83 -3.165e+08 2.042e+11 -0.002 0.998766
## L(Close.ts.diff, 1:110)84 -6.625e+09 2.037e+11 -0.033 0.974101
## L(Close.ts.diff, 1:110)85 -1.514e+11 2.030e+11 -0.746 0.456962
## L(Close.ts.diff, 1:110)86 6.248e+10 2.018e+11 0.310 0.757291
## L(Close.ts.diff, 1:110)87 1.008e+10 1.955e+11 0.052 0.958947
## L(Close.ts.diff, 1:110)88 1.621e+10 1.955e+11 0.083 0.934020
## L(Close.ts.diff, 1:110)89 1.850e+10 1.954e+11 0.095 0.924721
## L(Close.ts.diff, 1:110)90 -7.614e+10 1.949e+11 -0.391 0.696588
## L(Close.ts.diff, 1:110)91 7.648e+10 1.949e+11 0.393 0.695280
## L(Close.ts.diff, 1:110)92 8.090e+10 1.951e+11 0.415 0.679044
## L(Close.ts.diff, 1:110)93 3.490e+10 1.953e+11 0.179 0.858413
## L(Close.ts.diff, 1:110)94 8.301e+10 1.950e+11 0.426 0.670977
## L(Close.ts.diff, 1:110)95 1.086e+10 1.956e+11 0.056 0.955808
## L(Close.ts.diff, 1:110)96 -3.669e+10 1.954e+11 -0.188 0.851353
## L(Close.ts.diff, 1:110)97 1.097e+10 1.952e+11 0.056 0.955280
## L(Close.ts.diff, 1:110)98 3.885e+10 1.952e+11 0.199 0.842573
## L(Close.ts.diff, 1:110)99 1.531e+11 1.950e+11 0.785 0.433730
## L(Close.ts.diff, 1:110)100 2.930e+11 1.956e+11 1.498 0.136323
## L(Close.ts.diff, 1:110)101 -5.918e+10 1.972e+11 -0.300 0.764513
## L(Close.ts.diff, 1:110)102 -4.528e+09 1.971e+11 -0.023 0.981705
## L(Close.ts.diff, 1:110)103 1.211e+11 1.971e+11 0.615 0.539768
## L(Close.ts.diff, 1:110)104 3.255e+08 1.974e+11 0.002 0.998686
## L(Close.ts.diff, 1:110)105 -1.619e+11 1.942e+11 -0.833 0.406053
## L(Close.ts.diff, 1:110)106 -9.826e+10 1.953e+11 -0.503 0.615602
## L(Close.ts.diff, 1:110)107 -1.163e+11 1.953e+11 -0.595 0.552643
## L(Close.ts.diff, 1:110)108 -1.040e+11 1.952e+11 -0.533 0.595153
## L(Close.ts.diff, 1:110)109 2.938e+10 1.950e+11 0.151 0.880456
## L(Close.ts.diff, 1:110)110 8.288e+10 1.949e+11 0.425 0.671371
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.559e+14 on 139 degrees of freedom
## Multiple R-squared: 0.5018, Adjusted R-squared: 0.09325
## F-statistic: 1.228 on 114 and 139 DF, p-value: 0.1237ardl.turnover.close.3 <- dynlm(Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,61) + L(Turnover.ts, 75) + L(Turnover.ts,117) + L(Close.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.close.3)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 75) + L(Turnover.ts, 117) + L(Close.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.755e+14 -1.384e+14 -2.222e+13 1.007e+14 1.825e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.077e+13 5.152e+13 1.762 0.07939 .
## L(Turnover.ts, 2) 1.706e-01 5.747e-02 2.969 0.00329 **
## L(Turnover.ts, 61) 2.840e-01 5.778e-02 4.914 1.64e-06 ***
## L(Turnover.ts, 75) 4.264e-02 5.746e-02 0.742 0.45878
## L(Turnover.ts, 117) 2.884e-01 5.784e-02 4.987 1.17e-06 ***
## L(Close.ts.diff, 110) 1.181e+11 1.778e+11 0.665 0.50697
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.44e+14 on 242 degrees of freedom
## Multiple R-squared: 0.2045, Adjusted R-squared: 0.188
## F-statistic: 12.44 on 5 and 242 DF, p-value: 9.408e-11ardl.turnover.close.4 <- dynlm(Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,61) + L(Turnover.ts, 75) + L(Turnover.ts,117) + L(Close.ts.diff, 1:110), data = infy_stock)
summary(ardl.turnover.close.4)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 75) + L(Turnover.ts, 117) + L(Close.ts.diff,
## 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.384e+14 -1.097e+14 -2.262e+13 7.092e+13 1.108e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.106e+14 7.389e+13 1.498 0.13663
## L(Turnover.ts, 2) 1.818e-01 7.859e-02 2.313 0.02224 *
## L(Turnover.ts, 61) 2.717e-01 8.743e-02 3.108 0.00231 **
## L(Turnover.ts, 75) -9.467e-03 8.713e-02 -0.109 0.91364
## L(Turnover.ts, 117) 2.946e-01 9.255e-02 3.184 0.00181 **
## L(Close.ts.diff, 1:110)1 -2.861e+10 1.945e+11 -0.147 0.88326
## L(Close.ts.diff, 1:110)2 1.521e+11 1.957e+11 0.777 0.43848
## L(Close.ts.diff, 1:110)3 6.492e+08 1.942e+11 0.003 0.99734
## L(Close.ts.diff, 1:110)4 -9.810e+10 1.952e+11 -0.503 0.61612
## L(Close.ts.diff, 1:110)5 1.409e+11 1.944e+11 0.725 0.46979
## L(Close.ts.diff, 1:110)6 4.138e+11 2.227e+11 1.859 0.06530 .
## L(Close.ts.diff, 1:110)7 -4.007e+10 1.968e+11 -0.204 0.83900
## L(Close.ts.diff, 1:110)8 -8.854e+10 2.085e+11 -0.425 0.67183
## L(Close.ts.diff, 1:110)9 1.879e+11 1.961e+11 0.958 0.33956
## L(Close.ts.diff, 1:110)10 9.941e+09 1.952e+11 0.051 0.95947
## L(Close.ts.diff, 1:110)11 2.261e+10 1.950e+11 0.116 0.90786
## L(Close.ts.diff, 1:110)12 2.422e+11 2.183e+11 1.110 0.26922
## L(Close.ts.diff, 1:110)13 1.887e+11 1.954e+11 0.966 0.33585
## L(Close.ts.diff, 1:110)14 2.739e+11 1.954e+11 1.402 0.16338
## L(Close.ts.diff, 1:110)15 2.032e+11 1.960e+11 1.037 0.30179
## L(Close.ts.diff, 1:110)16 1.543e+11 1.973e+11 0.782 0.43563
## L(Close.ts.diff, 1:110)17 3.081e+11 1.950e+11 1.580 0.11658
## L(Close.ts.diff, 1:110)18 7.711e+10 1.956e+11 0.394 0.69413
## L(Close.ts.diff, 1:110)19 1.816e+11 1.962e+11 0.925 0.35659
## L(Close.ts.diff, 1:110)20 1.353e+11 2.040e+11 0.663 0.50838
## L(Close.ts.diff, 1:110)21 4.811e+10 1.965e+11 0.245 0.80699
## L(Close.ts.diff, 1:110)22 9.921e+10 1.968e+11 0.504 0.61506
## L(Close.ts.diff, 1:110)23 3.112e+10 1.960e+11 0.159 0.87411
## L(Close.ts.diff, 1:110)24 3.041e+11 1.961e+11 1.550 0.12346
## L(Close.ts.diff, 1:110)25 2.750e+11 1.962e+11 1.402 0.16337
## L(Close.ts.diff, 1:110)26 -5.933e+11 2.134e+11 -2.780 0.00622 **
## L(Close.ts.diff, 1:110)27 1.456e+10 1.993e+11 0.073 0.94188
## L(Close.ts.diff, 1:110)28 1.327e+11 2.072e+11 0.640 0.52307
## L(Close.ts.diff, 1:110)29 8.735e+10 1.972e+11 0.443 0.65850
## L(Close.ts.diff, 1:110)30 -1.742e+10 1.962e+11 -0.089 0.92939
## L(Close.ts.diff, 1:110)31 -1.962e+11 1.962e+11 -1.000 0.31914
## L(Close.ts.diff, 1:110)32 6.967e+10 1.964e+11 0.355 0.72332
## L(Close.ts.diff, 1:110)33 -4.210e+10 1.972e+11 -0.213 0.83127
## L(Close.ts.diff, 1:110)34 -1.024e+11 1.953e+11 -0.524 0.60083
## L(Close.ts.diff, 1:110)35 -6.332e+10 1.953e+11 -0.324 0.74631
## L(Close.ts.diff, 1:110)36 -1.464e+11 1.965e+11 -0.745 0.45778
## L(Close.ts.diff, 1:110)37 1.796e+10 1.964e+11 0.091 0.92725
## L(Close.ts.diff, 1:110)38 -1.741e+11 1.970e+11 -0.884 0.37847
## L(Close.ts.diff, 1:110)39 1.427e+11 1.949e+11 0.732 0.46517
## L(Close.ts.diff, 1:110)40 6.295e+10 2.128e+11 0.296 0.76781
## L(Close.ts.diff, 1:110)41 -1.481e+11 1.993e+11 -0.743 0.45874
## L(Close.ts.diff, 1:110)42 -2.085e+11 1.957e+11 -1.066 0.28852
## L(Close.ts.diff, 1:110)43 -1.441e+11 1.952e+11 -0.738 0.46159
## L(Close.ts.diff, 1:110)44 1.391e+11 1.963e+11 0.708 0.47994
## L(Close.ts.diff, 1:110)45 1.611e+11 1.955e+11 0.824 0.41134
## L(Close.ts.diff, 1:110)46 8.892e+10 1.949e+11 0.456 0.64891
## L(Close.ts.diff, 1:110)47 2.950e+10 1.952e+11 0.151 0.88009
## L(Close.ts.diff, 1:110)48 -1.250e+11 1.958e+11 -0.639 0.52419
## L(Close.ts.diff, 1:110)49 -1.461e+10 1.955e+11 -0.075 0.94053
## L(Close.ts.diff, 1:110)50 -6.991e+09 1.981e+11 -0.035 0.97190
## L(Close.ts.diff, 1:110)51 -4.997e+10 1.954e+11 -0.256 0.79858
## L(Close.ts.diff, 1:110)52 -2.406e+11 1.981e+11 -1.215 0.22666
## L(Close.ts.diff, 1:110)53 -2.213e+11 1.952e+11 -1.134 0.25902
## L(Close.ts.diff, 1:110)54 1.635e+10 1.955e+11 0.084 0.93348
## L(Close.ts.diff, 1:110)55 -8.485e+10 1.959e+11 -0.433 0.66563
## L(Close.ts.diff, 1:110)56 -4.230e+09 1.958e+11 -0.022 0.98280
## L(Close.ts.diff, 1:110)57 -8.049e+10 1.955e+11 -0.412 0.68129
## L(Close.ts.diff, 1:110)58 2.391e+11 1.957e+11 1.221 0.22409
## L(Close.ts.diff, 1:110)59 1.043e+11 1.955e+11 0.533 0.59476
## L(Close.ts.diff, 1:110)60 -8.921e+10 1.965e+11 -0.454 0.65052
## L(Close.ts.diff, 1:110)61 -2.069e+10 1.956e+11 -0.106 0.91592
## L(Close.ts.diff, 1:110)62 -3.194e+11 2.041e+11 -1.564 0.12009
## L(Close.ts.diff, 1:110)63 -1.170e+11 1.965e+11 -0.595 0.55264
## L(Close.ts.diff, 1:110)64 -1.089e+11 1.987e+11 -0.548 0.58461
## L(Close.ts.diff, 1:110)65 -4.240e+09 1.958e+11 -0.022 0.98275
## L(Close.ts.diff, 1:110)66 1.512e+11 1.958e+11 0.772 0.44137
## L(Close.ts.diff, 1:110)67 -1.484e+11 2.111e+11 -0.703 0.48342
## L(Close.ts.diff, 1:110)68 -2.021e+11 1.954e+11 -1.034 0.30278
## L(Close.ts.diff, 1:110)69 1.209e+11 1.947e+11 0.621 0.53587
## L(Close.ts.diff, 1:110)70 5.483e+10 1.956e+11 0.280 0.77968
## L(Close.ts.diff, 1:110)71 1.230e+11 1.957e+11 0.628 0.53097
## L(Close.ts.diff, 1:110)72 -7.109e+10 1.952e+11 -0.364 0.71630
## L(Close.ts.diff, 1:110)73 -3.854e+10 1.954e+11 -0.197 0.84398
## L(Close.ts.diff, 1:110)74 4.417e+10 1.956e+11 0.226 0.82173
## L(Close.ts.diff, 1:110)75 3.656e+09 1.960e+11 0.019 0.98514
## L(Close.ts.diff, 1:110)76 8.334e+11 1.959e+11 4.255 3.91e-05 ***
## L(Close.ts.diff, 1:110)77 2.712e+11 1.961e+11 1.383 0.16903
## L(Close.ts.diff, 1:110)78 -9.198e+10 2.092e+11 -0.440 0.66086
## L(Close.ts.diff, 1:110)79 -1.253e+11 1.986e+11 -0.631 0.52937
## L(Close.ts.diff, 1:110)80 1.007e+11 1.974e+11 0.510 0.61096
## L(Close.ts.diff, 1:110)81 5.203e+10 2.114e+11 0.246 0.80592
## L(Close.ts.diff, 1:110)82 -4.597e+11 2.156e+11 -2.132 0.03483 *
## L(Close.ts.diff, 1:110)83 -1.148e+11 2.000e+11 -0.574 0.56695
## L(Close.ts.diff, 1:110)84 7.064e+10 2.025e+11 0.349 0.72777
## L(Close.ts.diff, 1:110)85 -1.529e+11 1.958e+11 -0.781 0.43610
## L(Close.ts.diff, 1:110)86 -8.517e+09 1.957e+11 -0.044 0.96536
## L(Close.ts.diff, 1:110)87 2.762e+11 2.098e+11 1.317 0.19018
## L(Close.ts.diff, 1:110)88 4.054e+10 1.951e+11 0.208 0.83573
## L(Close.ts.diff, 1:110)89 4.640e+10 1.957e+11 0.237 0.81292
## L(Close.ts.diff, 1:110)90 -1.128e+11 1.952e+11 -0.578 0.56446
## L(Close.ts.diff, 1:110)91 8.581e+10 1.951e+11 0.440 0.66083
## L(Close.ts.diff, 1:110)92 9.266e+10 1.968e+11 0.471 0.63857
## L(Close.ts.diff, 1:110)93 3.228e+10 1.954e+11 0.165 0.86907
## L(Close.ts.diff, 1:110)94 -9.814e+09 1.978e+11 -0.050 0.96050
## L(Close.ts.diff, 1:110)95 7.836e+10 1.954e+11 0.401 0.68901
## L(Close.ts.diff, 1:110)96 3.101e+09 1.956e+11 0.016 0.98738
## L(Close.ts.diff, 1:110)97 3.338e+10 1.948e+11 0.171 0.86422
## L(Close.ts.diff, 1:110)98 7.496e+10 1.949e+11 0.385 0.70115
## L(Close.ts.diff, 1:110)99 2.078e+11 1.950e+11 1.066 0.28857
## L(Close.ts.diff, 1:110)100 3.745e+11 1.956e+11 1.915 0.05766 .
## L(Close.ts.diff, 1:110)101 3.678e+10 2.096e+11 0.175 0.86098
## L(Close.ts.diff, 1:110)102 3.637e+09 1.970e+11 0.018 0.98530
## L(Close.ts.diff, 1:110)103 1.728e+11 1.958e+11 0.882 0.37917
## L(Close.ts.diff, 1:110)104 1.298e+11 1.954e+11 0.664 0.50775
## L(Close.ts.diff, 1:110)105 -1.281e+11 1.946e+11 -0.658 0.51165
## L(Close.ts.diff, 1:110)106 -8.310e+10 1.972e+11 -0.421 0.67415
## L(Close.ts.diff, 1:110)107 -1.727e+11 1.947e+11 -0.887 0.37657
## L(Close.ts.diff, 1:110)108 -1.724e+11 1.944e+11 -0.887 0.37680
## L(Close.ts.diff, 1:110)109 -1.502e+09 1.947e+11 -0.008 0.99386
## L(Close.ts.diff, 1:110)110 1.082e+11 1.946e+11 0.556 0.57925
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.551e+14 on 133 degrees of freedom
## Multiple R-squared: 0.5223, Adjusted R-squared: 0.1128
## F-statistic: 1.276 on 114 and 133 DF, p-value: 0.08804ARDL of Turnover and Open
ardl.turnover.open.1 <- dynlm(Turnover.ts ~ L(Turnover.ts, 1:4) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.close.1)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.759e+14 -1.190e+14 -4.453e+13 5.802e+13 1.781e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.379e+14 4.188e+13 5.679 3.78e-08 ***
## L(Turnover.ts, 1:4)1 3.277e-01 6.329e-02 5.178 4.65e-07 ***
## L(Turnover.ts, 1:4)2 3.515e-02 6.661e-02 0.528 0.598
## L(Turnover.ts, 1:4)3 -1.813e-02 6.671e-02 -0.272 0.786
## L(Turnover.ts, 1:4)4 8.763e-02 6.337e-02 1.383 0.168
## L(Close.ts.diff, 110) 4.385e+10 1.844e+11 0.238 0.812
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.537e+14 on 248 degrees of freedom
## Multiple R-squared: 0.1263, Adjusted R-squared: 0.1087
## F-statistic: 7.172 on 5 and 248 DF, p-value: 2.743e-06ardl.turnover.open.2 <- dynlm(Turnover.ts ~ L(Turnover.ts, 1:4) + L(Open.ts.diff, 35) + L (Open.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.close.2)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff,
## 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.735e+14 -9.649e+13 -3.265e+13 4.919e+13 1.050e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.329e+14 5.284e+13 4.407 2.08e-05 ***
## L(Turnover.ts, 1:4)1 3.394e-01 8.448e-02 4.017 9.60e-05 ***
## L(Turnover.ts, 1:4)2 7.559e-02 8.914e-02 0.848 0.397897
## L(Turnover.ts, 1:4)3 -5.991e-02 8.919e-02 -0.672 0.502864
## L(Turnover.ts, 1:4)4 9.371e-02 8.434e-02 1.111 0.268478
## L(Close.ts.diff, 1:110)1 7.339e+10 1.611e+11 0.456 0.649388
## L(Close.ts.diff, 1:110)2 1.657e+11 1.612e+11 1.028 0.305817
## L(Close.ts.diff, 1:110)3 4.332e+10 1.617e+11 0.268 0.789204
## L(Close.ts.diff, 1:110)4 -8.638e+10 1.618e+11 -0.534 0.594402
## L(Close.ts.diff, 1:110)5 1.430e+11 1.620e+11 0.883 0.378722
## L(Close.ts.diff, 1:110)6 8.402e+11 1.957e+11 4.293 3.29e-05 ***
## L(Close.ts.diff, 1:110)7 -2.172e+11 2.088e+11 -1.040 0.299955
## L(Close.ts.diff, 1:110)8 -1.052e+11 2.092e+11 -0.503 0.615890
## L(Close.ts.diff, 1:110)9 1.464e+11 2.088e+11 0.701 0.484299
## L(Close.ts.diff, 1:110)10 -9.255e+10 2.086e+11 -0.444 0.657961
## L(Close.ts.diff, 1:110)11 -1.621e+10 1.954e+11 -0.083 0.934008
## L(Close.ts.diff, 1:110)12 -6.319e+10 1.951e+11 -0.324 0.746579
## L(Close.ts.diff, 1:110)13 1.828e+11 1.953e+11 0.936 0.350926
## L(Close.ts.diff, 1:110)14 1.700e+11 1.959e+11 0.868 0.387061
## L(Close.ts.diff, 1:110)15 7.128e+10 1.965e+11 0.363 0.717289
## L(Close.ts.diff, 1:110)16 1.206e+11 1.968e+11 0.613 0.540998
## L(Close.ts.diff, 1:110)17 2.457e+11 1.962e+11 1.252 0.212560
## L(Close.ts.diff, 1:110)18 3.434e+10 1.972e+11 0.174 0.861992
## L(Close.ts.diff, 1:110)19 1.181e+11 1.968e+11 0.600 0.549307
## L(Close.ts.diff, 1:110)20 3.291e+09 1.966e+11 0.017 0.986670
## L(Close.ts.diff, 1:110)21 -1.867e+10 1.967e+11 -0.095 0.924545
## L(Close.ts.diff, 1:110)22 4.037e+10 1.957e+11 0.206 0.836893
## L(Close.ts.diff, 1:110)23 -6.412e+10 1.956e+11 -0.328 0.743565
## L(Close.ts.diff, 1:110)24 1.775e+11 1.946e+11 0.912 0.363203
## L(Close.ts.diff, 1:110)25 9.822e+10 1.954e+11 0.503 0.615977
## L(Close.ts.diff, 1:110)26 -9.431e+11 1.955e+11 -4.823 3.67e-06 ***
## L(Close.ts.diff, 1:110)27 1.977e+11 2.113e+11 0.935 0.351197
## L(Close.ts.diff, 1:110)28 3.297e+10 2.116e+11 0.156 0.876418
## L(Close.ts.diff, 1:110)29 7.482e+10 2.110e+11 0.355 0.723470
## L(Close.ts.diff, 1:110)30 -1.721e+10 2.076e+11 -0.083 0.934058
## L(Close.ts.diff, 1:110)31 -1.372e+11 1.961e+11 -0.700 0.485290
## L(Close.ts.diff, 1:110)32 1.895e+11 1.964e+11 0.965 0.336298
## L(Close.ts.diff, 1:110)33 -6.174e+10 1.968e+11 -0.314 0.754153
## L(Close.ts.diff, 1:110)34 -8.987e+10 1.964e+11 -0.458 0.647906
## L(Close.ts.diff, 1:110)35 4.004e+09 1.957e+11 0.020 0.983701
## L(Close.ts.diff, 1:110)36 -5.505e+10 1.955e+11 -0.282 0.778705
## L(Close.ts.diff, 1:110)37 8.448e+10 1.952e+11 0.433 0.665822
## L(Close.ts.diff, 1:110)38 -1.034e+11 1.951e+11 -0.530 0.596762
## L(Close.ts.diff, 1:110)39 1.527e+11 1.950e+11 0.783 0.435093
## L(Close.ts.diff, 1:110)40 3.860e+10 1.956e+11 0.197 0.843839
## L(Close.ts.diff, 1:110)41 -1.435e+11 1.959e+11 -0.733 0.465072
## L(Close.ts.diff, 1:110)42 -1.637e+11 1.961e+11 -0.835 0.405096
## L(Close.ts.diff, 1:110)43 -8.991e+10 1.962e+11 -0.458 0.647521
## L(Close.ts.diff, 1:110)44 1.694e+11 1.962e+11 0.863 0.389466
## L(Close.ts.diff, 1:110)45 9.928e+10 1.967e+11 0.505 0.614490
## L(Close.ts.diff, 1:110)46 8.374e+10 1.968e+11 0.426 0.671100
## L(Close.ts.diff, 1:110)47 1.267e+10 1.964e+11 0.065 0.948629
## L(Close.ts.diff, 1:110)48 -7.329e+10 1.956e+11 -0.375 0.708483
## L(Close.ts.diff, 1:110)49 -2.369e+10 1.957e+11 -0.121 0.903837
## L(Close.ts.diff, 1:110)50 -7.656e+10 1.957e+11 -0.391 0.696191
## L(Close.ts.diff, 1:110)51 -6.874e+10 1.956e+11 -0.351 0.725829
## L(Close.ts.diff, 1:110)52 -1.316e+11 1.955e+11 -0.673 0.502071
## L(Close.ts.diff, 1:110)53 -1.302e+11 1.956e+11 -0.666 0.506643
## L(Close.ts.diff, 1:110)54 4.434e+10 1.962e+11 0.226 0.821527
## L(Close.ts.diff, 1:110)55 -6.630e+10 1.962e+11 -0.338 0.735944
## L(Close.ts.diff, 1:110)56 5.868e+10 1.962e+11 0.299 0.765380
## L(Close.ts.diff, 1:110)57 -7.955e+10 1.960e+11 -0.406 0.685506
## L(Close.ts.diff, 1:110)58 3.189e+11 1.957e+11 1.630 0.105448
## L(Close.ts.diff, 1:110)59 -6.487e+09 1.976e+11 -0.033 0.973855
## L(Close.ts.diff, 1:110)60 -6.811e+10 1.974e+11 -0.345 0.730630
## L(Close.ts.diff, 1:110)61 5.678e+09 1.972e+11 0.029 0.977077
## L(Close.ts.diff, 1:110)62 -1.244e+11 1.965e+11 -0.633 0.527797
## L(Close.ts.diff, 1:110)63 2.182e+10 1.953e+11 0.112 0.911218
## L(Close.ts.diff, 1:110)64 -1.290e+11 1.954e+11 -0.660 0.510300
## L(Close.ts.diff, 1:110)65 -4.913e+10 1.956e+11 -0.251 0.802104
## L(Close.ts.diff, 1:110)66 1.716e+11 1.956e+11 0.877 0.381862
## L(Close.ts.diff, 1:110)67 3.261e+10 1.961e+11 0.166 0.868160
## L(Close.ts.diff, 1:110)68 -1.529e+11 1.959e+11 -0.780 0.436597
## L(Close.ts.diff, 1:110)69 1.901e+11 1.963e+11 0.969 0.334410
## L(Close.ts.diff, 1:110)70 -1.062e+10 1.965e+11 -0.054 0.956999
## L(Close.ts.diff, 1:110)71 7.715e+10 1.961e+11 0.394 0.694545
## L(Close.ts.diff, 1:110)72 -1.286e+11 1.960e+11 -0.656 0.512991
## L(Close.ts.diff, 1:110)73 -2.963e+10 1.956e+11 -0.151 0.879828
## L(Close.ts.diff, 1:110)74 1.183e+11 1.959e+11 0.604 0.546719
## L(Close.ts.diff, 1:110)75 1.475e+10 1.963e+11 0.075 0.940220
## L(Close.ts.diff, 1:110)76 8.400e+11 1.958e+11 4.291 3.32e-05 ***
## L(Close.ts.diff, 1:110)77 3.778e+10 2.075e+11 0.182 0.855775
## L(Close.ts.diff, 1:110)78 -8.592e+10 2.074e+11 -0.414 0.679314
## L(Close.ts.diff, 1:110)79 -9.532e+10 2.074e+11 -0.460 0.646531
## L(Close.ts.diff, 1:110)80 6.725e+10 2.065e+11 0.326 0.745186
## L(Close.ts.diff, 1:110)81 -2.137e+10 1.975e+11 -0.108 0.913998
## L(Close.ts.diff, 1:110)82 -7.124e+11 1.958e+11 -3.638 0.000386 ***
## L(Close.ts.diff, 1:110)83 -3.165e+08 2.042e+11 -0.002 0.998766
## L(Close.ts.diff, 1:110)84 -6.625e+09 2.037e+11 -0.033 0.974101
## L(Close.ts.diff, 1:110)85 -1.514e+11 2.030e+11 -0.746 0.456962
## L(Close.ts.diff, 1:110)86 6.248e+10 2.018e+11 0.310 0.757291
## L(Close.ts.diff, 1:110)87 1.008e+10 1.955e+11 0.052 0.958947
## L(Close.ts.diff, 1:110)88 1.621e+10 1.955e+11 0.083 0.934020
## L(Close.ts.diff, 1:110)89 1.850e+10 1.954e+11 0.095 0.924721
## L(Close.ts.diff, 1:110)90 -7.614e+10 1.949e+11 -0.391 0.696588
## L(Close.ts.diff, 1:110)91 7.648e+10 1.949e+11 0.393 0.695280
## L(Close.ts.diff, 1:110)92 8.090e+10 1.951e+11 0.415 0.679044
## L(Close.ts.diff, 1:110)93 3.490e+10 1.953e+11 0.179 0.858413
## L(Close.ts.diff, 1:110)94 8.301e+10 1.950e+11 0.426 0.670977
## L(Close.ts.diff, 1:110)95 1.086e+10 1.956e+11 0.056 0.955808
## L(Close.ts.diff, 1:110)96 -3.669e+10 1.954e+11 -0.188 0.851353
## L(Close.ts.diff, 1:110)97 1.097e+10 1.952e+11 0.056 0.955280
## L(Close.ts.diff, 1:110)98 3.885e+10 1.952e+11 0.199 0.842573
## L(Close.ts.diff, 1:110)99 1.531e+11 1.950e+11 0.785 0.433730
## L(Close.ts.diff, 1:110)100 2.930e+11 1.956e+11 1.498 0.136323
## L(Close.ts.diff, 1:110)101 -5.918e+10 1.972e+11 -0.300 0.764513
## L(Close.ts.diff, 1:110)102 -4.528e+09 1.971e+11 -0.023 0.981705
## L(Close.ts.diff, 1:110)103 1.211e+11 1.971e+11 0.615 0.539768
## L(Close.ts.diff, 1:110)104 3.255e+08 1.974e+11 0.002 0.998686
## L(Close.ts.diff, 1:110)105 -1.619e+11 1.942e+11 -0.833 0.406053
## L(Close.ts.diff, 1:110)106 -9.826e+10 1.953e+11 -0.503 0.615602
## L(Close.ts.diff, 1:110)107 -1.163e+11 1.953e+11 -0.595 0.552643
## L(Close.ts.diff, 1:110)108 -1.040e+11 1.952e+11 -0.533 0.595153
## L(Close.ts.diff, 1:110)109 2.938e+10 1.950e+11 0.151 0.880456
## L(Close.ts.diff, 1:110)110 8.288e+10 1.949e+11 0.425 0.671371
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.559e+14 on 139 degrees of freedom
## Multiple R-squared: 0.5018, Adjusted R-squared: 0.09325
## F-statistic: 1.228 on 114 and 139 DF, p-value: 0.1237ardl.turnover.open.3 <- dynlm(Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,61) + L(Turnover.ts, 75) + L(Turnover.ts,117) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.close.3)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 75) + L(Turnover.ts, 117) + L(Close.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.755e+14 -1.384e+14 -2.222e+13 1.007e+14 1.825e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.077e+13 5.152e+13 1.762 0.07939 .
## L(Turnover.ts, 2) 1.706e-01 5.747e-02 2.969 0.00329 **
## L(Turnover.ts, 61) 2.840e-01 5.778e-02 4.914 1.64e-06 ***
## L(Turnover.ts, 75) 4.264e-02 5.746e-02 0.742 0.45878
## L(Turnover.ts, 117) 2.884e-01 5.784e-02 4.987 1.17e-06 ***
## L(Close.ts.diff, 110) 1.181e+11 1.778e+11 0.665 0.50697
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.44e+14 on 242 degrees of freedom
## Multiple R-squared: 0.2045, Adjusted R-squared: 0.188
## F-statistic: 12.44 on 5 and 242 DF, p-value: 9.408e-11ardl.turnover.open.4 <- dynlm(Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,61) + L(Turnover.ts, 75) + L(Turnover.ts,117) + L(Open.ts.diff, 35) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.close.4)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 75) + L(Turnover.ts, 117) + L(Close.ts.diff,
## 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.384e+14 -1.097e+14 -2.262e+13 7.092e+13 1.108e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.106e+14 7.389e+13 1.498 0.13663
## L(Turnover.ts, 2) 1.818e-01 7.859e-02 2.313 0.02224 *
## L(Turnover.ts, 61) 2.717e-01 8.743e-02 3.108 0.00231 **
## L(Turnover.ts, 75) -9.467e-03 8.713e-02 -0.109 0.91364
## L(Turnover.ts, 117) 2.946e-01 9.255e-02 3.184 0.00181 **
## L(Close.ts.diff, 1:110)1 -2.861e+10 1.945e+11 -0.147 0.88326
## L(Close.ts.diff, 1:110)2 1.521e+11 1.957e+11 0.777 0.43848
## L(Close.ts.diff, 1:110)3 6.492e+08 1.942e+11 0.003 0.99734
## L(Close.ts.diff, 1:110)4 -9.810e+10 1.952e+11 -0.503 0.61612
## L(Close.ts.diff, 1:110)5 1.409e+11 1.944e+11 0.725 0.46979
## L(Close.ts.diff, 1:110)6 4.138e+11 2.227e+11 1.859 0.06530 .
## L(Close.ts.diff, 1:110)7 -4.007e+10 1.968e+11 -0.204 0.83900
## L(Close.ts.diff, 1:110)8 -8.854e+10 2.085e+11 -0.425 0.67183
## L(Close.ts.diff, 1:110)9 1.879e+11 1.961e+11 0.958 0.33956
## L(Close.ts.diff, 1:110)10 9.941e+09 1.952e+11 0.051 0.95947
## L(Close.ts.diff, 1:110)11 2.261e+10 1.950e+11 0.116 0.90786
## L(Close.ts.diff, 1:110)12 2.422e+11 2.183e+11 1.110 0.26922
## L(Close.ts.diff, 1:110)13 1.887e+11 1.954e+11 0.966 0.33585
## L(Close.ts.diff, 1:110)14 2.739e+11 1.954e+11 1.402 0.16338
## L(Close.ts.diff, 1:110)15 2.032e+11 1.960e+11 1.037 0.30179
## L(Close.ts.diff, 1:110)16 1.543e+11 1.973e+11 0.782 0.43563
## L(Close.ts.diff, 1:110)17 3.081e+11 1.950e+11 1.580 0.11658
## L(Close.ts.diff, 1:110)18 7.711e+10 1.956e+11 0.394 0.69413
## L(Close.ts.diff, 1:110)19 1.816e+11 1.962e+11 0.925 0.35659
## L(Close.ts.diff, 1:110)20 1.353e+11 2.040e+11 0.663 0.50838
## L(Close.ts.diff, 1:110)21 4.811e+10 1.965e+11 0.245 0.80699
## L(Close.ts.diff, 1:110)22 9.921e+10 1.968e+11 0.504 0.61506
## L(Close.ts.diff, 1:110)23 3.112e+10 1.960e+11 0.159 0.87411
## L(Close.ts.diff, 1:110)24 3.041e+11 1.961e+11 1.550 0.12346
## L(Close.ts.diff, 1:110)25 2.750e+11 1.962e+11 1.402 0.16337
## L(Close.ts.diff, 1:110)26 -5.933e+11 2.134e+11 -2.780 0.00622 **
## L(Close.ts.diff, 1:110)27 1.456e+10 1.993e+11 0.073 0.94188
## L(Close.ts.diff, 1:110)28 1.327e+11 2.072e+11 0.640 0.52307
## L(Close.ts.diff, 1:110)29 8.735e+10 1.972e+11 0.443 0.65850
## L(Close.ts.diff, 1:110)30 -1.742e+10 1.962e+11 -0.089 0.92939
## L(Close.ts.diff, 1:110)31 -1.962e+11 1.962e+11 -1.000 0.31914
## L(Close.ts.diff, 1:110)32 6.967e+10 1.964e+11 0.355 0.72332
## L(Close.ts.diff, 1:110)33 -4.210e+10 1.972e+11 -0.213 0.83127
## L(Close.ts.diff, 1:110)34 -1.024e+11 1.953e+11 -0.524 0.60083
## L(Close.ts.diff, 1:110)35 -6.332e+10 1.953e+11 -0.324 0.74631
## L(Close.ts.diff, 1:110)36 -1.464e+11 1.965e+11 -0.745 0.45778
## L(Close.ts.diff, 1:110)37 1.796e+10 1.964e+11 0.091 0.92725
## L(Close.ts.diff, 1:110)38 -1.741e+11 1.970e+11 -0.884 0.37847
## L(Close.ts.diff, 1:110)39 1.427e+11 1.949e+11 0.732 0.46517
## L(Close.ts.diff, 1:110)40 6.295e+10 2.128e+11 0.296 0.76781
## L(Close.ts.diff, 1:110)41 -1.481e+11 1.993e+11 -0.743 0.45874
## L(Close.ts.diff, 1:110)42 -2.085e+11 1.957e+11 -1.066 0.28852
## L(Close.ts.diff, 1:110)43 -1.441e+11 1.952e+11 -0.738 0.46159
## L(Close.ts.diff, 1:110)44 1.391e+11 1.963e+11 0.708 0.47994
## L(Close.ts.diff, 1:110)45 1.611e+11 1.955e+11 0.824 0.41134
## L(Close.ts.diff, 1:110)46 8.892e+10 1.949e+11 0.456 0.64891
## L(Close.ts.diff, 1:110)47 2.950e+10 1.952e+11 0.151 0.88009
## L(Close.ts.diff, 1:110)48 -1.250e+11 1.958e+11 -0.639 0.52419
## L(Close.ts.diff, 1:110)49 -1.461e+10 1.955e+11 -0.075 0.94053
## L(Close.ts.diff, 1:110)50 -6.991e+09 1.981e+11 -0.035 0.97190
## L(Close.ts.diff, 1:110)51 -4.997e+10 1.954e+11 -0.256 0.79858
## L(Close.ts.diff, 1:110)52 -2.406e+11 1.981e+11 -1.215 0.22666
## L(Close.ts.diff, 1:110)53 -2.213e+11 1.952e+11 -1.134 0.25902
## L(Close.ts.diff, 1:110)54 1.635e+10 1.955e+11 0.084 0.93348
## L(Close.ts.diff, 1:110)55 -8.485e+10 1.959e+11 -0.433 0.66563
## L(Close.ts.diff, 1:110)56 -4.230e+09 1.958e+11 -0.022 0.98280
## L(Close.ts.diff, 1:110)57 -8.049e+10 1.955e+11 -0.412 0.68129
## L(Close.ts.diff, 1:110)58 2.391e+11 1.957e+11 1.221 0.22409
## L(Close.ts.diff, 1:110)59 1.043e+11 1.955e+11 0.533 0.59476
## L(Close.ts.diff, 1:110)60 -8.921e+10 1.965e+11 -0.454 0.65052
## L(Close.ts.diff, 1:110)61 -2.069e+10 1.956e+11 -0.106 0.91592
## L(Close.ts.diff, 1:110)62 -3.194e+11 2.041e+11 -1.564 0.12009
## L(Close.ts.diff, 1:110)63 -1.170e+11 1.965e+11 -0.595 0.55264
## L(Close.ts.diff, 1:110)64 -1.089e+11 1.987e+11 -0.548 0.58461
## L(Close.ts.diff, 1:110)65 -4.240e+09 1.958e+11 -0.022 0.98275
## L(Close.ts.diff, 1:110)66 1.512e+11 1.958e+11 0.772 0.44137
## L(Close.ts.diff, 1:110)67 -1.484e+11 2.111e+11 -0.703 0.48342
## L(Close.ts.diff, 1:110)68 -2.021e+11 1.954e+11 -1.034 0.30278
## L(Close.ts.diff, 1:110)69 1.209e+11 1.947e+11 0.621 0.53587
## L(Close.ts.diff, 1:110)70 5.483e+10 1.956e+11 0.280 0.77968
## L(Close.ts.diff, 1:110)71 1.230e+11 1.957e+11 0.628 0.53097
## L(Close.ts.diff, 1:110)72 -7.109e+10 1.952e+11 -0.364 0.71630
## L(Close.ts.diff, 1:110)73 -3.854e+10 1.954e+11 -0.197 0.84398
## L(Close.ts.diff, 1:110)74 4.417e+10 1.956e+11 0.226 0.82173
## L(Close.ts.diff, 1:110)75 3.656e+09 1.960e+11 0.019 0.98514
## L(Close.ts.diff, 1:110)76 8.334e+11 1.959e+11 4.255 3.91e-05 ***
## L(Close.ts.diff, 1:110)77 2.712e+11 1.961e+11 1.383 0.16903
## L(Close.ts.diff, 1:110)78 -9.198e+10 2.092e+11 -0.440 0.66086
## L(Close.ts.diff, 1:110)79 -1.253e+11 1.986e+11 -0.631 0.52937
## L(Close.ts.diff, 1:110)80 1.007e+11 1.974e+11 0.510 0.61096
## L(Close.ts.diff, 1:110)81 5.203e+10 2.114e+11 0.246 0.80592
## L(Close.ts.diff, 1:110)82 -4.597e+11 2.156e+11 -2.132 0.03483 *
## L(Close.ts.diff, 1:110)83 -1.148e+11 2.000e+11 -0.574 0.56695
## L(Close.ts.diff, 1:110)84 7.064e+10 2.025e+11 0.349 0.72777
## L(Close.ts.diff, 1:110)85 -1.529e+11 1.958e+11 -0.781 0.43610
## L(Close.ts.diff, 1:110)86 -8.517e+09 1.957e+11 -0.044 0.96536
## L(Close.ts.diff, 1:110)87 2.762e+11 2.098e+11 1.317 0.19018
## L(Close.ts.diff, 1:110)88 4.054e+10 1.951e+11 0.208 0.83573
## L(Close.ts.diff, 1:110)89 4.640e+10 1.957e+11 0.237 0.81292
## L(Close.ts.diff, 1:110)90 -1.128e+11 1.952e+11 -0.578 0.56446
## L(Close.ts.diff, 1:110)91 8.581e+10 1.951e+11 0.440 0.66083
## L(Close.ts.diff, 1:110)92 9.266e+10 1.968e+11 0.471 0.63857
## L(Close.ts.diff, 1:110)93 3.228e+10 1.954e+11 0.165 0.86907
## L(Close.ts.diff, 1:110)94 -9.814e+09 1.978e+11 -0.050 0.96050
## L(Close.ts.diff, 1:110)95 7.836e+10 1.954e+11 0.401 0.68901
## L(Close.ts.diff, 1:110)96 3.101e+09 1.956e+11 0.016 0.98738
## L(Close.ts.diff, 1:110)97 3.338e+10 1.948e+11 0.171 0.86422
## L(Close.ts.diff, 1:110)98 7.496e+10 1.949e+11 0.385 0.70115
## L(Close.ts.diff, 1:110)99 2.078e+11 1.950e+11 1.066 0.28857
## L(Close.ts.diff, 1:110)100 3.745e+11 1.956e+11 1.915 0.05766 .
## L(Close.ts.diff, 1:110)101 3.678e+10 2.096e+11 0.175 0.86098
## L(Close.ts.diff, 1:110)102 3.637e+09 1.970e+11 0.018 0.98530
## L(Close.ts.diff, 1:110)103 1.728e+11 1.958e+11 0.882 0.37917
## L(Close.ts.diff, 1:110)104 1.298e+11 1.954e+11 0.664 0.50775
## L(Close.ts.diff, 1:110)105 -1.281e+11 1.946e+11 -0.658 0.51165
## L(Close.ts.diff, 1:110)106 -8.310e+10 1.972e+11 -0.421 0.67415
## L(Close.ts.diff, 1:110)107 -1.727e+11 1.947e+11 -0.887 0.37657
## L(Close.ts.diff, 1:110)108 -1.724e+11 1.944e+11 -0.887 0.37680
## L(Close.ts.diff, 1:110)109 -1.502e+09 1.947e+11 -0.008 0.99386
## L(Close.ts.diff, 1:110)110 1.082e+11 1.946e+11 0.556 0.57925
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.551e+14 on 133 degrees of freedom
## Multiple R-squared: 0.5223, Adjusted R-squared: 0.1128
## F-statistic: 1.276 on 114 and 133 DF, p-value: 0.08804ARDL of Volume and Close
ardl.volume.close.1 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff, 110), data = infy_stock)
summary(ardl.volume.close.1)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2655876 -835982 -253740 406222 16602471
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.428e+05 4.000e+05 1.357 0.1762
## L(Volume.ts, 1:32)1 3.211e-01 6.739e-02 4.766 3.42e-06 ***
## L(Volume.ts, 1:32)2 5.738e-02 7.077e-02 0.811 0.4184
## L(Volume.ts, 1:32)3 -4.028e-02 7.105e-02 -0.567 0.5714
## L(Volume.ts, 1:32)4 9.029e-02 7.045e-02 1.282 0.2013
## L(Volume.ts, 1:32)5 2.284e-03 7.043e-02 0.032 0.9742
## L(Volume.ts, 1:32)6 5.138e-02 7.046e-02 0.729 0.4666
## L(Volume.ts, 1:32)7 1.222e-01 7.049e-02 1.733 0.0845 .
## L(Volume.ts, 1:32)8 -2.718e-03 7.091e-02 -0.038 0.9695
## L(Volume.ts, 1:32)9 -6.121e-03 7.072e-02 -0.087 0.9311
## L(Volume.ts, 1:32)10 5.304e-02 7.130e-02 0.744 0.4577
## L(Volume.ts, 1:32)11 -7.402e-02 7.035e-02 -1.052 0.2938
## L(Volume.ts, 1:32)12 1.587e-02 7.050e-02 0.225 0.8221
## L(Volume.ts, 1:32)13 -3.196e-02 7.051e-02 -0.453 0.6508
## L(Volume.ts, 1:32)14 -3.331e-02 7.062e-02 -0.472 0.6376
## L(Volume.ts, 1:32)15 7.403e-02 7.049e-02 1.050 0.2948
## L(Volume.ts, 1:32)16 -3.776e-02 7.078e-02 -0.534 0.5942
## L(Volume.ts, 1:32)17 -1.413e-02 7.114e-02 -0.199 0.8428
## L(Volume.ts, 1:32)18 4.508e-02 7.084e-02 0.636 0.5252
## L(Volume.ts, 1:32)19 -1.906e-02 7.087e-02 -0.269 0.7882
## L(Volume.ts, 1:32)20 1.334e-02 7.086e-02 0.188 0.8508
## L(Volume.ts, 1:32)21 -2.452e-02 7.099e-02 -0.345 0.7301
## L(Volume.ts, 1:32)22 1.536e-02 7.073e-02 0.217 0.8283
## L(Volume.ts, 1:32)23 -6.945e-03 7.063e-02 -0.098 0.9218
## L(Volume.ts, 1:32)24 8.218e-02 7.068e-02 1.163 0.2462
## L(Volume.ts, 1:32)25 3.781e-02 7.105e-02 0.532 0.5952
## L(Volume.ts, 1:32)26 3.019e-02 7.045e-02 0.428 0.6687
## L(Volume.ts, 1:32)27 1.034e-02 7.041e-02 0.147 0.8834
## L(Volume.ts, 1:32)28 -8.898e-02 7.311e-02 -1.217 0.2249
## L(Volume.ts, 1:32)29 1.327e-01 7.052e-02 1.882 0.0611 .
## L(Volume.ts, 1:32)30 -2.937e-02 7.094e-02 -0.414 0.6793
## L(Volume.ts, 1:32)31 3.599e-02 7.102e-02 0.507 0.6128
## L(Volume.ts, 1:32)32 3.964e-02 6.747e-02 0.588 0.5575
## L(Close.ts.diff, 110) -1.808e+02 1.437e+03 -0.126 0.9000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1854000 on 220 degrees of freedom
## Multiple R-squared: 0.268, Adjusted R-squared: 0.1582
## F-statistic: 2.441 on 33 and 220 DF, p-value: 6.89e-05ardl.volume.close.2 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff, 1:110), data = infy_stock)
summary(ardl.volume.close.2)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff,
## 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2616765 -664712 -77535 379842 6043927
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.834e+06 7.916e+05 2.317 0.02233 *
## L(Volume.ts, 1:32)1 2.839e-01 9.492e-02 2.991 0.00342 **
## L(Volume.ts, 1:32)2 5.724e-02 9.894e-02 0.579 0.56407
## L(Volume.ts, 1:32)3 -1.020e-01 9.886e-02 -1.032 0.30455
## L(Volume.ts, 1:32)4 9.376e-02 9.862e-02 0.951 0.34381
## L(Volume.ts, 1:32)5 -3.309e-02 9.817e-02 -0.337 0.73669
## L(Volume.ts, 1:32)6 2.138e-01 9.814e-02 2.179 0.03145 *
## L(Volume.ts, 1:32)7 1.283e-01 1.001e-01 1.282 0.20258
## L(Volume.ts, 1:32)8 -5.782e-02 1.004e-01 -0.576 0.56602
## L(Volume.ts, 1:32)9 3.384e-02 9.988e-02 0.339 0.73539
## L(Volume.ts, 1:32)10 3.517e-03 1.010e-01 0.035 0.97228
## L(Volume.ts, 1:32)11 -1.465e-01 9.978e-02 -1.468 0.14488
## L(Volume.ts, 1:32)12 1.599e-03 1.016e-01 0.016 0.98747
## L(Volume.ts, 1:32)13 -1.056e-01 9.988e-02 -1.057 0.29272
## L(Volume.ts, 1:32)14 -1.012e-01 1.004e-01 -1.008 0.31589
## L(Volume.ts, 1:32)15 2.966e-02 1.005e-01 0.295 0.76849
## L(Volume.ts, 1:32)16 -5.455e-02 1.004e-01 -0.543 0.58804
## L(Volume.ts, 1:32)17 6.465e-02 1.006e-01 0.643 0.52163
## L(Volume.ts, 1:32)18 3.846e-02 1.002e-01 0.384 0.70175
## L(Volume.ts, 1:32)19 -3.670e-02 9.987e-02 -0.367 0.71397
## L(Volume.ts, 1:32)20 1.803e-01 9.958e-02 1.811 0.07291 .
## L(Volume.ts, 1:32)21 -6.883e-02 1.007e-01 -0.683 0.49579
## L(Volume.ts, 1:32)22 -5.455e-02 9.966e-02 -0.547 0.58520
## L(Volume.ts, 1:32)23 -8.851e-02 1.000e-01 -0.885 0.37819
## L(Volume.ts, 1:32)24 5.916e-02 1.016e-01 0.582 0.56153
## L(Volume.ts, 1:32)25 4.650e-02 1.016e-01 0.458 0.64813
## L(Volume.ts, 1:32)26 -1.093e-01 1.011e-01 -1.082 0.28163
## L(Volume.ts, 1:32)27 7.259e-03 9.953e-02 0.073 0.94199
## L(Volume.ts, 1:32)28 -8.456e-02 9.970e-02 -0.848 0.39817
## L(Volume.ts, 1:32)29 1.139e-01 9.412e-02 1.211 0.22858
## L(Volume.ts, 1:32)30 -9.664e-03 9.409e-02 -0.103 0.91838
## L(Volume.ts, 1:32)31 -2.868e-02 9.391e-02 -0.305 0.76063
## L(Volume.ts, 1:32)32 1.110e-01 8.762e-02 1.267 0.20769
## L(Close.ts.diff, 1:110)1 -1.462e+02 1.210e+03 -0.121 0.90406
## L(Close.ts.diff, 1:110)2 5.881e+02 1.210e+03 0.486 0.62798
## L(Close.ts.diff, 1:110)3 2.747e+02 1.211e+03 0.227 0.82104
## L(Close.ts.diff, 1:110)4 -1.140e+03 1.212e+03 -0.940 0.34902
## L(Close.ts.diff, 1:110)5 3.560e+02 1.218e+03 0.292 0.77065
## L(Close.ts.diff, 1:110)6 3.366e+03 1.455e+03 2.313 0.02256 *
## L(Close.ts.diff, 1:110)7 -1.147e+03 1.494e+03 -0.768 0.44419
## L(Close.ts.diff, 1:110)8 -1.230e+03 1.494e+03 -0.823 0.41213
## L(Close.ts.diff, 1:110)9 -3.403e+02 1.496e+03 -0.227 0.82051
## L(Close.ts.diff, 1:110)10 -5.076e+02 1.475e+03 -0.344 0.73145
## L(Close.ts.diff, 1:110)11 -8.795e+02 1.475e+03 -0.596 0.55210
## L(Close.ts.diff, 1:110)12 -1.557e+03 1.476e+03 -1.055 0.29377
## L(Close.ts.diff, 1:110)13 8.243e+02 1.476e+03 0.558 0.57775
## L(Close.ts.diff, 1:110)14 1.228e+03 1.481e+03 0.829 0.40889
## L(Close.ts.diff, 1:110)15 -4.525e+01 1.485e+03 -0.030 0.97574
## L(Close.ts.diff, 1:110)16 3.690e+02 1.484e+03 0.249 0.80415
## L(Close.ts.diff, 1:110)17 1.378e+03 1.482e+03 0.930 0.35456
## L(Close.ts.diff, 1:110)18 -3.476e+02 1.487e+03 -0.234 0.81563
## L(Close.ts.diff, 1:110)19 -6.267e+00 1.483e+03 -0.004 0.99664
## L(Close.ts.diff, 1:110)20 -9.261e+01 1.473e+03 -0.063 0.94999
## L(Close.ts.diff, 1:110)21 -7.406e+02 1.473e+03 -0.503 0.61609
## L(Close.ts.diff, 1:110)22 -4.984e+01 1.469e+03 -0.034 0.97299
## L(Close.ts.diff, 1:110)23 -1.833e+03 1.469e+03 -1.248 0.21474
## L(Close.ts.diff, 1:110)24 3.469e+02 1.469e+03 0.236 0.81381
## L(Close.ts.diff, 1:110)25 9.659e+02 1.469e+03 0.658 0.51212
## L(Close.ts.diff, 1:110)26 -9.938e+03 1.471e+03 -6.755 6.86e-10 ***
## L(Close.ts.diff, 1:110)27 1.209e+03 1.761e+03 0.686 0.49399
## L(Close.ts.diff, 1:110)28 3.478e+02 1.763e+03 0.197 0.84400
## L(Close.ts.diff, 1:110)29 3.762e+02 1.762e+03 0.214 0.83129
## L(Close.ts.diff, 1:110)30 -4.712e+02 1.760e+03 -0.268 0.78943
## L(Close.ts.diff, 1:110)31 -2.620e+03 1.760e+03 -1.489 0.13930
## L(Close.ts.diff, 1:110)32 2.837e+03 1.773e+03 1.600 0.11239
## L(Close.ts.diff, 1:110)33 2.161e+02 1.777e+03 0.122 0.90343
## L(Close.ts.diff, 1:110)34 -1.469e+03 1.776e+03 -0.827 0.41016
## L(Close.ts.diff, 1:110)35 -9.850e+02 1.763e+03 -0.559 0.57755
## L(Close.ts.diff, 1:110)36 -7.892e+02 1.769e+03 -0.446 0.65635
## L(Close.ts.diff, 1:110)37 -2.313e+02 1.772e+03 -0.131 0.89638
## L(Close.ts.diff, 1:110)38 -1.650e+03 1.758e+03 -0.939 0.34981
## L(Close.ts.diff, 1:110)39 -4.083e+02 1.670e+03 -0.244 0.80733
## L(Close.ts.diff, 1:110)40 -5.623e+01 1.672e+03 -0.034 0.97324
## L(Close.ts.diff, 1:110)41 -1.010e+03 1.667e+03 -0.606 0.54576
## L(Close.ts.diff, 1:110)42 -1.927e+03 1.670e+03 -1.154 0.25117
## L(Close.ts.diff, 1:110)43 -5.776e+02 1.679e+03 -0.344 0.73151
## L(Close.ts.diff, 1:110)44 9.991e+02 1.674e+03 0.597 0.55177
## L(Close.ts.diff, 1:110)45 4.668e+01 1.663e+03 0.028 0.97766
## L(Close.ts.diff, 1:110)46 1.295e+03 1.662e+03 0.779 0.43751
## L(Close.ts.diff, 1:110)47 -7.589e+02 1.653e+03 -0.459 0.64698
## L(Close.ts.diff, 1:110)48 -6.981e+02 1.652e+03 -0.423 0.67334
## L(Close.ts.diff, 1:110)49 -1.960e+03 1.653e+03 -1.185 0.23838
## L(Close.ts.diff, 1:110)50 -1.290e+03 1.669e+03 -0.773 0.44126
## L(Close.ts.diff, 1:110)51 -8.033e+02 1.673e+03 -0.480 0.63217
## L(Close.ts.diff, 1:110)52 -3.024e+03 1.671e+03 -1.809 0.07310 .
## L(Close.ts.diff, 1:110)53 -2.420e+03 1.689e+03 -1.433 0.15462
## L(Close.ts.diff, 1:110)54 -1.194e+03 1.703e+03 -0.701 0.48488
## L(Close.ts.diff, 1:110)55 5.645e+01 1.665e+03 0.034 0.97301
## L(Close.ts.diff, 1:110)56 -5.048e+01 1.661e+03 -0.030 0.97581
## L(Close.ts.diff, 1:110)57 -1.431e+03 1.656e+03 -0.864 0.38966
## L(Close.ts.diff, 1:110)58 2.823e+03 1.618e+03 1.745 0.08373 .
## L(Close.ts.diff, 1:110)59 6.819e+02 1.479e+03 0.461 0.64563
## L(Close.ts.diff, 1:110)60 -1.525e+02 1.474e+03 -0.103 0.91780
## L(Close.ts.diff, 1:110)61 -6.843e+02 1.471e+03 -0.465 0.64276
## L(Close.ts.diff, 1:110)62 -1.538e+03 1.470e+03 -1.046 0.29762
## L(Close.ts.diff, 1:110)63 -2.373e+02 1.477e+03 -0.161 0.87264
## L(Close.ts.diff, 1:110)64 -3.029e+03 1.474e+03 -2.055 0.04226 *
## L(Close.ts.diff, 1:110)65 -1.621e+03 1.494e+03 -1.085 0.28013
## L(Close.ts.diff, 1:110)66 1.213e+02 1.500e+03 0.081 0.93567
## L(Close.ts.diff, 1:110)67 -1.577e+02 1.492e+03 -0.106 0.91598
## L(Close.ts.diff, 1:110)68 -1.641e+03 1.487e+03 -1.103 0.27242
## L(Close.ts.diff, 1:110)69 8.109e+02 1.491e+03 0.544 0.58754
## L(Close.ts.diff, 1:110)70 -3.972e+02 1.485e+03 -0.268 0.78957
## L(Close.ts.diff, 1:110)71 8.528e+02 1.480e+03 0.576 0.56560
## L(Close.ts.diff, 1:110)72 -1.410e+03 1.482e+03 -0.951 0.34343
## L(Close.ts.diff, 1:110)73 -1.310e+03 1.486e+03 -0.882 0.37976
## L(Close.ts.diff, 1:110)74 6.551e+02 1.500e+03 0.437 0.66315
## L(Close.ts.diff, 1:110)75 -1.075e+03 1.493e+03 -0.720 0.47320
## L(Close.ts.diff, 1:110)76 2.771e+03 1.489e+03 1.861 0.06535 .
## L(Close.ts.diff, 1:110)77 2.118e+02 1.504e+03 0.141 0.88823
## L(Close.ts.diff, 1:110)78 -1.321e+03 1.502e+03 -0.879 0.38108
## L(Close.ts.diff, 1:110)79 -8.237e+02 1.504e+03 -0.548 0.58491
## L(Close.ts.diff, 1:110)80 -1.501e+02 1.503e+03 -0.100 0.92063
## L(Close.ts.diff, 1:110)81 -9.441e+02 1.503e+03 -0.628 0.53116
## L(Close.ts.diff, 1:110)82 -6.434e+03 1.506e+03 -4.274 4.08e-05 ***
## L(Close.ts.diff, 1:110)83 -2.066e+03 1.627e+03 -1.270 0.20674
## L(Close.ts.diff, 1:110)84 -7.141e+02 1.637e+03 -0.436 0.66362
## L(Close.ts.diff, 1:110)85 -1.535e+03 1.619e+03 -0.948 0.34509
## L(Close.ts.diff, 1:110)86 -1.035e+02 1.618e+03 -0.064 0.94913
## L(Close.ts.diff, 1:110)87 -3.230e+02 1.616e+03 -0.200 0.84196
## L(Close.ts.diff, 1:110)88 1.091e+03 1.609e+03 0.678 0.49919
## L(Close.ts.diff, 1:110)89 1.524e+03 1.610e+03 0.947 0.34588
## L(Close.ts.diff, 1:110)90 -3.577e+02 1.607e+03 -0.223 0.82425
## L(Close.ts.diff, 1:110)91 6.251e+02 1.597e+03 0.391 0.69627
## L(Close.ts.diff, 1:110)92 6.443e+02 1.612e+03 0.400 0.69008
## L(Close.ts.diff, 1:110)93 -1.056e+03 1.616e+03 -0.654 0.51466
## L(Close.ts.diff, 1:110)94 -6.949e+02 1.616e+03 -0.430 0.66810
## L(Close.ts.diff, 1:110)95 -1.323e+03 1.623e+03 -0.815 0.41685
## L(Close.ts.diff, 1:110)96 -2.106e+03 1.626e+03 -1.295 0.19786
## L(Close.ts.diff, 1:110)97 2.237e+02 1.635e+03 0.137 0.89143
## L(Close.ts.diff, 1:110)98 -9.916e+02 1.635e+03 -0.606 0.54552
## L(Close.ts.diff, 1:110)99 1.304e+03 1.624e+03 0.803 0.42397
## L(Close.ts.diff, 1:110)100 1.578e+03 1.625e+03 0.971 0.33380
## L(Close.ts.diff, 1:110)101 -1.005e+03 1.612e+03 -0.623 0.53440
## L(Close.ts.diff, 1:110)102 1.229e+03 1.615e+03 0.761 0.44824
## L(Close.ts.diff, 1:110)103 6.648e+02 1.610e+03 0.413 0.68049
## L(Close.ts.diff, 1:110)104 -1.361e+02 1.611e+03 -0.085 0.93280
## L(Close.ts.diff, 1:110)105 -2.105e+03 1.581e+03 -1.331 0.18591
## L(Close.ts.diff, 1:110)106 -1.955e+03 1.592e+03 -1.228 0.22202
## L(Close.ts.diff, 1:110)107 -1.605e+03 1.603e+03 -1.002 0.31866
## L(Close.ts.diff, 1:110)108 -2.038e+03 1.596e+03 -1.277 0.20423
## L(Close.ts.diff, 1:110)109 -8.089e+02 1.566e+03 -0.517 0.60642
## L(Close.ts.diff, 1:110)110 -6.369e+02 1.557e+03 -0.409 0.68322
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1807000 on 111 degrees of freedom
## Multiple R-squared: 0.6492, Adjusted R-squared: 0.2005
## F-statistic: 1.447 on 142 and 111 DF, p-value: 0.02121ardl.volume.close.3 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts, 91:122) + L(Close.ts.diff, 110), data = infy_stock)
summary(ardl.volume.close.3)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122) + L(Close.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3162262 -836678 -195987 521126 15845331
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.078e+06 9.549e+05 2.176 0.03086 *
## L(Volume.ts, 1:32)1 3.079e-01 7.492e-02 4.110 6.04e-05 ***
## L(Volume.ts, 1:32)2 8.519e-02 7.857e-02 1.084 0.27971
## L(Volume.ts, 1:32)3 -7.064e-02 7.980e-02 -0.885 0.37723
## L(Volume.ts, 1:32)4 4.374e-02 7.981e-02 0.548 0.58433
## L(Volume.ts, 1:32)5 2.636e-02 7.908e-02 0.333 0.73931
## L(Volume.ts, 1:32)6 4.160e-02 7.708e-02 0.540 0.59007
## L(Volume.ts, 1:32)7 9.882e-02 7.685e-02 1.286 0.20016
## L(Volume.ts, 1:32)8 -1.168e-02 7.688e-02 -0.152 0.87942
## L(Volume.ts, 1:32)9 6.567e-03 7.643e-02 0.086 0.93162
## L(Volume.ts, 1:32)10 6.030e-02 7.706e-02 0.782 0.43503
## L(Volume.ts, 1:32)11 -1.064e-01 7.676e-02 -1.387 0.16733
## L(Volume.ts, 1:32)12 3.283e-02 7.709e-02 0.426 0.67069
## L(Volume.ts, 1:32)13 -7.042e-02 7.724e-02 -0.912 0.36312
## L(Volume.ts, 1:32)14 -3.211e-02 7.745e-02 -0.415 0.67899
## L(Volume.ts, 1:32)15 5.738e-02 7.723e-02 0.743 0.45852
## L(Volume.ts, 1:32)16 -3.638e-02 7.757e-02 -0.469 0.63969
## L(Volume.ts, 1:32)17 -3.244e-02 7.787e-02 -0.417 0.67745
## L(Volume.ts, 1:32)18 1.844e-02 7.744e-02 0.238 0.81204
## L(Volume.ts, 1:32)19 6.324e-03 7.746e-02 0.082 0.93503
## L(Volume.ts, 1:32)20 1.090e-02 7.735e-02 0.141 0.88807
## L(Volume.ts, 1:32)21 -2.162e-02 7.788e-02 -0.278 0.78160
## L(Volume.ts, 1:32)22 1.143e-02 7.797e-02 0.147 0.88365
## L(Volume.ts, 1:32)23 3.903e-03 7.776e-02 0.050 0.96002
## L(Volume.ts, 1:32)24 5.468e-02 7.744e-02 0.706 0.48105
## L(Volume.ts, 1:32)25 3.664e-02 7.755e-02 0.472 0.63721
## L(Volume.ts, 1:32)26 3.145e-02 7.672e-02 0.410 0.68233
## L(Volume.ts, 1:32)27 3.461e-02 7.671e-02 0.451 0.65242
## L(Volume.ts, 1:32)28 -8.312e-02 7.972e-02 -1.043 0.29850
## L(Volume.ts, 1:32)29 6.754e-02 7.660e-02 0.882 0.37910
## L(Volume.ts, 1:32)30 3.911e-02 8.053e-02 0.486 0.62783
## L(Volume.ts, 1:32)31 -6.293e-03 8.094e-02 -0.078 0.93812
## L(Volume.ts, 1:32)32 5.716e-02 7.646e-02 0.748 0.45571
## L(Volume.ts, 91:122)91 -6.240e-02 7.642e-02 -0.817 0.41527
## L(Volume.ts, 91:122)92 4.233e-02 8.076e-02 0.524 0.60089
## L(Volume.ts, 91:122)93 -2.370e-02 8.073e-02 -0.294 0.76940
## L(Volume.ts, 91:122)94 8.186e-03 7.669e-02 0.107 0.91512
## L(Volume.ts, 91:122)95 -5.600e-02 7.660e-02 -0.731 0.46568
## L(Volume.ts, 91:122)96 -1.704e-02 7.682e-02 -0.222 0.82472
## L(Volume.ts, 91:122)97 -4.758e-02 7.688e-02 -0.619 0.53682
## L(Volume.ts, 91:122)98 -8.314e-02 7.748e-02 -1.073 0.28473
## L(Volume.ts, 91:122)99 9.454e-02 7.752e-02 1.220 0.22427
## L(Volume.ts, 91:122)100 -6.465e-02 7.813e-02 -0.827 0.40911
## L(Volume.ts, 91:122)101 3.458e-02 7.846e-02 0.441 0.65994
## L(Volume.ts, 91:122)102 1.127e-03 7.769e-02 0.015 0.98845
## L(Volume.ts, 91:122)103 -1.182e-02 7.723e-02 -0.153 0.87857
## L(Volume.ts, 91:122)104 1.468e-02 7.909e-02 0.186 0.85299
## L(Volume.ts, 91:122)105 2.418e-02 7.766e-02 0.311 0.75592
## L(Volume.ts, 91:122)106 -5.411e-02 7.774e-02 -0.696 0.48731
## L(Volume.ts, 91:122)107 4.041e-02 7.773e-02 0.520 0.60375
## L(Volume.ts, 91:122)108 -4.923e-02 7.752e-02 -0.635 0.52616
## L(Volume.ts, 91:122)109 -5.262e-02 7.745e-02 -0.679 0.49774
## L(Volume.ts, 91:122)110 3.794e-02 7.718e-02 0.492 0.62360
## L(Volume.ts, 91:122)111 -1.403e-01 8.131e-02 -1.726 0.08617 .
## L(Volume.ts, 91:122)112 1.460e-02 8.154e-02 0.179 0.85807
## L(Volume.ts, 91:122)113 9.254e-02 8.117e-02 1.140 0.25585
## L(Volume.ts, 91:122)114 -9.978e-02 8.134e-02 -1.227 0.22156
## L(Volume.ts, 91:122)115 -8.866e-02 8.179e-02 -1.084 0.27983
## L(Volume.ts, 91:122)116 6.144e-02 7.700e-02 0.798 0.42600
## L(Volume.ts, 91:122)117 2.540e-01 7.742e-02 3.281 0.00124 **
## L(Volume.ts, 91:122)118 -1.302e-01 7.951e-02 -1.637 0.10333
## L(Volume.ts, 91:122)119 -6.888e-02 8.027e-02 -0.858 0.39197
## L(Volume.ts, 91:122)120 5.118e-02 7.974e-02 0.642 0.52186
## L(Volume.ts, 91:122)121 -2.605e-02 7.892e-02 -0.330 0.74174
## L(Volume.ts, 91:122)122 -5.801e-02 7.499e-02 -0.773 0.44028
## L(Close.ts.diff, 110) -2.788e+02 1.530e+03 -0.182 0.85563
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1890000 on 177 degrees of freedom
## Multiple R-squared: 0.3864, Adjusted R-squared: 0.161
## F-statistic: 1.715 on 65 and 177 DF, p-value: 0.002947ardl.volume.close.4 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts, 91:122) + L(Close.ts.diff, 1:110), data = infy_stock)
summary(ardl.volume.close.4)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122) + L(Close.ts.diff, 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2450151 -629268 -161738 590886 5117462
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.953e+06 2.672e+06 1.854 0.068104 .
## L(Volume.ts, 1:32)1 3.387e-01 1.199e-01 2.825 0.006201 **
## L(Volume.ts, 1:32)2 1.105e-02 1.276e-01 0.087 0.931237
## L(Volume.ts, 1:32)3 -1.208e-01 1.309e-01 -0.923 0.359391
## L(Volume.ts, 1:32)4 1.092e-01 1.317e-01 0.829 0.410051
## L(Volume.ts, 1:32)5 -9.374e-02 1.292e-01 -0.726 0.470510
## L(Volume.ts, 1:32)6 2.617e-01 1.293e-01 2.024 0.046865 *
## L(Volume.ts, 1:32)7 5.899e-02 1.320e-01 0.447 0.656323
## L(Volume.ts, 1:32)8 5.241e-02 1.313e-01 0.399 0.691137
## L(Volume.ts, 1:32)9 6.382e-02 1.331e-01 0.479 0.633124
## L(Volume.ts, 1:32)10 -1.797e-03 1.353e-01 -0.013 0.989437
## L(Volume.ts, 1:32)11 -1.139e-01 1.336e-01 -0.853 0.396828
## L(Volume.ts, 1:32)12 -1.645e-02 1.347e-01 -0.122 0.903173
## L(Volume.ts, 1:32)13 -2.077e-02 1.302e-01 -0.160 0.873723
## L(Volume.ts, 1:32)14 -1.528e-01 1.303e-01 -1.173 0.244944
## L(Volume.ts, 1:32)15 8.337e-02 1.312e-01 0.636 0.527121
## L(Volume.ts, 1:32)16 -5.681e-02 1.311e-01 -0.433 0.666158
## L(Volume.ts, 1:32)17 -7.015e-02 1.317e-01 -0.533 0.595884
## L(Volume.ts, 1:32)18 5.269e-02 1.338e-01 0.394 0.694927
## L(Volume.ts, 1:32)19 -1.250e-01 1.323e-01 -0.945 0.348148
## L(Volume.ts, 1:32)20 2.338e-01 1.326e-01 1.764 0.082234 .
## L(Volume.ts, 1:32)21 -1.616e-01 1.365e-01 -1.184 0.240703
## L(Volume.ts, 1:32)22 -4.644e-02 1.363e-01 -0.341 0.734426
## L(Volume.ts, 1:32)23 -4.703e-02 1.345e-01 -0.350 0.727629
## L(Volume.ts, 1:32)24 -2.692e-02 1.318e-01 -0.204 0.838810
## L(Volume.ts, 1:32)25 7.401e-02 1.302e-01 0.569 0.571556
## L(Volume.ts, 1:32)26 -1.817e-01 1.294e-01 -1.404 0.164810
## L(Volume.ts, 1:32)27 1.197e-01 1.270e-01 0.943 0.349006
## L(Volume.ts, 1:32)28 -8.826e-02 1.288e-01 -0.685 0.495577
## L(Volume.ts, 1:32)29 -6.342e-02 1.180e-01 -0.538 0.592649
## L(Volume.ts, 1:32)30 6.081e-02 1.175e-01 0.518 0.606378
## L(Volume.ts, 1:32)31 -9.698e-02 1.190e-01 -0.815 0.417840
## L(Volume.ts, 1:32)32 1.413e-01 1.112e-01 1.271 0.208174
## L(Volume.ts, 91:122)91 5.711e-02 1.049e-01 0.545 0.587761
## L(Volume.ts, 91:122)92 -6.727e-02 1.103e-01 -0.610 0.543802
## L(Volume.ts, 91:122)93 6.234e-02 1.102e-01 0.566 0.573427
## L(Volume.ts, 91:122)94 -1.881e-01 1.103e-01 -1.705 0.092753 .
## L(Volume.ts, 91:122)95 1.742e-02 1.088e-01 0.160 0.873229
## L(Volume.ts, 91:122)96 -1.150e-01 1.097e-01 -1.048 0.298124
## L(Volume.ts, 91:122)97 -4.370e-02 1.105e-01 -0.395 0.693732
## L(Volume.ts, 91:122)98 -6.807e-02 1.100e-01 -0.619 0.538174
## L(Volume.ts, 91:122)99 4.654e-02 1.088e-01 0.428 0.670319
## L(Volume.ts, 91:122)100 -6.340e-02 1.094e-01 -0.580 0.564097
## L(Volume.ts, 91:122)101 -3.195e-02 1.095e-01 -0.292 0.771352
## L(Volume.ts, 91:122)102 8.306e-02 1.092e-01 0.760 0.449614
## L(Volume.ts, 91:122)103 -1.334e-01 1.087e-01 -1.228 0.223774
## L(Volume.ts, 91:122)104 5.985e-02 1.104e-01 0.542 0.589454
## L(Volume.ts, 91:122)105 9.617e-02 1.087e-01 0.885 0.379280
## L(Volume.ts, 91:122)106 -1.286e-01 1.120e-01 -1.149 0.254777
## L(Volume.ts, 91:122)107 1.112e-01 1.142e-01 0.974 0.333699
## L(Volume.ts, 91:122)108 -1.472e-01 1.151e-01 -1.279 0.205108
## L(Volume.ts, 91:122)109 -2.626e-02 1.171e-01 -0.224 0.823274
## L(Volume.ts, 91:122)110 1.753e-01 1.136e-01 1.544 0.127310
## L(Volume.ts, 91:122)111 -1.110e-01 1.191e-01 -0.932 0.354566
## L(Volume.ts, 91:122)112 1.189e-01 1.472e-01 0.808 0.422185
## L(Volume.ts, 91:122)113 -6.881e-02 1.438e-01 -0.478 0.633921
## L(Volume.ts, 91:122)114 -1.011e-02 1.408e-01 -0.072 0.942957
## L(Volume.ts, 91:122)115 -1.743e-01 1.404e-01 -1.241 0.218814
## L(Volume.ts, 91:122)116 6.476e-03 1.364e-01 0.047 0.962271
## L(Volume.ts, 91:122)117 1.531e-01 1.545e-01 0.991 0.325176
## L(Volume.ts, 91:122)118 -1.516e-01 1.534e-01 -0.988 0.326636
## L(Volume.ts, 91:122)119 -1.675e-01 1.559e-01 -1.074 0.286404
## L(Volume.ts, 91:122)120 -5.380e-02 1.554e-01 -0.346 0.730190
## L(Volume.ts, 91:122)121 -4.933e-02 1.532e-01 -0.322 0.748456
## L(Volume.ts, 91:122)122 -4.175e-02 1.295e-01 -0.322 0.748219
## L(Close.ts.diff, 1:110)1 -8.393e+02 2.191e+03 -0.383 0.702853
## L(Close.ts.diff, 1:110)2 2.256e+03 2.159e+03 1.045 0.299786
## L(Close.ts.diff, 1:110)3 -3.011e+02 2.212e+03 -0.136 0.892111
## L(Close.ts.diff, 1:110)4 5.762e+02 2.230e+03 0.258 0.796874
## L(Close.ts.diff, 1:110)5 1.705e+03 2.209e+03 0.772 0.442928
## L(Close.ts.diff, 1:110)6 5.648e+03 3.588e+03 1.574 0.120086
## L(Close.ts.diff, 1:110)7 -8.154e+02 3.695e+03 -0.221 0.825998
## L(Close.ts.diff, 1:110)8 3.707e+03 3.719e+03 0.997 0.322366
## L(Close.ts.diff, 1:110)9 1.053e+03 3.786e+03 0.278 0.781679
## L(Close.ts.diff, 1:110)10 2.840e+03 3.749e+03 0.758 0.451307
## L(Close.ts.diff, 1:110)11 3.009e+02 2.308e+03 0.130 0.896668
## L(Close.ts.diff, 1:110)12 7.292e+02 1.996e+03 0.365 0.715990
## L(Close.ts.diff, 1:110)13 1.733e+03 1.969e+03 0.880 0.381896
## L(Close.ts.diff, 1:110)14 1.099e+03 1.976e+03 0.556 0.579734
## L(Close.ts.diff, 1:110)15 7.498e+02 1.977e+03 0.379 0.705716
## L(Close.ts.diff, 1:110)16 9.805e+02 1.978e+03 0.496 0.621680
## L(Close.ts.diff, 1:110)17 1.407e+03 1.926e+03 0.731 0.467486
## L(Close.ts.diff, 1:110)18 -7.842e+01 1.816e+03 -0.043 0.965685
## L(Close.ts.diff, 1:110)19 9.498e+02 1.802e+03 0.527 0.599906
## L(Close.ts.diff, 1:110)20 1.458e+03 1.782e+03 0.818 0.416089
## L(Close.ts.diff, 1:110)21 -1.678e+02 1.763e+03 -0.095 0.924453
## L(Close.ts.diff, 1:110)22 -4.866e+01 1.759e+03 -0.028 0.978009
## L(Close.ts.diff, 1:110)23 -8.880e+02 1.759e+03 -0.505 0.615301
## L(Close.ts.diff, 1:110)24 6.887e+02 1.740e+03 0.396 0.693553
## L(Close.ts.diff, 1:110)25 1.736e+03 1.729e+03 1.004 0.318737
## L(Close.ts.diff, 1:110)26 -1.072e+04 1.754e+03 -6.114 5.36e-08 ***
## L(Close.ts.diff, 1:110)27 3.316e+03 2.238e+03 1.482 0.143002
## L(Close.ts.diff, 1:110)28 1.805e+02 2.250e+03 0.080 0.936286
## L(Close.ts.diff, 1:110)29 3.777e+02 2.289e+03 0.165 0.869408
## L(Close.ts.diff, 1:110)30 3.503e+02 2.299e+03 0.152 0.879333
## L(Close.ts.diff, 1:110)31 -1.687e+03 2.333e+03 -0.723 0.472175
## L(Close.ts.diff, 1:110)32 4.818e+03 2.356e+03 2.045 0.044730 *
## L(Close.ts.diff, 1:110)33 4.828e+02 2.422e+03 0.199 0.842624
## L(Close.ts.diff, 1:110)34 2.063e+03 2.425e+03 0.851 0.397778
## L(Close.ts.diff, 1:110)35 1.453e+03 2.419e+03 0.601 0.549904
## L(Close.ts.diff, 1:110)36 6.778e+01 2.506e+03 0.027 0.978505
## L(Close.ts.diff, 1:110)37 1.323e+03 2.457e+03 0.539 0.591836
## L(Close.ts.diff, 1:110)38 -7.929e+02 2.464e+03 -0.322 0.748629
## L(Close.ts.diff, 1:110)39 3.266e+03 2.283e+03 1.431 0.157074
## L(Close.ts.diff, 1:110)40 4.758e+02 2.264e+03 0.210 0.834196
## L(Close.ts.diff, 1:110)41 1.013e+03 2.284e+03 0.444 0.658740
## L(Close.ts.diff, 1:110)42 -3.978e+02 2.226e+03 -0.179 0.858720
## L(Close.ts.diff, 1:110)43 -1.148e+03 2.246e+03 -0.511 0.610983
## L(Close.ts.diff, 1:110)44 2.125e+03 2.231e+03 0.952 0.344290
## L(Close.ts.diff, 1:110)45 1.455e+02 2.225e+03 0.065 0.948048
## L(Close.ts.diff, 1:110)46 3.478e+03 2.207e+03 1.576 0.119756
## L(Close.ts.diff, 1:110)47 -1.565e+03 2.249e+03 -0.696 0.488791
## L(Close.ts.diff, 1:110)48 -2.593e+01 2.257e+03 -0.011 0.990867
## L(Close.ts.diff, 1:110)49 -8.677e+02 2.211e+03 -0.392 0.695994
## L(Close.ts.diff, 1:110)50 -1.951e+03 2.213e+03 -0.882 0.381134
## L(Close.ts.diff, 1:110)51 1.092e+03 2.193e+03 0.498 0.620204
## L(Close.ts.diff, 1:110)52 -4.137e+03 2.188e+03 -1.891 0.062924 .
## L(Close.ts.diff, 1:110)53 1.545e+02 2.249e+03 0.069 0.945451
## L(Close.ts.diff, 1:110)54 2.292e+02 2.243e+03 0.102 0.918898
## L(Close.ts.diff, 1:110)55 -2.372e+03 2.134e+03 -1.111 0.270272
## L(Close.ts.diff, 1:110)56 1.086e+03 2.198e+03 0.494 0.622696
## L(Close.ts.diff, 1:110)57 -2.077e+03 2.295e+03 -0.905 0.368713
## L(Close.ts.diff, 1:110)58 4.068e+03 2.145e+03 1.896 0.062180 .
## L(Close.ts.diff, 1:110)59 5.600e+02 1.971e+03 0.284 0.777210
## L(Close.ts.diff, 1:110)60 7.366e+02 1.956e+03 0.376 0.707721
## L(Close.ts.diff, 1:110)61 -3.065e+01 1.958e+03 -0.016 0.987556
## L(Close.ts.diff, 1:110)62 -2.949e+03 2.048e+03 -1.440 0.154403
## L(Close.ts.diff, 1:110)63 8.277e+02 2.085e+03 0.397 0.692555
## L(Close.ts.diff, 1:110)64 -1.286e+03 2.078e+03 -0.619 0.538137
## L(Close.ts.diff, 1:110)65 1.826e+02 2.051e+03 0.089 0.929314
## L(Close.ts.diff, 1:110)66 8.585e+02 2.035e+03 0.422 0.674460
## L(Close.ts.diff, 1:110)67 -2.610e+02 1.923e+03 -0.136 0.892437
## L(Close.ts.diff, 1:110)68 -1.806e+03 1.797e+03 -1.005 0.318505
## L(Close.ts.diff, 1:110)69 6.626e+02 1.802e+03 0.368 0.714226
## L(Close.ts.diff, 1:110)70 2.690e+02 1.792e+03 0.150 0.881140
## L(Close.ts.diff, 1:110)71 1.100e+03 1.766e+03 0.623 0.535463
## L(Close.ts.diff, 1:110)72 -1.234e+03 1.753e+03 -0.704 0.483730
## L(Close.ts.diff, 1:110)73 -1.026e+03 1.757e+03 -0.584 0.561082
## L(Close.ts.diff, 1:110)74 -4.279e+00 1.788e+03 -0.002 0.998098
## L(Close.ts.diff, 1:110)75 -2.122e+01 1.786e+03 -0.012 0.990553
## L(Close.ts.diff, 1:110)76 3.120e+03 1.776e+03 1.757 0.083411 .
## L(Close.ts.diff, 1:110)77 4.751e+02 1.818e+03 0.261 0.794631
## L(Close.ts.diff, 1:110)78 -7.639e+02 1.815e+03 -0.421 0.675254
## L(Close.ts.diff, 1:110)79 -8.090e+02 1.821e+03 -0.444 0.658203
## L(Close.ts.diff, 1:110)80 -3.270e+02 1.822e+03 -0.179 0.858080
## L(Close.ts.diff, 1:110)81 -1.701e+03 1.827e+03 -0.931 0.354968
## L(Close.ts.diff, 1:110)82 -6.581e+03 1.856e+03 -3.546 0.000713 ***
## L(Close.ts.diff, 1:110)83 -8.662e+02 2.020e+03 -0.429 0.669378
## L(Close.ts.diff, 1:110)84 -2.531e+03 2.020e+03 -1.253 0.214449
## L(Close.ts.diff, 1:110)85 -2.127e+03 2.015e+03 -1.056 0.294770
## L(Close.ts.diff, 1:110)86 -2.249e+01 2.025e+03 -0.011 0.991169
## L(Close.ts.diff, 1:110)87 -1.378e+03 2.002e+03 -0.688 0.493670
## L(Close.ts.diff, 1:110)88 2.165e+03 1.976e+03 1.096 0.276940
## L(Close.ts.diff, 1:110)89 9.805e+01 1.965e+03 0.050 0.960356
## L(Close.ts.diff, 1:110)90 1.031e+03 1.959e+03 0.526 0.600394
## L(Close.ts.diff, 1:110)91 1.291e+03 1.966e+03 0.657 0.513507
## L(Close.ts.diff, 1:110)92 1.087e+03 1.962e+03 0.554 0.581304
## L(Close.ts.diff, 1:110)93 1.606e+02 1.958e+03 0.082 0.934882
## L(Close.ts.diff, 1:110)94 -1.090e+03 2.002e+03 -0.544 0.587938
## L(Close.ts.diff, 1:110)95 1.053e+03 2.001e+03 0.526 0.600533
## L(Close.ts.diff, 1:110)96 -2.277e+03 1.995e+03 -1.142 0.257574
## L(Close.ts.diff, 1:110)97 1.128e+03 2.040e+03 0.553 0.582026
## L(Close.ts.diff, 1:110)98 -6.654e+02 2.001e+03 -0.333 0.740472
## L(Close.ts.diff, 1:110)99 1.019e+03 1.951e+03 0.522 0.603052
## L(Close.ts.diff, 1:110)100 2.804e+03 1.933e+03 1.451 0.151482
## L(Close.ts.diff, 1:110)101 -2.683e+03 1.892e+03 -1.418 0.160785
## L(Close.ts.diff, 1:110)102 1.914e+03 1.933e+03 0.990 0.325466
## L(Close.ts.diff, 1:110)103 -3.829e+00 1.938e+03 -0.002 0.998429
## L(Close.ts.diff, 1:110)104 -6.315e+02 1.932e+03 -0.327 0.744804
## L(Close.ts.diff, 1:110)105 -1.105e+03 1.876e+03 -0.589 0.557622
## L(Close.ts.diff, 1:110)106 -2.065e+03 1.883e+03 -1.097 0.276677
## L(Close.ts.diff, 1:110)107 -1.550e+03 1.909e+03 -0.812 0.419686
## L(Close.ts.diff, 1:110)108 -3.232e+03 1.901e+03 -1.700 0.093710 .
## L(Close.ts.diff, 1:110)109 3.884e+02 1.889e+03 0.206 0.837679
## L(Close.ts.diff, 1:110)110 -4.634e+02 1.891e+03 -0.245 0.807154
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1917000 on 68 degrees of freedom
## Multiple R-squared: 0.7575, Adjusted R-squared: 0.1369
## F-statistic: 1.221 on 174 and 68 DF, p-value: 0.1738ARDL of Volume and Open
ardl.volume.open.1 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.volume.open.1)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Open.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2622514 -846166 -262527 432638 16612825
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.486e+05 3.997e+05 1.372 0.1713
## L(Volume.ts, 1:32)1 3.214e-01 6.738e-02 4.770 3.35e-06 ***
## L(Volume.ts, 1:32)2 5.707e-02 7.077e-02 0.806 0.4209
## L(Volume.ts, 1:32)3 -4.049e-02 7.095e-02 -0.571 0.5688
## L(Volume.ts, 1:32)4 9.003e-02 7.044e-02 1.278 0.2026
## L(Volume.ts, 1:32)5 1.597e-03 7.047e-02 0.023 0.9819
## L(Volume.ts, 1:32)6 5.137e-02 7.042e-02 0.730 0.4664
## L(Volume.ts, 1:32)7 1.236e-01 7.070e-02 1.748 0.0819 .
## L(Volume.ts, 1:32)8 -3.481e-03 7.097e-02 -0.049 0.9609
## L(Volume.ts, 1:32)9 -6.644e-03 7.073e-02 -0.094 0.9252
## L(Volume.ts, 1:32)10 5.447e-02 7.128e-02 0.764 0.4456
## L(Volume.ts, 1:32)11 -7.348e-02 7.037e-02 -1.044 0.2975
## L(Volume.ts, 1:32)12 1.580e-02 7.049e-02 0.224 0.8228
## L(Volume.ts, 1:32)13 -3.200e-02 7.049e-02 -0.454 0.6503
## L(Volume.ts, 1:32)14 -3.337e-02 7.053e-02 -0.473 0.6366
## L(Volume.ts, 1:32)15 7.360e-02 7.050e-02 1.044 0.2977
## L(Volume.ts, 1:32)16 -3.783e-02 7.072e-02 -0.535 0.5933
## L(Volume.ts, 1:32)17 -1.469e-02 7.114e-02 -0.207 0.8366
## L(Volume.ts, 1:32)18 4.622e-02 7.096e-02 0.651 0.5155
## L(Volume.ts, 1:32)19 -1.960e-02 7.086e-02 -0.277 0.7823
## L(Volume.ts, 1:32)20 1.328e-02 7.083e-02 0.188 0.8514
## L(Volume.ts, 1:32)21 -2.454e-02 7.085e-02 -0.346 0.7294
## L(Volume.ts, 1:32)22 1.593e-02 7.067e-02 0.225 0.8219
## L(Volume.ts, 1:32)23 -7.492e-03 7.061e-02 -0.106 0.9156
## L(Volume.ts, 1:32)24 8.295e-02 7.074e-02 1.173 0.2422
## L(Volume.ts, 1:32)25 3.720e-02 7.103e-02 0.524 0.6010
## L(Volume.ts, 1:32)26 3.017e-02 7.044e-02 0.428 0.6689
## L(Volume.ts, 1:32)27 1.040e-02 7.040e-02 0.148 0.8827
## L(Volume.ts, 1:32)28 -9.240e-02 7.360e-02 -1.255 0.2107
## L(Volume.ts, 1:32)29 1.339e-01 7.065e-02 1.895 0.0594 .
## L(Volume.ts, 1:32)30 -2.942e-02 7.085e-02 -0.415 0.6784
## L(Volume.ts, 1:32)31 3.618e-02 7.081e-02 0.511 0.6099
## L(Volume.ts, 1:32)32 3.936e-02 6.740e-02 0.584 0.5599
## L(Open.ts.diff, 110) -3.881e+02 1.416e+03 -0.274 0.7843
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1854000 on 220 degrees of freedom
## Multiple R-squared: 0.2682, Adjusted R-squared: 0.1584
## F-statistic: 2.443 on 33 and 220 DF, p-value: 6.762e-05ardl.volume.open.2 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff, 35) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.volume.open.2)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff,
## 35) + L(Open.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2612945 -830527 -232826 421930 16574526
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.749e+05 3.999e+05 1.438 0.1520
## L(Volume.ts, 1:32)1 3.203e-01 6.732e-02 4.758 3.54e-06 ***
## L(Volume.ts, 1:32)2 5.762e-02 7.070e-02 0.815 0.4160
## L(Volume.ts, 1:32)3 -4.257e-02 7.090e-02 -0.600 0.5488
## L(Volume.ts, 1:32)4 8.482e-02 7.050e-02 1.203 0.2303
## L(Volume.ts, 1:32)5 3.206e-03 7.042e-02 0.046 0.9637
## L(Volume.ts, 1:32)6 5.477e-02 7.040e-02 0.778 0.4374
## L(Volume.ts, 1:32)7 1.225e-01 7.064e-02 1.735 0.0842 .
## L(Volume.ts, 1:32)8 2.506e-03 7.107e-02 0.035 0.9719
## L(Volume.ts, 1:32)9 -4.600e-02 7.794e-02 -0.590 0.5557
## L(Volume.ts, 1:32)10 6.816e-02 7.212e-02 0.945 0.3457
## L(Volume.ts, 1:32)11 -6.939e-02 7.038e-02 -0.986 0.3253
## L(Volume.ts, 1:32)12 1.163e-02 7.051e-02 0.165 0.8692
## L(Volume.ts, 1:32)13 -3.010e-02 7.044e-02 -0.427 0.6695
## L(Volume.ts, 1:32)14 -3.204e-02 7.047e-02 -0.455 0.6499
## L(Volume.ts, 1:32)15 7.158e-02 7.046e-02 1.016 0.3108
## L(Volume.ts, 1:32)16 -2.897e-02 7.104e-02 -0.408 0.6838
## L(Volume.ts, 1:32)17 -1.907e-02 7.116e-02 -0.268 0.7889
## L(Volume.ts, 1:32)18 5.015e-02 7.097e-02 0.707 0.4805
## L(Volume.ts, 1:32)19 -1.619e-02 7.084e-02 -0.229 0.8195
## L(Volume.ts, 1:32)20 8.890e-03 7.086e-02 0.125 0.9003
## L(Volume.ts, 1:32)21 -1.966e-02 7.089e-02 -0.277 0.7818
## L(Volume.ts, 1:32)22 1.260e-02 7.065e-02 0.178 0.8586
## L(Volume.ts, 1:32)23 -1.347e-02 7.072e-02 -0.190 0.8491
## L(Volume.ts, 1:32)24 8.634e-02 7.073e-02 1.221 0.2235
## L(Volume.ts, 1:32)25 3.649e-02 7.096e-02 0.514 0.6076
## L(Volume.ts, 1:32)26 3.078e-02 7.037e-02 0.437 0.6622
## L(Volume.ts, 1:32)27 9.942e-03 7.033e-02 0.141 0.8877
## L(Volume.ts, 1:32)28 -9.932e-02 7.376e-02 -1.347 0.1795
## L(Volume.ts, 1:32)29 1.547e-01 7.268e-02 2.128 0.0345 *
## L(Volume.ts, 1:32)30 -3.241e-02 7.082e-02 -0.458 0.6477
## L(Volume.ts, 1:32)31 3.125e-02 7.086e-02 0.441 0.6596
## L(Volume.ts, 1:32)32 4.074e-02 6.735e-02 0.605 0.5458
## L(Close.ts.diff, 35) -1.836e+03 1.534e+03 -1.197 0.2327
## L(Open.ts.diff, 110) -4.993e+02 1.418e+03 -0.352 0.7251
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1852000 on 219 degrees of freedom
## Multiple R-squared: 0.273, Adjusted R-squared: 0.1601
## F-statistic: 2.418 on 34 and 219 DF, p-value: 6.968e-05ardl.volume.open.3 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts, 91:122) + L(Close.ts.diff, 110), data = infy_stock)
summary(ardl.volume.open.3)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122) + L(Close.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3162262 -836678 -195987 521126 15845331
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.078e+06 9.549e+05 2.176 0.03086 *
## L(Volume.ts, 1:32)1 3.079e-01 7.492e-02 4.110 6.04e-05 ***
## L(Volume.ts, 1:32)2 8.519e-02 7.857e-02 1.084 0.27971
## L(Volume.ts, 1:32)3 -7.064e-02 7.980e-02 -0.885 0.37723
## L(Volume.ts, 1:32)4 4.374e-02 7.981e-02 0.548 0.58433
## L(Volume.ts, 1:32)5 2.636e-02 7.908e-02 0.333 0.73931
## L(Volume.ts, 1:32)6 4.160e-02 7.708e-02 0.540 0.59007
## L(Volume.ts, 1:32)7 9.882e-02 7.685e-02 1.286 0.20016
## L(Volume.ts, 1:32)8 -1.168e-02 7.688e-02 -0.152 0.87942
## L(Volume.ts, 1:32)9 6.567e-03 7.643e-02 0.086 0.93162
## L(Volume.ts, 1:32)10 6.030e-02 7.706e-02 0.782 0.43503
## L(Volume.ts, 1:32)11 -1.064e-01 7.676e-02 -1.387 0.16733
## L(Volume.ts, 1:32)12 3.283e-02 7.709e-02 0.426 0.67069
## L(Volume.ts, 1:32)13 -7.042e-02 7.724e-02 -0.912 0.36312
## L(Volume.ts, 1:32)14 -3.211e-02 7.745e-02 -0.415 0.67899
## L(Volume.ts, 1:32)15 5.738e-02 7.723e-02 0.743 0.45852
## L(Volume.ts, 1:32)16 -3.638e-02 7.757e-02 -0.469 0.63969
## L(Volume.ts, 1:32)17 -3.244e-02 7.787e-02 -0.417 0.67745
## L(Volume.ts, 1:32)18 1.844e-02 7.744e-02 0.238 0.81204
## L(Volume.ts, 1:32)19 6.324e-03 7.746e-02 0.082 0.93503
## L(Volume.ts, 1:32)20 1.090e-02 7.735e-02 0.141 0.88807
## L(Volume.ts, 1:32)21 -2.162e-02 7.788e-02 -0.278 0.78160
## L(Volume.ts, 1:32)22 1.143e-02 7.797e-02 0.147 0.88365
## L(Volume.ts, 1:32)23 3.903e-03 7.776e-02 0.050 0.96002
## L(Volume.ts, 1:32)24 5.468e-02 7.744e-02 0.706 0.48105
## L(Volume.ts, 1:32)25 3.664e-02 7.755e-02 0.472 0.63721
## L(Volume.ts, 1:32)26 3.145e-02 7.672e-02 0.410 0.68233
## L(Volume.ts, 1:32)27 3.461e-02 7.671e-02 0.451 0.65242
## L(Volume.ts, 1:32)28 -8.312e-02 7.972e-02 -1.043 0.29850
## L(Volume.ts, 1:32)29 6.754e-02 7.660e-02 0.882 0.37910
## L(Volume.ts, 1:32)30 3.911e-02 8.053e-02 0.486 0.62783
## L(Volume.ts, 1:32)31 -6.293e-03 8.094e-02 -0.078 0.93812
## L(Volume.ts, 1:32)32 5.716e-02 7.646e-02 0.748 0.45571
## L(Volume.ts, 91:122)91 -6.240e-02 7.642e-02 -0.817 0.41527
## L(Volume.ts, 91:122)92 4.233e-02 8.076e-02 0.524 0.60089
## L(Volume.ts, 91:122)93 -2.370e-02 8.073e-02 -0.294 0.76940
## L(Volume.ts, 91:122)94 8.186e-03 7.669e-02 0.107 0.91512
## L(Volume.ts, 91:122)95 -5.600e-02 7.660e-02 -0.731 0.46568
## L(Volume.ts, 91:122)96 -1.704e-02 7.682e-02 -0.222 0.82472
## L(Volume.ts, 91:122)97 -4.758e-02 7.688e-02 -0.619 0.53682
## L(Volume.ts, 91:122)98 -8.314e-02 7.748e-02 -1.073 0.28473
## L(Volume.ts, 91:122)99 9.454e-02 7.752e-02 1.220 0.22427
## L(Volume.ts, 91:122)100 -6.465e-02 7.813e-02 -0.827 0.40911
## L(Volume.ts, 91:122)101 3.458e-02 7.846e-02 0.441 0.65994
## L(Volume.ts, 91:122)102 1.127e-03 7.769e-02 0.015 0.98845
## L(Volume.ts, 91:122)103 -1.182e-02 7.723e-02 -0.153 0.87857
## L(Volume.ts, 91:122)104 1.468e-02 7.909e-02 0.186 0.85299
## L(Volume.ts, 91:122)105 2.418e-02 7.766e-02 0.311 0.75592
## L(Volume.ts, 91:122)106 -5.411e-02 7.774e-02 -0.696 0.48731
## L(Volume.ts, 91:122)107 4.041e-02 7.773e-02 0.520 0.60375
## L(Volume.ts, 91:122)108 -4.923e-02 7.752e-02 -0.635 0.52616
## L(Volume.ts, 91:122)109 -5.262e-02 7.745e-02 -0.679 0.49774
## L(Volume.ts, 91:122)110 3.794e-02 7.718e-02 0.492 0.62360
## L(Volume.ts, 91:122)111 -1.403e-01 8.131e-02 -1.726 0.08617 .
## L(Volume.ts, 91:122)112 1.460e-02 8.154e-02 0.179 0.85807
## L(Volume.ts, 91:122)113 9.254e-02 8.117e-02 1.140 0.25585
## L(Volume.ts, 91:122)114 -9.978e-02 8.134e-02 -1.227 0.22156
## L(Volume.ts, 91:122)115 -8.866e-02 8.179e-02 -1.084 0.27983
## L(Volume.ts, 91:122)116 6.144e-02 7.700e-02 0.798 0.42600
## L(Volume.ts, 91:122)117 2.540e-01 7.742e-02 3.281 0.00124 **
## L(Volume.ts, 91:122)118 -1.302e-01 7.951e-02 -1.637 0.10333
## L(Volume.ts, 91:122)119 -6.888e-02 8.027e-02 -0.858 0.39197
## L(Volume.ts, 91:122)120 5.118e-02 7.974e-02 0.642 0.52186
## L(Volume.ts, 91:122)121 -2.605e-02 7.892e-02 -0.330 0.74174
## L(Volume.ts, 91:122)122 -5.801e-02 7.499e-02 -0.773 0.44028
## L(Close.ts.diff, 110) -2.788e+02 1.530e+03 -0.182 0.85563
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1890000 on 177 degrees of freedom
## Multiple R-squared: 0.3864, Adjusted R-squared: 0.161
## F-statistic: 1.715 on 65 and 177 DF, p-value: 0.002947ardl.volume.open.4 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts, 91:122) + L(Close.ts.diff, 35) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.volume.open.4)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122) + L(Close.ts.diff, 35) + L(Open.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3136183 -840361 -195259 515199 15856611
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.040e+06 9.635e+05 2.117 0.03565 *
## L(Volume.ts, 1:32)1 3.091e-01 7.517e-02 4.112 6.02e-05 ***
## L(Volume.ts, 1:32)2 8.446e-02 7.890e-02 1.071 0.28585
## L(Volume.ts, 1:32)3 -7.176e-02 7.993e-02 -0.898 0.37054
## L(Volume.ts, 1:32)4 4.267e-02 8.009e-02 0.533 0.59488
## L(Volume.ts, 1:32)5 2.608e-02 7.935e-02 0.329 0.74277
## L(Volume.ts, 1:32)6 4.293e-02 7.734e-02 0.555 0.57954
## L(Volume.ts, 1:32)7 9.987e-02 7.724e-02 1.293 0.19767
## L(Volume.ts, 1:32)8 -9.560e-03 7.756e-02 -0.123 0.90204
## L(Volume.ts, 1:32)9 -7.331e-03 8.655e-02 -0.085 0.93259
## L(Volume.ts, 1:32)10 6.608e-02 7.855e-02 0.841 0.40134
## L(Volume.ts, 1:32)11 -1.034e-01 7.726e-02 -1.338 0.18266
## L(Volume.ts, 1:32)12 3.100e-02 7.744e-02 0.400 0.68938
## L(Volume.ts, 1:32)13 -6.825e-02 7.773e-02 -0.878 0.38118
## L(Volume.ts, 1:32)14 -3.182e-02 7.754e-02 -0.410 0.68201
## L(Volume.ts, 1:32)15 5.676e-02 7.747e-02 0.733 0.46473
## L(Volume.ts, 1:32)16 -3.445e-02 7.797e-02 -0.442 0.65915
## L(Volume.ts, 1:32)17 -3.349e-02 7.812e-02 -0.429 0.66871
## L(Volume.ts, 1:32)18 2.039e-02 7.780e-02 0.262 0.79362
## L(Volume.ts, 1:32)19 8.272e-03 7.806e-02 0.106 0.91573
## L(Volume.ts, 1:32)20 8.804e-03 7.778e-02 0.113 0.91001
## L(Volume.ts, 1:32)21 -2.018e-02 7.810e-02 -0.258 0.79640
## L(Volume.ts, 1:32)22 1.177e-02 7.831e-02 0.150 0.88068
## L(Volume.ts, 1:32)23 7.627e-04 7.827e-02 0.010 0.99224
## L(Volume.ts, 1:32)24 5.780e-02 7.802e-02 0.741 0.45981
## L(Volume.ts, 1:32)25 3.580e-02 7.765e-02 0.461 0.64529
## L(Volume.ts, 1:32)26 3.149e-02 7.693e-02 0.409 0.68279
## L(Volume.ts, 1:32)27 3.479e-02 7.700e-02 0.452 0.65192
## L(Volume.ts, 1:32)28 -8.764e-02 8.103e-02 -1.082 0.28091
## L(Volume.ts, 1:32)29 7.474e-02 7.893e-02 0.947 0.34495
## L(Volume.ts, 1:32)30 3.819e-02 8.066e-02 0.473 0.63645
## L(Volume.ts, 1:32)31 -7.198e-03 8.102e-02 -0.089 0.92931
## L(Volume.ts, 1:32)32 5.731e-02 7.659e-02 0.748 0.45528
## L(Volume.ts, 91:122)91 -6.121e-02 7.666e-02 -0.799 0.42565
## L(Volume.ts, 91:122)92 4.070e-02 8.105e-02 0.502 0.61616
## L(Volume.ts, 91:122)93 -2.346e-02 8.091e-02 -0.290 0.77222
## L(Volume.ts, 91:122)94 8.079e-03 7.683e-02 0.105 0.91637
## L(Volume.ts, 91:122)95 -5.468e-02 7.684e-02 -0.712 0.47771
## L(Volume.ts, 91:122)96 -1.578e-02 7.704e-02 -0.205 0.83796
## L(Volume.ts, 91:122)97 -4.506e-02 7.756e-02 -0.581 0.56201
## L(Volume.ts, 91:122)98 -8.417e-02 7.768e-02 -1.084 0.28006
## L(Volume.ts, 91:122)99 9.383e-02 7.770e-02 1.207 0.22886
## L(Volume.ts, 91:122)100 -6.418e-02 7.841e-02 -0.819 0.41418
## L(Volume.ts, 91:122)101 3.317e-02 7.899e-02 0.420 0.67503
## L(Volume.ts, 91:122)102 1.920e-03 7.803e-02 0.025 0.98040
## L(Volume.ts, 91:122)103 -1.300e-02 7.745e-02 -0.168 0.86689
## L(Volume.ts, 91:122)104 1.757e-02 7.929e-02 0.222 0.82492
## L(Volume.ts, 91:122)105 2.227e-02 7.798e-02 0.286 0.77555
## L(Volume.ts, 91:122)106 -5.287e-02 7.802e-02 -0.678 0.49886
## L(Volume.ts, 91:122)107 3.868e-02 7.858e-02 0.492 0.62314
## L(Volume.ts, 91:122)108 -4.692e-02 7.851e-02 -0.598 0.55083
## L(Volume.ts, 91:122)109 -5.258e-02 7.765e-02 -0.677 0.49918
## L(Volume.ts, 91:122)110 3.818e-02 7.755e-02 0.492 0.62307
## L(Volume.ts, 91:122)111 -1.392e-01 8.158e-02 -1.707 0.08963 .
## L(Volume.ts, 91:122)112 1.268e-02 8.191e-02 0.155 0.87716
## L(Volume.ts, 91:122)113 9.116e-02 8.143e-02 1.120 0.26444
## L(Volume.ts, 91:122)114 -9.830e-02 8.162e-02 -1.204 0.23005
## L(Volume.ts, 91:122)115 -8.967e-02 8.201e-02 -1.093 0.27572
## L(Volume.ts, 91:122)116 6.354e-02 7.745e-02 0.820 0.41309
## L(Volume.ts, 91:122)117 2.541e-01 7.778e-02 3.267 0.00131 **
## L(Volume.ts, 91:122)118 -1.326e-01 7.995e-02 -1.659 0.09899 .
## L(Volume.ts, 91:122)119 -6.365e-02 8.158e-02 -0.780 0.43634
## L(Volume.ts, 91:122)120 5.062e-02 8.010e-02 0.632 0.52822
## L(Volume.ts, 91:122)121 -2.533e-02 7.926e-02 -0.320 0.74967
## L(Volume.ts, 91:122)122 -5.590e-02 7.534e-02 -0.742 0.45912
## L(Close.ts.diff, 35) -5.703e+02 1.687e+03 -0.338 0.73565
## L(Open.ts.diff, 110) -4.591e+02 1.527e+03 -0.301 0.76400
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1895000 on 176 degrees of freedom
## Multiple R-squared: 0.3869, Adjusted R-squared: 0.157
## F-statistic: 1.683 on 66 and 176 DF, p-value: 0.00383Analyzing ARDL Residuals with ACF and PACF
plot_acf_pacf <- function(model_residuals, model_name) {
par(mfrow = c(1, 2)) # Set up a 1x2 plotting area
acf(model_residuals, main = paste("ACF of Residuals:", model_name))
pacf(model_residuals, main = paste("PACF of Residuals:", model_name))
}Turnover and Close
ACF and PACF show that residuals are within the confidence bound meaning there is no autocorrelation or partial autocorrelation found in the residuals.
ardl.turnover.close.1 <- dynlm(Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff, 110))
summary(ardl.turnover.close.1)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff,
## 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.759e+14 -1.190e+14 -4.453e+13 5.802e+13 1.781e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.379e+14 4.188e+13 5.679 3.78e-08 ***
## L(Turnover.ts, 1:4)1 3.277e-01 6.329e-02 5.178 4.65e-07 ***
## L(Turnover.ts, 1:4)2 3.515e-02 6.661e-02 0.528 0.598
## L(Turnover.ts, 1:4)3 -1.813e-02 6.671e-02 -0.272 0.786
## L(Turnover.ts, 1:4)4 8.763e-02 6.337e-02 1.383 0.168
## L(Close.ts.diff, 110) 4.385e+10 1.844e+11 0.238 0.812
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.537e+14 on 248 degrees of freedom
## Multiple R-squared: 0.1263, Adjusted R-squared: 0.1087
## F-statistic: 7.172 on 5 and 248 DF, p-value: 2.743e-06plot_acf_pacf(residuals(ardl.turnover.close.1), "ardl.turnover.close.1")
The ACF graph of the residuals show that in between lag 0.01 and 0.02 there is very slight autocorrelation (touching the bound). The PACF graph has long spikes, with onw crossing the confidence bound between 0.05 and 0.06.
ardl.turnover.close.2 <- dynlm(Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff, 1:110))
summary(ardl.turnover.close.2)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4) + L(Close.ts.diff,
## 1:110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.735e+14 -9.649e+13 -3.265e+13 4.919e+13 1.050e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.329e+14 5.284e+13 4.407 2.08e-05 ***
## L(Turnover.ts, 1:4)1 3.394e-01 8.448e-02 4.017 9.60e-05 ***
## L(Turnover.ts, 1:4)2 7.559e-02 8.914e-02 0.848 0.397897
## L(Turnover.ts, 1:4)3 -5.991e-02 8.919e-02 -0.672 0.502864
## L(Turnover.ts, 1:4)4 9.371e-02 8.434e-02 1.111 0.268478
## L(Close.ts.diff, 1:110)1 7.339e+10 1.611e+11 0.456 0.649388
## L(Close.ts.diff, 1:110)2 1.657e+11 1.612e+11 1.028 0.305817
## L(Close.ts.diff, 1:110)3 4.332e+10 1.617e+11 0.268 0.789204
## L(Close.ts.diff, 1:110)4 -8.638e+10 1.618e+11 -0.534 0.594402
## L(Close.ts.diff, 1:110)5 1.430e+11 1.620e+11 0.883 0.378722
## L(Close.ts.diff, 1:110)6 8.402e+11 1.957e+11 4.293 3.29e-05 ***
## L(Close.ts.diff, 1:110)7 -2.172e+11 2.088e+11 -1.040 0.299955
## L(Close.ts.diff, 1:110)8 -1.052e+11 2.092e+11 -0.503 0.615890
## L(Close.ts.diff, 1:110)9 1.464e+11 2.088e+11 0.701 0.484299
## L(Close.ts.diff, 1:110)10 -9.255e+10 2.086e+11 -0.444 0.657961
## L(Close.ts.diff, 1:110)11 -1.621e+10 1.954e+11 -0.083 0.934008
## L(Close.ts.diff, 1:110)12 -6.319e+10 1.951e+11 -0.324 0.746579
## L(Close.ts.diff, 1:110)13 1.828e+11 1.953e+11 0.936 0.350926
## L(Close.ts.diff, 1:110)14 1.700e+11 1.959e+11 0.868 0.387061
## L(Close.ts.diff, 1:110)15 7.128e+10 1.965e+11 0.363 0.717289
## L(Close.ts.diff, 1:110)16 1.206e+11 1.968e+11 0.613 0.540998
## L(Close.ts.diff, 1:110)17 2.457e+11 1.962e+11 1.252 0.212560
## L(Close.ts.diff, 1:110)18 3.434e+10 1.972e+11 0.174 0.861992
## L(Close.ts.diff, 1:110)19 1.181e+11 1.968e+11 0.600 0.549307
## L(Close.ts.diff, 1:110)20 3.291e+09 1.966e+11 0.017 0.986670
## L(Close.ts.diff, 1:110)21 -1.867e+10 1.967e+11 -0.095 0.924545
## L(Close.ts.diff, 1:110)22 4.037e+10 1.957e+11 0.206 0.836893
## L(Close.ts.diff, 1:110)23 -6.412e+10 1.956e+11 -0.328 0.743565
## L(Close.ts.diff, 1:110)24 1.775e+11 1.946e+11 0.912 0.363203
## L(Close.ts.diff, 1:110)25 9.822e+10 1.954e+11 0.503 0.615977
## L(Close.ts.diff, 1:110)26 -9.431e+11 1.955e+11 -4.823 3.67e-06 ***
## L(Close.ts.diff, 1:110)27 1.977e+11 2.113e+11 0.935 0.351197
## L(Close.ts.diff, 1:110)28 3.297e+10 2.116e+11 0.156 0.876418
## L(Close.ts.diff, 1:110)29 7.482e+10 2.110e+11 0.355 0.723470
## L(Close.ts.diff, 1:110)30 -1.721e+10 2.076e+11 -0.083 0.934058
## L(Close.ts.diff, 1:110)31 -1.372e+11 1.961e+11 -0.700 0.485290
## L(Close.ts.diff, 1:110)32 1.895e+11 1.964e+11 0.965 0.336298
## L(Close.ts.diff, 1:110)33 -6.174e+10 1.968e+11 -0.314 0.754153
## L(Close.ts.diff, 1:110)34 -8.987e+10 1.964e+11 -0.458 0.647906
## L(Close.ts.diff, 1:110)35 4.004e+09 1.957e+11 0.020 0.983701
## L(Close.ts.diff, 1:110)36 -5.505e+10 1.955e+11 -0.282 0.778705
## L(Close.ts.diff, 1:110)37 8.448e+10 1.952e+11 0.433 0.665822
## L(Close.ts.diff, 1:110)38 -1.034e+11 1.951e+11 -0.530 0.596762
## L(Close.ts.diff, 1:110)39 1.527e+11 1.950e+11 0.783 0.435093
## L(Close.ts.diff, 1:110)40 3.860e+10 1.956e+11 0.197 0.843839
## L(Close.ts.diff, 1:110)41 -1.435e+11 1.959e+11 -0.733 0.465072
## L(Close.ts.diff, 1:110)42 -1.637e+11 1.961e+11 -0.835 0.405096
## L(Close.ts.diff, 1:110)43 -8.991e+10 1.962e+11 -0.458 0.647521
## L(Close.ts.diff, 1:110)44 1.694e+11 1.962e+11 0.863 0.389466
## L(Close.ts.diff, 1:110)45 9.928e+10 1.967e+11 0.505 0.614490
## L(Close.ts.diff, 1:110)46 8.374e+10 1.968e+11 0.426 0.671100
## L(Close.ts.diff, 1:110)47 1.267e+10 1.964e+11 0.065 0.948629
## L(Close.ts.diff, 1:110)48 -7.329e+10 1.956e+11 -0.375 0.708483
## L(Close.ts.diff, 1:110)49 -2.369e+10 1.957e+11 -0.121 0.903837
## L(Close.ts.diff, 1:110)50 -7.656e+10 1.957e+11 -0.391 0.696191
## L(Close.ts.diff, 1:110)51 -6.874e+10 1.956e+11 -0.351 0.725829
## L(Close.ts.diff, 1:110)52 -1.316e+11 1.955e+11 -0.673 0.502071
## L(Close.ts.diff, 1:110)53 -1.302e+11 1.956e+11 -0.666 0.506643
## L(Close.ts.diff, 1:110)54 4.434e+10 1.962e+11 0.226 0.821527
## L(Close.ts.diff, 1:110)55 -6.630e+10 1.962e+11 -0.338 0.735944
## L(Close.ts.diff, 1:110)56 5.868e+10 1.962e+11 0.299 0.765380
## L(Close.ts.diff, 1:110)57 -7.955e+10 1.960e+11 -0.406 0.685506
## L(Close.ts.diff, 1:110)58 3.189e+11 1.957e+11 1.630 0.105448
## L(Close.ts.diff, 1:110)59 -6.487e+09 1.976e+11 -0.033 0.973855
## L(Close.ts.diff, 1:110)60 -6.811e+10 1.974e+11 -0.345 0.730630
## L(Close.ts.diff, 1:110)61 5.678e+09 1.972e+11 0.029 0.977077
## L(Close.ts.diff, 1:110)62 -1.244e+11 1.965e+11 -0.633 0.527797
## L(Close.ts.diff, 1:110)63 2.182e+10 1.953e+11 0.112 0.911218
## L(Close.ts.diff, 1:110)64 -1.290e+11 1.954e+11 -0.660 0.510300
## L(Close.ts.diff, 1:110)65 -4.913e+10 1.956e+11 -0.251 0.802104
## L(Close.ts.diff, 1:110)66 1.716e+11 1.956e+11 0.877 0.381862
## L(Close.ts.diff, 1:110)67 3.261e+10 1.961e+11 0.166 0.868160
## L(Close.ts.diff, 1:110)68 -1.529e+11 1.959e+11 -0.780 0.436597
## L(Close.ts.diff, 1:110)69 1.901e+11 1.963e+11 0.969 0.334410
## L(Close.ts.diff, 1:110)70 -1.062e+10 1.965e+11 -0.054 0.956999
## L(Close.ts.diff, 1:110)71 7.715e+10 1.961e+11 0.394 0.694545
## L(Close.ts.diff, 1:110)72 -1.286e+11 1.960e+11 -0.656 0.512991
## L(Close.ts.diff, 1:110)73 -2.963e+10 1.956e+11 -0.151 0.879828
## L(Close.ts.diff, 1:110)74 1.183e+11 1.959e+11 0.604 0.546719
## L(Close.ts.diff, 1:110)75 1.475e+10 1.963e+11 0.075 0.940220
## L(Close.ts.diff, 1:110)76 8.400e+11 1.958e+11 4.291 3.32e-05 ***
## L(Close.ts.diff, 1:110)77 3.778e+10 2.075e+11 0.182 0.855775
## L(Close.ts.diff, 1:110)78 -8.592e+10 2.074e+11 -0.414 0.679314
## L(Close.ts.diff, 1:110)79 -9.532e+10 2.074e+11 -0.460 0.646531
## L(Close.ts.diff, 1:110)80 6.725e+10 2.065e+11 0.326 0.745186
## L(Close.ts.diff, 1:110)81 -2.137e+10 1.975e+11 -0.108 0.913998
## L(Close.ts.diff, 1:110)82 -7.124e+11 1.958e+11 -3.638 0.000386 ***
## L(Close.ts.diff, 1:110)83 -3.165e+08 2.042e+11 -0.002 0.998766
## L(Close.ts.diff, 1:110)84 -6.625e+09 2.037e+11 -0.033 0.974101
## L(Close.ts.diff, 1:110)85 -1.514e+11 2.030e+11 -0.746 0.456962
## L(Close.ts.diff, 1:110)86 6.248e+10 2.018e+11 0.310 0.757291
## L(Close.ts.diff, 1:110)87 1.008e+10 1.955e+11 0.052 0.958947
## L(Close.ts.diff, 1:110)88 1.621e+10 1.955e+11 0.083 0.934020
## L(Close.ts.diff, 1:110)89 1.850e+10 1.954e+11 0.095 0.924721
## L(Close.ts.diff, 1:110)90 -7.614e+10 1.949e+11 -0.391 0.696588
## L(Close.ts.diff, 1:110)91 7.648e+10 1.949e+11 0.393 0.695280
## L(Close.ts.diff, 1:110)92 8.090e+10 1.951e+11 0.415 0.679044
## L(Close.ts.diff, 1:110)93 3.490e+10 1.953e+11 0.179 0.858413
## L(Close.ts.diff, 1:110)94 8.301e+10 1.950e+11 0.426 0.670977
## L(Close.ts.diff, 1:110)95 1.086e+10 1.956e+11 0.056 0.955808
## L(Close.ts.diff, 1:110)96 -3.669e+10 1.954e+11 -0.188 0.851353
## L(Close.ts.diff, 1:110)97 1.097e+10 1.952e+11 0.056 0.955280
## L(Close.ts.diff, 1:110)98 3.885e+10 1.952e+11 0.199 0.842573
## L(Close.ts.diff, 1:110)99 1.531e+11 1.950e+11 0.785 0.433730
## L(Close.ts.diff, 1:110)100 2.930e+11 1.956e+11 1.498 0.136323
## L(Close.ts.diff, 1:110)101 -5.918e+10 1.972e+11 -0.300 0.764513
## L(Close.ts.diff, 1:110)102 -4.528e+09 1.971e+11 -0.023 0.981705
## L(Close.ts.diff, 1:110)103 1.211e+11 1.971e+11 0.615 0.539768
## L(Close.ts.diff, 1:110)104 3.255e+08 1.974e+11 0.002 0.998686
## L(Close.ts.diff, 1:110)105 -1.619e+11 1.942e+11 -0.833 0.406053
## L(Close.ts.diff, 1:110)106 -9.826e+10 1.953e+11 -0.503 0.615602
## L(Close.ts.diff, 1:110)107 -1.163e+11 1.953e+11 -0.595 0.552643
## L(Close.ts.diff, 1:110)108 -1.040e+11 1.952e+11 -0.533 0.595153
## L(Close.ts.diff, 1:110)109 2.938e+10 1.950e+11 0.151 0.880456
## L(Close.ts.diff, 1:110)110 8.288e+10 1.949e+11 0.425 0.671371
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.559e+14 on 139 degrees of freedom
## Multiple R-squared: 0.5018, Adjusted R-squared: 0.09325
## F-statistic: 1.228 on 114 and 139 DF, p-value: 0.1237plot_acf_pacf(residuals(ardl.turnover.close.2), "ardl.turnover.close.2")
ACF graph shows autocorrelation of residuals between 0 and 0.01. PACF graph shows spikes reaching almost to the confidence bounds, but is still contained meaning there is still no significant partial autocorrelation between residuals.
ardl.turnover.close.3 <- dynlm(Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,61) + L(Turnover.ts, 75) + L(Turnover.ts,117) + L(Close.ts.diff, 110))
summary(ardl.turnover.close.3)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 75) + L(Turnover.ts, 117) + L(Close.ts.diff,
## 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.755e+14 -1.384e+14 -2.222e+13 1.007e+14 1.825e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.077e+13 5.152e+13 1.762 0.07939 .
## L(Turnover.ts, 2) 1.706e-01 5.747e-02 2.969 0.00329 **
## L(Turnover.ts, 61) 2.840e-01 5.778e-02 4.914 1.64e-06 ***
## L(Turnover.ts, 75) 4.264e-02 5.746e-02 0.742 0.45878
## L(Turnover.ts, 117) 2.884e-01 5.784e-02 4.987 1.17e-06 ***
## L(Close.ts.diff, 110) 1.181e+11 1.778e+11 0.665 0.50697
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.44e+14 on 242 degrees of freedom
## Multiple R-squared: 0.2045, Adjusted R-squared: 0.188
## F-statistic: 12.44 on 5 and 242 DF, p-value: 9.408e-11plot_acf_pacf(residuals(ardl.turnover.close.3), "ardl.turnover.close.3")
The ACF graph shows autocorrelation of residuals at lags (between 0 and 0.01 ) and 0.02. The PACF graph doesn’t show any partial autocorrelation.
ardl.turnover.close.4 <- dynlm(Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,61) + L(Turnover.ts, 75) + L(Turnover.ts,117) + L(Close.ts.diff, 1:110))
summary(ardl.turnover.close.4)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 75) + L(Turnover.ts, 117) + L(Close.ts.diff,
## 1:110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.384e+14 -1.097e+14 -2.262e+13 7.092e+13 1.108e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.106e+14 7.389e+13 1.498 0.13663
## L(Turnover.ts, 2) 1.818e-01 7.859e-02 2.313 0.02224 *
## L(Turnover.ts, 61) 2.717e-01 8.743e-02 3.108 0.00231 **
## L(Turnover.ts, 75) -9.467e-03 8.713e-02 -0.109 0.91364
## L(Turnover.ts, 117) 2.946e-01 9.255e-02 3.184 0.00181 **
## L(Close.ts.diff, 1:110)1 -2.861e+10 1.945e+11 -0.147 0.88326
## L(Close.ts.diff, 1:110)2 1.521e+11 1.957e+11 0.777 0.43848
## L(Close.ts.diff, 1:110)3 6.492e+08 1.942e+11 0.003 0.99734
## L(Close.ts.diff, 1:110)4 -9.810e+10 1.952e+11 -0.503 0.61612
## L(Close.ts.diff, 1:110)5 1.409e+11 1.944e+11 0.725 0.46979
## L(Close.ts.diff, 1:110)6 4.138e+11 2.227e+11 1.859 0.06530 .
## L(Close.ts.diff, 1:110)7 -4.007e+10 1.968e+11 -0.204 0.83900
## L(Close.ts.diff, 1:110)8 -8.854e+10 2.085e+11 -0.425 0.67183
## L(Close.ts.diff, 1:110)9 1.879e+11 1.961e+11 0.958 0.33956
## L(Close.ts.diff, 1:110)10 9.941e+09 1.952e+11 0.051 0.95947
## L(Close.ts.diff, 1:110)11 2.261e+10 1.950e+11 0.116 0.90786
## L(Close.ts.diff, 1:110)12 2.422e+11 2.183e+11 1.110 0.26922
## L(Close.ts.diff, 1:110)13 1.887e+11 1.954e+11 0.966 0.33585
## L(Close.ts.diff, 1:110)14 2.739e+11 1.954e+11 1.402 0.16338
## L(Close.ts.diff, 1:110)15 2.032e+11 1.960e+11 1.037 0.30179
## L(Close.ts.diff, 1:110)16 1.543e+11 1.973e+11 0.782 0.43563
## L(Close.ts.diff, 1:110)17 3.081e+11 1.950e+11 1.580 0.11658
## L(Close.ts.diff, 1:110)18 7.711e+10 1.956e+11 0.394 0.69413
## L(Close.ts.diff, 1:110)19 1.816e+11 1.962e+11 0.925 0.35659
## L(Close.ts.diff, 1:110)20 1.353e+11 2.040e+11 0.663 0.50838
## L(Close.ts.diff, 1:110)21 4.811e+10 1.965e+11 0.245 0.80699
## L(Close.ts.diff, 1:110)22 9.921e+10 1.968e+11 0.504 0.61506
## L(Close.ts.diff, 1:110)23 3.112e+10 1.960e+11 0.159 0.87411
## L(Close.ts.diff, 1:110)24 3.041e+11 1.961e+11 1.550 0.12346
## L(Close.ts.diff, 1:110)25 2.750e+11 1.962e+11 1.402 0.16337
## L(Close.ts.diff, 1:110)26 -5.933e+11 2.134e+11 -2.780 0.00622 **
## L(Close.ts.diff, 1:110)27 1.456e+10 1.993e+11 0.073 0.94188
## L(Close.ts.diff, 1:110)28 1.327e+11 2.072e+11 0.640 0.52307
## L(Close.ts.diff, 1:110)29 8.735e+10 1.972e+11 0.443 0.65850
## L(Close.ts.diff, 1:110)30 -1.742e+10 1.962e+11 -0.089 0.92939
## L(Close.ts.diff, 1:110)31 -1.962e+11 1.962e+11 -1.000 0.31914
## L(Close.ts.diff, 1:110)32 6.967e+10 1.964e+11 0.355 0.72332
## L(Close.ts.diff, 1:110)33 -4.210e+10 1.972e+11 -0.213 0.83127
## L(Close.ts.diff, 1:110)34 -1.024e+11 1.953e+11 -0.524 0.60083
## L(Close.ts.diff, 1:110)35 -6.332e+10 1.953e+11 -0.324 0.74631
## L(Close.ts.diff, 1:110)36 -1.464e+11 1.965e+11 -0.745 0.45778
## L(Close.ts.diff, 1:110)37 1.796e+10 1.964e+11 0.091 0.92725
## L(Close.ts.diff, 1:110)38 -1.741e+11 1.970e+11 -0.884 0.37847
## L(Close.ts.diff, 1:110)39 1.427e+11 1.949e+11 0.732 0.46517
## L(Close.ts.diff, 1:110)40 6.295e+10 2.128e+11 0.296 0.76781
## L(Close.ts.diff, 1:110)41 -1.481e+11 1.993e+11 -0.743 0.45874
## L(Close.ts.diff, 1:110)42 -2.085e+11 1.957e+11 -1.066 0.28852
## L(Close.ts.diff, 1:110)43 -1.441e+11 1.952e+11 -0.738 0.46159
## L(Close.ts.diff, 1:110)44 1.391e+11 1.963e+11 0.708 0.47994
## L(Close.ts.diff, 1:110)45 1.611e+11 1.955e+11 0.824 0.41134
## L(Close.ts.diff, 1:110)46 8.892e+10 1.949e+11 0.456 0.64891
## L(Close.ts.diff, 1:110)47 2.950e+10 1.952e+11 0.151 0.88009
## L(Close.ts.diff, 1:110)48 -1.250e+11 1.958e+11 -0.639 0.52419
## L(Close.ts.diff, 1:110)49 -1.461e+10 1.955e+11 -0.075 0.94053
## L(Close.ts.diff, 1:110)50 -6.991e+09 1.981e+11 -0.035 0.97190
## L(Close.ts.diff, 1:110)51 -4.997e+10 1.954e+11 -0.256 0.79858
## L(Close.ts.diff, 1:110)52 -2.406e+11 1.981e+11 -1.215 0.22666
## L(Close.ts.diff, 1:110)53 -2.213e+11 1.952e+11 -1.134 0.25902
## L(Close.ts.diff, 1:110)54 1.635e+10 1.955e+11 0.084 0.93348
## L(Close.ts.diff, 1:110)55 -8.485e+10 1.959e+11 -0.433 0.66563
## L(Close.ts.diff, 1:110)56 -4.230e+09 1.958e+11 -0.022 0.98280
## L(Close.ts.diff, 1:110)57 -8.049e+10 1.955e+11 -0.412 0.68129
## L(Close.ts.diff, 1:110)58 2.391e+11 1.957e+11 1.221 0.22409
## L(Close.ts.diff, 1:110)59 1.043e+11 1.955e+11 0.533 0.59476
## L(Close.ts.diff, 1:110)60 -8.921e+10 1.965e+11 -0.454 0.65052
## L(Close.ts.diff, 1:110)61 -2.069e+10 1.956e+11 -0.106 0.91592
## L(Close.ts.diff, 1:110)62 -3.194e+11 2.041e+11 -1.564 0.12009
## L(Close.ts.diff, 1:110)63 -1.170e+11 1.965e+11 -0.595 0.55264
## L(Close.ts.diff, 1:110)64 -1.089e+11 1.987e+11 -0.548 0.58461
## L(Close.ts.diff, 1:110)65 -4.240e+09 1.958e+11 -0.022 0.98275
## L(Close.ts.diff, 1:110)66 1.512e+11 1.958e+11 0.772 0.44137
## L(Close.ts.diff, 1:110)67 -1.484e+11 2.111e+11 -0.703 0.48342
## L(Close.ts.diff, 1:110)68 -2.021e+11 1.954e+11 -1.034 0.30278
## L(Close.ts.diff, 1:110)69 1.209e+11 1.947e+11 0.621 0.53587
## L(Close.ts.diff, 1:110)70 5.483e+10 1.956e+11 0.280 0.77968
## L(Close.ts.diff, 1:110)71 1.230e+11 1.957e+11 0.628 0.53097
## L(Close.ts.diff, 1:110)72 -7.109e+10 1.952e+11 -0.364 0.71630
## L(Close.ts.diff, 1:110)73 -3.854e+10 1.954e+11 -0.197 0.84398
## L(Close.ts.diff, 1:110)74 4.417e+10 1.956e+11 0.226 0.82173
## L(Close.ts.diff, 1:110)75 3.656e+09 1.960e+11 0.019 0.98514
## L(Close.ts.diff, 1:110)76 8.334e+11 1.959e+11 4.255 3.91e-05 ***
## L(Close.ts.diff, 1:110)77 2.712e+11 1.961e+11 1.383 0.16903
## L(Close.ts.diff, 1:110)78 -9.198e+10 2.092e+11 -0.440 0.66086
## L(Close.ts.diff, 1:110)79 -1.253e+11 1.986e+11 -0.631 0.52937
## L(Close.ts.diff, 1:110)80 1.007e+11 1.974e+11 0.510 0.61096
## L(Close.ts.diff, 1:110)81 5.203e+10 2.114e+11 0.246 0.80592
## L(Close.ts.diff, 1:110)82 -4.597e+11 2.156e+11 -2.132 0.03483 *
## L(Close.ts.diff, 1:110)83 -1.148e+11 2.000e+11 -0.574 0.56695
## L(Close.ts.diff, 1:110)84 7.064e+10 2.025e+11 0.349 0.72777
## L(Close.ts.diff, 1:110)85 -1.529e+11 1.958e+11 -0.781 0.43610
## L(Close.ts.diff, 1:110)86 -8.517e+09 1.957e+11 -0.044 0.96536
## L(Close.ts.diff, 1:110)87 2.762e+11 2.098e+11 1.317 0.19018
## L(Close.ts.diff, 1:110)88 4.054e+10 1.951e+11 0.208 0.83573
## L(Close.ts.diff, 1:110)89 4.640e+10 1.957e+11 0.237 0.81292
## L(Close.ts.diff, 1:110)90 -1.128e+11 1.952e+11 -0.578 0.56446
## L(Close.ts.diff, 1:110)91 8.581e+10 1.951e+11 0.440 0.66083
## L(Close.ts.diff, 1:110)92 9.266e+10 1.968e+11 0.471 0.63857
## L(Close.ts.diff, 1:110)93 3.228e+10 1.954e+11 0.165 0.86907
## L(Close.ts.diff, 1:110)94 -9.814e+09 1.978e+11 -0.050 0.96050
## L(Close.ts.diff, 1:110)95 7.836e+10 1.954e+11 0.401 0.68901
## L(Close.ts.diff, 1:110)96 3.101e+09 1.956e+11 0.016 0.98738
## L(Close.ts.diff, 1:110)97 3.338e+10 1.948e+11 0.171 0.86422
## L(Close.ts.diff, 1:110)98 7.496e+10 1.949e+11 0.385 0.70115
## L(Close.ts.diff, 1:110)99 2.078e+11 1.950e+11 1.066 0.28857
## L(Close.ts.diff, 1:110)100 3.745e+11 1.956e+11 1.915 0.05766 .
## L(Close.ts.diff, 1:110)101 3.678e+10 2.096e+11 0.175 0.86098
## L(Close.ts.diff, 1:110)102 3.637e+09 1.970e+11 0.018 0.98530
## L(Close.ts.diff, 1:110)103 1.728e+11 1.958e+11 0.882 0.37917
## L(Close.ts.diff, 1:110)104 1.298e+11 1.954e+11 0.664 0.50775
## L(Close.ts.diff, 1:110)105 -1.281e+11 1.946e+11 -0.658 0.51165
## L(Close.ts.diff, 1:110)106 -8.310e+10 1.972e+11 -0.421 0.67415
## L(Close.ts.diff, 1:110)107 -1.727e+11 1.947e+11 -0.887 0.37657
## L(Close.ts.diff, 1:110)108 -1.724e+11 1.944e+11 -0.887 0.37680
## L(Close.ts.diff, 1:110)109 -1.502e+09 1.947e+11 -0.008 0.99386
## L(Close.ts.diff, 1:110)110 1.082e+11 1.946e+11 0.556 0.57925
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.551e+14 on 133 degrees of freedom
## Multiple R-squared: 0.5223, Adjusted R-squared: 0.1128
## F-statistic: 1.276 on 114 and 133 DF, p-value: 0.08804plot_acf_pacf(residuals(ardl.turnover.close.4), "ardl.turnover.close.4")
BASED ON ALL 4 ACF AND PACF GRAPHS MODEL: ardl.turnover.close.1 is the best fitted model since there is no correlation in the residuals and they are centered around 0. This means that there is no misspecification in this model.
Turnover and Open
ACF and PACF show that residuals are within the confidence bound meaning there is no autocorrelation or partial autocorrelation found in the residuals.
ardl.turnover.open.1 <- dynlm(Turnover.ts ~ L(Turnover.ts, 1:4) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.open.1)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4) + L(Open.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.749e+14 -1.200e+14 -4.689e+13 5.768e+13 1.780e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.376e+14 4.187e+13 5.675 3.86e-08 ***
## L(Turnover.ts, 1:4)1 3.277e-01 6.326e-02 5.180 4.59e-07 ***
## L(Turnover.ts, 1:4)2 3.542e-02 6.660e-02 0.532 0.595
## L(Turnover.ts, 1:4)3 -1.833e-02 6.665e-02 -0.275 0.784
## L(Turnover.ts, 1:4)4 8.819e-02 6.338e-02 1.391 0.165
## L(Open.ts.diff, 110) 7.057e+10 1.803e+11 0.391 0.696
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.536e+14 on 248 degrees of freedom
## Multiple R-squared: 0.1267, Adjusted R-squared: 0.1091
## F-statistic: 7.194 on 5 and 248 DF, p-value: 2.624e-06plot_acf_pacf(residuals(ardl.turnover.open.1), "ardl.turnover.open.1")
ACF and PACF show that residuals are within the confidence bound meaning there is no autocorrelation or partial autocorrelation found in the residuals.
ardl.turnover.open.2 <- dynlm(Turnover.ts ~ L(Turnover.ts, 1:4) + L(Open.ts.diff, 35) + L (Open.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.open.2)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 1:4) + L(Open.ts.diff,
## 35) + L(Open.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.740e+14 -1.181e+14 -4.666e+13 5.844e+13 1.779e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.378e+14 4.196e+13 5.667 4.03e-08 ***
## L(Turnover.ts, 1:4)1 3.277e-01 6.338e-02 5.171 4.81e-07 ***
## L(Turnover.ts, 1:4)2 3.482e-02 6.677e-02 0.522 0.602
## L(Turnover.ts, 1:4)3 -1.781e-02 6.681e-02 -0.267 0.790
## L(Turnover.ts, 1:4)4 8.773e-02 6.353e-02 1.381 0.169
## L(Open.ts.diff, 35) -4.377e+10 1.797e+11 -0.244 0.808
## L(Open.ts.diff, 110) 7.082e+10 1.806e+11 0.392 0.695
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.541e+14 on 247 degrees of freedom
## Multiple R-squared: 0.1269, Adjusted R-squared: 0.1057
## F-statistic: 5.982 on 6 and 247 DF, p-value: 7.42e-06plot_acf_pacf(residuals(ardl.turnover.open.2), "ardl.turnover.open.2")
ACF graph shows a few residuals extending outside of the confience bounds, and PACF does not show any significant correlation of residuals but does have long spikes. This is an indicator that there is misspecfication within the model.
ardl.turnover.open.3 <- dynlm(Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,61) + L(Turnover.ts, 75) + L(Turnover.ts,117) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.open.3)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 75) + L(Turnover.ts, 117) + L(Open.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.737e+14 -1.372e+14 -1.935e+13 1.007e+14 1.827e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.040e+13 5.152e+13 1.755 0.08061 .
## L(Turnover.ts, 2) 1.709e-01 5.746e-02 2.974 0.00323 **
## L(Turnover.ts, 61) 2.830e-01 5.774e-02 4.902 1.74e-06 ***
## L(Turnover.ts, 75) 4.284e-02 5.745e-02 0.746 0.45658
## L(Turnover.ts, 117) 2.897e-01 5.788e-02 5.006 1.07e-06 ***
## L(Open.ts.diff, 110) 1.286e+11 1.736e+11 0.741 0.45937
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.44e+14 on 242 degrees of freedom
## Multiple R-squared: 0.2048, Adjusted R-squared: 0.1884
## F-statistic: 12.47 on 5 and 242 DF, p-value: 8.938e-11plot_acf_pacf(residuals(ardl.turnover.open.3), "ardl.turnover.open.3")
ACF graph shows a few residuals extending outside of the confience bounds, and PACF does not show any significant correlation of residuals but does have long spikes. This is an indicator that there is misspecfication within the model.
ardl.turnover.open.4 <- dynlm(Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,61) + L(Turnover.ts, 75) + L(Turnover.ts,117) + L(Open.ts.diff, 35) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.turnover.open.4)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = Turnover.ts ~ L(Turnover.ts, 2) + L(Turnover.ts,
## 61) + L(Turnover.ts, 75) + L(Turnover.ts, 117) + L(Open.ts.diff,
## 35) + L(Open.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.790e+14 -1.361e+14 -2.027e+13 9.983e+13 1.829e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.102e+13 5.163e+13 1.763 0.07918 .
## L(Turnover.ts, 2) 1.701e-01 5.758e-02 2.955 0.00344 **
## L(Turnover.ts, 61) 2.824e-01 5.785e-02 4.882 1.91e-06 ***
## L(Turnover.ts, 75) 4.174e-02 5.760e-02 0.725 0.46938
## L(Turnover.ts, 117) 2.907e-01 5.801e-02 5.011 1.05e-06 ***
## L(Open.ts.diff, 35) -7.722e+10 1.739e+11 -0.444 0.65740
## L(Open.ts.diff, 110) 1.293e+11 1.738e+11 0.744 0.45782
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.444e+14 on 241 degrees of freedom
## Multiple R-squared: 0.2055, Adjusted R-squared: 0.1857
## F-statistic: 10.39 on 6 and 241 DF, p-value: 3.077e-10plot_acf_pacf(residuals(ardl.turnover.open.4), "ardl.turnover.open.4")
BASED ON ALL 4 ACF AND PACF GRAPHS, models ardl.turnover.open.1 and ardl.turnover.open.2 represent the data the best.
Volume and Close
ACF and PACF graph shows that residuals are cenetered around 0 and within the confidence bound, and spikes are short. This means that the residuals are white noise and the model is successfully capturting the data.
ardl.volume.close.1 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff, 110), data = infy_stock)
summary(ardl.volume.close.1)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2655876 -835982 -253740 406222 16602471
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.428e+05 4.000e+05 1.357 0.1762
## L(Volume.ts, 1:32)1 3.211e-01 6.739e-02 4.766 3.42e-06 ***
## L(Volume.ts, 1:32)2 5.738e-02 7.077e-02 0.811 0.4184
## L(Volume.ts, 1:32)3 -4.028e-02 7.105e-02 -0.567 0.5714
## L(Volume.ts, 1:32)4 9.029e-02 7.045e-02 1.282 0.2013
## L(Volume.ts, 1:32)5 2.284e-03 7.043e-02 0.032 0.9742
## L(Volume.ts, 1:32)6 5.138e-02 7.046e-02 0.729 0.4666
## L(Volume.ts, 1:32)7 1.222e-01 7.049e-02 1.733 0.0845 .
## L(Volume.ts, 1:32)8 -2.718e-03 7.091e-02 -0.038 0.9695
## L(Volume.ts, 1:32)9 -6.121e-03 7.072e-02 -0.087 0.9311
## L(Volume.ts, 1:32)10 5.304e-02 7.130e-02 0.744 0.4577
## L(Volume.ts, 1:32)11 -7.402e-02 7.035e-02 -1.052 0.2938
## L(Volume.ts, 1:32)12 1.587e-02 7.050e-02 0.225 0.8221
## L(Volume.ts, 1:32)13 -3.196e-02 7.051e-02 -0.453 0.6508
## L(Volume.ts, 1:32)14 -3.331e-02 7.062e-02 -0.472 0.6376
## L(Volume.ts, 1:32)15 7.403e-02 7.049e-02 1.050 0.2948
## L(Volume.ts, 1:32)16 -3.776e-02 7.078e-02 -0.534 0.5942
## L(Volume.ts, 1:32)17 -1.413e-02 7.114e-02 -0.199 0.8428
## L(Volume.ts, 1:32)18 4.508e-02 7.084e-02 0.636 0.5252
## L(Volume.ts, 1:32)19 -1.906e-02 7.087e-02 -0.269 0.7882
## L(Volume.ts, 1:32)20 1.334e-02 7.086e-02 0.188 0.8508
## L(Volume.ts, 1:32)21 -2.452e-02 7.099e-02 -0.345 0.7301
## L(Volume.ts, 1:32)22 1.536e-02 7.073e-02 0.217 0.8283
## L(Volume.ts, 1:32)23 -6.945e-03 7.063e-02 -0.098 0.9218
## L(Volume.ts, 1:32)24 8.218e-02 7.068e-02 1.163 0.2462
## L(Volume.ts, 1:32)25 3.781e-02 7.105e-02 0.532 0.5952
## L(Volume.ts, 1:32)26 3.019e-02 7.045e-02 0.428 0.6687
## L(Volume.ts, 1:32)27 1.034e-02 7.041e-02 0.147 0.8834
## L(Volume.ts, 1:32)28 -8.898e-02 7.311e-02 -1.217 0.2249
## L(Volume.ts, 1:32)29 1.327e-01 7.052e-02 1.882 0.0611 .
## L(Volume.ts, 1:32)30 -2.937e-02 7.094e-02 -0.414 0.6793
## L(Volume.ts, 1:32)31 3.599e-02 7.102e-02 0.507 0.6128
## L(Volume.ts, 1:32)32 3.964e-02 6.747e-02 0.588 0.5575
## L(Close.ts.diff, 110) -1.808e+02 1.437e+03 -0.126 0.9000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1854000 on 220 degrees of freedom
## Multiple R-squared: 0.268, Adjusted R-squared: 0.1582
## F-statistic: 2.441 on 33 and 220 DF, p-value: 6.89e-05plot_acf_pacf(residuals(ardl.volume.close.1), "ardl.volume.close.1")
ACF and PACF graph shows that residuals are centered around 0 and within the confidence, and spikes are mostly short. In the PACF graph however there are longer spikes. This means that the residuals are white noise and the model is successfully capturing the data.
ardl.volume.close.2 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff, 1:110), data = infy_stock)
summary(ardl.volume.close.2)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Close.ts.diff,
## 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2616765 -664712 -77535 379842 6043927
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.834e+06 7.916e+05 2.317 0.02233 *
## L(Volume.ts, 1:32)1 2.839e-01 9.492e-02 2.991 0.00342 **
## L(Volume.ts, 1:32)2 5.724e-02 9.894e-02 0.579 0.56407
## L(Volume.ts, 1:32)3 -1.020e-01 9.886e-02 -1.032 0.30455
## L(Volume.ts, 1:32)4 9.376e-02 9.862e-02 0.951 0.34381
## L(Volume.ts, 1:32)5 -3.309e-02 9.817e-02 -0.337 0.73669
## L(Volume.ts, 1:32)6 2.138e-01 9.814e-02 2.179 0.03145 *
## L(Volume.ts, 1:32)7 1.283e-01 1.001e-01 1.282 0.20258
## L(Volume.ts, 1:32)8 -5.782e-02 1.004e-01 -0.576 0.56602
## L(Volume.ts, 1:32)9 3.384e-02 9.988e-02 0.339 0.73539
## L(Volume.ts, 1:32)10 3.517e-03 1.010e-01 0.035 0.97228
## L(Volume.ts, 1:32)11 -1.465e-01 9.978e-02 -1.468 0.14488
## L(Volume.ts, 1:32)12 1.599e-03 1.016e-01 0.016 0.98747
## L(Volume.ts, 1:32)13 -1.056e-01 9.988e-02 -1.057 0.29272
## L(Volume.ts, 1:32)14 -1.012e-01 1.004e-01 -1.008 0.31589
## L(Volume.ts, 1:32)15 2.966e-02 1.005e-01 0.295 0.76849
## L(Volume.ts, 1:32)16 -5.455e-02 1.004e-01 -0.543 0.58804
## L(Volume.ts, 1:32)17 6.465e-02 1.006e-01 0.643 0.52163
## L(Volume.ts, 1:32)18 3.846e-02 1.002e-01 0.384 0.70175
## L(Volume.ts, 1:32)19 -3.670e-02 9.987e-02 -0.367 0.71397
## L(Volume.ts, 1:32)20 1.803e-01 9.958e-02 1.811 0.07291 .
## L(Volume.ts, 1:32)21 -6.883e-02 1.007e-01 -0.683 0.49579
## L(Volume.ts, 1:32)22 -5.455e-02 9.966e-02 -0.547 0.58520
## L(Volume.ts, 1:32)23 -8.851e-02 1.000e-01 -0.885 0.37819
## L(Volume.ts, 1:32)24 5.916e-02 1.016e-01 0.582 0.56153
## L(Volume.ts, 1:32)25 4.650e-02 1.016e-01 0.458 0.64813
## L(Volume.ts, 1:32)26 -1.093e-01 1.011e-01 -1.082 0.28163
## L(Volume.ts, 1:32)27 7.259e-03 9.953e-02 0.073 0.94199
## L(Volume.ts, 1:32)28 -8.456e-02 9.970e-02 -0.848 0.39817
## L(Volume.ts, 1:32)29 1.139e-01 9.412e-02 1.211 0.22858
## L(Volume.ts, 1:32)30 -9.664e-03 9.409e-02 -0.103 0.91838
## L(Volume.ts, 1:32)31 -2.868e-02 9.391e-02 -0.305 0.76063
## L(Volume.ts, 1:32)32 1.110e-01 8.762e-02 1.267 0.20769
## L(Close.ts.diff, 1:110)1 -1.462e+02 1.210e+03 -0.121 0.90406
## L(Close.ts.diff, 1:110)2 5.881e+02 1.210e+03 0.486 0.62798
## L(Close.ts.diff, 1:110)3 2.747e+02 1.211e+03 0.227 0.82104
## L(Close.ts.diff, 1:110)4 -1.140e+03 1.212e+03 -0.940 0.34902
## L(Close.ts.diff, 1:110)5 3.560e+02 1.218e+03 0.292 0.77065
## L(Close.ts.diff, 1:110)6 3.366e+03 1.455e+03 2.313 0.02256 *
## L(Close.ts.diff, 1:110)7 -1.147e+03 1.494e+03 -0.768 0.44419
## L(Close.ts.diff, 1:110)8 -1.230e+03 1.494e+03 -0.823 0.41213
## L(Close.ts.diff, 1:110)9 -3.403e+02 1.496e+03 -0.227 0.82051
## L(Close.ts.diff, 1:110)10 -5.076e+02 1.475e+03 -0.344 0.73145
## L(Close.ts.diff, 1:110)11 -8.795e+02 1.475e+03 -0.596 0.55210
## L(Close.ts.diff, 1:110)12 -1.557e+03 1.476e+03 -1.055 0.29377
## L(Close.ts.diff, 1:110)13 8.243e+02 1.476e+03 0.558 0.57775
## L(Close.ts.diff, 1:110)14 1.228e+03 1.481e+03 0.829 0.40889
## L(Close.ts.diff, 1:110)15 -4.525e+01 1.485e+03 -0.030 0.97574
## L(Close.ts.diff, 1:110)16 3.690e+02 1.484e+03 0.249 0.80415
## L(Close.ts.diff, 1:110)17 1.378e+03 1.482e+03 0.930 0.35456
## L(Close.ts.diff, 1:110)18 -3.476e+02 1.487e+03 -0.234 0.81563
## L(Close.ts.diff, 1:110)19 -6.267e+00 1.483e+03 -0.004 0.99664
## L(Close.ts.diff, 1:110)20 -9.261e+01 1.473e+03 -0.063 0.94999
## L(Close.ts.diff, 1:110)21 -7.406e+02 1.473e+03 -0.503 0.61609
## L(Close.ts.diff, 1:110)22 -4.984e+01 1.469e+03 -0.034 0.97299
## L(Close.ts.diff, 1:110)23 -1.833e+03 1.469e+03 -1.248 0.21474
## L(Close.ts.diff, 1:110)24 3.469e+02 1.469e+03 0.236 0.81381
## L(Close.ts.diff, 1:110)25 9.659e+02 1.469e+03 0.658 0.51212
## L(Close.ts.diff, 1:110)26 -9.938e+03 1.471e+03 -6.755 6.86e-10 ***
## L(Close.ts.diff, 1:110)27 1.209e+03 1.761e+03 0.686 0.49399
## L(Close.ts.diff, 1:110)28 3.478e+02 1.763e+03 0.197 0.84400
## L(Close.ts.diff, 1:110)29 3.762e+02 1.762e+03 0.214 0.83129
## L(Close.ts.diff, 1:110)30 -4.712e+02 1.760e+03 -0.268 0.78943
## L(Close.ts.diff, 1:110)31 -2.620e+03 1.760e+03 -1.489 0.13930
## L(Close.ts.diff, 1:110)32 2.837e+03 1.773e+03 1.600 0.11239
## L(Close.ts.diff, 1:110)33 2.161e+02 1.777e+03 0.122 0.90343
## L(Close.ts.diff, 1:110)34 -1.469e+03 1.776e+03 -0.827 0.41016
## L(Close.ts.diff, 1:110)35 -9.850e+02 1.763e+03 -0.559 0.57755
## L(Close.ts.diff, 1:110)36 -7.892e+02 1.769e+03 -0.446 0.65635
## L(Close.ts.diff, 1:110)37 -2.313e+02 1.772e+03 -0.131 0.89638
## L(Close.ts.diff, 1:110)38 -1.650e+03 1.758e+03 -0.939 0.34981
## L(Close.ts.diff, 1:110)39 -4.083e+02 1.670e+03 -0.244 0.80733
## L(Close.ts.diff, 1:110)40 -5.623e+01 1.672e+03 -0.034 0.97324
## L(Close.ts.diff, 1:110)41 -1.010e+03 1.667e+03 -0.606 0.54576
## L(Close.ts.diff, 1:110)42 -1.927e+03 1.670e+03 -1.154 0.25117
## L(Close.ts.diff, 1:110)43 -5.776e+02 1.679e+03 -0.344 0.73151
## L(Close.ts.diff, 1:110)44 9.991e+02 1.674e+03 0.597 0.55177
## L(Close.ts.diff, 1:110)45 4.668e+01 1.663e+03 0.028 0.97766
## L(Close.ts.diff, 1:110)46 1.295e+03 1.662e+03 0.779 0.43751
## L(Close.ts.diff, 1:110)47 -7.589e+02 1.653e+03 -0.459 0.64698
## L(Close.ts.diff, 1:110)48 -6.981e+02 1.652e+03 -0.423 0.67334
## L(Close.ts.diff, 1:110)49 -1.960e+03 1.653e+03 -1.185 0.23838
## L(Close.ts.diff, 1:110)50 -1.290e+03 1.669e+03 -0.773 0.44126
## L(Close.ts.diff, 1:110)51 -8.033e+02 1.673e+03 -0.480 0.63217
## L(Close.ts.diff, 1:110)52 -3.024e+03 1.671e+03 -1.809 0.07310 .
## L(Close.ts.diff, 1:110)53 -2.420e+03 1.689e+03 -1.433 0.15462
## L(Close.ts.diff, 1:110)54 -1.194e+03 1.703e+03 -0.701 0.48488
## L(Close.ts.diff, 1:110)55 5.645e+01 1.665e+03 0.034 0.97301
## L(Close.ts.diff, 1:110)56 -5.048e+01 1.661e+03 -0.030 0.97581
## L(Close.ts.diff, 1:110)57 -1.431e+03 1.656e+03 -0.864 0.38966
## L(Close.ts.diff, 1:110)58 2.823e+03 1.618e+03 1.745 0.08373 .
## L(Close.ts.diff, 1:110)59 6.819e+02 1.479e+03 0.461 0.64563
## L(Close.ts.diff, 1:110)60 -1.525e+02 1.474e+03 -0.103 0.91780
## L(Close.ts.diff, 1:110)61 -6.843e+02 1.471e+03 -0.465 0.64276
## L(Close.ts.diff, 1:110)62 -1.538e+03 1.470e+03 -1.046 0.29762
## L(Close.ts.diff, 1:110)63 -2.373e+02 1.477e+03 -0.161 0.87264
## L(Close.ts.diff, 1:110)64 -3.029e+03 1.474e+03 -2.055 0.04226 *
## L(Close.ts.diff, 1:110)65 -1.621e+03 1.494e+03 -1.085 0.28013
## L(Close.ts.diff, 1:110)66 1.213e+02 1.500e+03 0.081 0.93567
## L(Close.ts.diff, 1:110)67 -1.577e+02 1.492e+03 -0.106 0.91598
## L(Close.ts.diff, 1:110)68 -1.641e+03 1.487e+03 -1.103 0.27242
## L(Close.ts.diff, 1:110)69 8.109e+02 1.491e+03 0.544 0.58754
## L(Close.ts.diff, 1:110)70 -3.972e+02 1.485e+03 -0.268 0.78957
## L(Close.ts.diff, 1:110)71 8.528e+02 1.480e+03 0.576 0.56560
## L(Close.ts.diff, 1:110)72 -1.410e+03 1.482e+03 -0.951 0.34343
## L(Close.ts.diff, 1:110)73 -1.310e+03 1.486e+03 -0.882 0.37976
## L(Close.ts.diff, 1:110)74 6.551e+02 1.500e+03 0.437 0.66315
## L(Close.ts.diff, 1:110)75 -1.075e+03 1.493e+03 -0.720 0.47320
## L(Close.ts.diff, 1:110)76 2.771e+03 1.489e+03 1.861 0.06535 .
## L(Close.ts.diff, 1:110)77 2.118e+02 1.504e+03 0.141 0.88823
## L(Close.ts.diff, 1:110)78 -1.321e+03 1.502e+03 -0.879 0.38108
## L(Close.ts.diff, 1:110)79 -8.237e+02 1.504e+03 -0.548 0.58491
## L(Close.ts.diff, 1:110)80 -1.501e+02 1.503e+03 -0.100 0.92063
## L(Close.ts.diff, 1:110)81 -9.441e+02 1.503e+03 -0.628 0.53116
## L(Close.ts.diff, 1:110)82 -6.434e+03 1.506e+03 -4.274 4.08e-05 ***
## L(Close.ts.diff, 1:110)83 -2.066e+03 1.627e+03 -1.270 0.20674
## L(Close.ts.diff, 1:110)84 -7.141e+02 1.637e+03 -0.436 0.66362
## L(Close.ts.diff, 1:110)85 -1.535e+03 1.619e+03 -0.948 0.34509
## L(Close.ts.diff, 1:110)86 -1.035e+02 1.618e+03 -0.064 0.94913
## L(Close.ts.diff, 1:110)87 -3.230e+02 1.616e+03 -0.200 0.84196
## L(Close.ts.diff, 1:110)88 1.091e+03 1.609e+03 0.678 0.49919
## L(Close.ts.diff, 1:110)89 1.524e+03 1.610e+03 0.947 0.34588
## L(Close.ts.diff, 1:110)90 -3.577e+02 1.607e+03 -0.223 0.82425
## L(Close.ts.diff, 1:110)91 6.251e+02 1.597e+03 0.391 0.69627
## L(Close.ts.diff, 1:110)92 6.443e+02 1.612e+03 0.400 0.69008
## L(Close.ts.diff, 1:110)93 -1.056e+03 1.616e+03 -0.654 0.51466
## L(Close.ts.diff, 1:110)94 -6.949e+02 1.616e+03 -0.430 0.66810
## L(Close.ts.diff, 1:110)95 -1.323e+03 1.623e+03 -0.815 0.41685
## L(Close.ts.diff, 1:110)96 -2.106e+03 1.626e+03 -1.295 0.19786
## L(Close.ts.diff, 1:110)97 2.237e+02 1.635e+03 0.137 0.89143
## L(Close.ts.diff, 1:110)98 -9.916e+02 1.635e+03 -0.606 0.54552
## L(Close.ts.diff, 1:110)99 1.304e+03 1.624e+03 0.803 0.42397
## L(Close.ts.diff, 1:110)100 1.578e+03 1.625e+03 0.971 0.33380
## L(Close.ts.diff, 1:110)101 -1.005e+03 1.612e+03 -0.623 0.53440
## L(Close.ts.diff, 1:110)102 1.229e+03 1.615e+03 0.761 0.44824
## L(Close.ts.diff, 1:110)103 6.648e+02 1.610e+03 0.413 0.68049
## L(Close.ts.diff, 1:110)104 -1.361e+02 1.611e+03 -0.085 0.93280
## L(Close.ts.diff, 1:110)105 -2.105e+03 1.581e+03 -1.331 0.18591
## L(Close.ts.diff, 1:110)106 -1.955e+03 1.592e+03 -1.228 0.22202
## L(Close.ts.diff, 1:110)107 -1.605e+03 1.603e+03 -1.002 0.31866
## L(Close.ts.diff, 1:110)108 -2.038e+03 1.596e+03 -1.277 0.20423
## L(Close.ts.diff, 1:110)109 -8.089e+02 1.566e+03 -0.517 0.60642
## L(Close.ts.diff, 1:110)110 -6.369e+02 1.557e+03 -0.409 0.68322
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1807000 on 111 degrees of freedom
## Multiple R-squared: 0.6492, Adjusted R-squared: 0.2005
## F-statistic: 1.447 on 142 and 111 DF, p-value: 0.02121plot_acf_pacf(residuals(ardl.volume.close.2), "ardl.volume.close.2")
ACF and PACF graph shows that residuals are centered around 0 and within the confidence, and spikes are mostly short. In the PACF graph however there are longer spikes. This means that the residuals are white noise and the model is successfully capturing the data.
ardl.volume.close.3 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts, 91:122) + L(Close.ts.diff, 110), data = infy_stock)
summary(ardl.volume.close.3)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122) + L(Close.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3162262 -836678 -195987 521126 15845331
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.078e+06 9.549e+05 2.176 0.03086 *
## L(Volume.ts, 1:32)1 3.079e-01 7.492e-02 4.110 6.04e-05 ***
## L(Volume.ts, 1:32)2 8.519e-02 7.857e-02 1.084 0.27971
## L(Volume.ts, 1:32)3 -7.064e-02 7.980e-02 -0.885 0.37723
## L(Volume.ts, 1:32)4 4.374e-02 7.981e-02 0.548 0.58433
## L(Volume.ts, 1:32)5 2.636e-02 7.908e-02 0.333 0.73931
## L(Volume.ts, 1:32)6 4.160e-02 7.708e-02 0.540 0.59007
## L(Volume.ts, 1:32)7 9.882e-02 7.685e-02 1.286 0.20016
## L(Volume.ts, 1:32)8 -1.168e-02 7.688e-02 -0.152 0.87942
## L(Volume.ts, 1:32)9 6.567e-03 7.643e-02 0.086 0.93162
## L(Volume.ts, 1:32)10 6.030e-02 7.706e-02 0.782 0.43503
## L(Volume.ts, 1:32)11 -1.064e-01 7.676e-02 -1.387 0.16733
## L(Volume.ts, 1:32)12 3.283e-02 7.709e-02 0.426 0.67069
## L(Volume.ts, 1:32)13 -7.042e-02 7.724e-02 -0.912 0.36312
## L(Volume.ts, 1:32)14 -3.211e-02 7.745e-02 -0.415 0.67899
## L(Volume.ts, 1:32)15 5.738e-02 7.723e-02 0.743 0.45852
## L(Volume.ts, 1:32)16 -3.638e-02 7.757e-02 -0.469 0.63969
## L(Volume.ts, 1:32)17 -3.244e-02 7.787e-02 -0.417 0.67745
## L(Volume.ts, 1:32)18 1.844e-02 7.744e-02 0.238 0.81204
## L(Volume.ts, 1:32)19 6.324e-03 7.746e-02 0.082 0.93503
## L(Volume.ts, 1:32)20 1.090e-02 7.735e-02 0.141 0.88807
## L(Volume.ts, 1:32)21 -2.162e-02 7.788e-02 -0.278 0.78160
## L(Volume.ts, 1:32)22 1.143e-02 7.797e-02 0.147 0.88365
## L(Volume.ts, 1:32)23 3.903e-03 7.776e-02 0.050 0.96002
## L(Volume.ts, 1:32)24 5.468e-02 7.744e-02 0.706 0.48105
## L(Volume.ts, 1:32)25 3.664e-02 7.755e-02 0.472 0.63721
## L(Volume.ts, 1:32)26 3.145e-02 7.672e-02 0.410 0.68233
## L(Volume.ts, 1:32)27 3.461e-02 7.671e-02 0.451 0.65242
## L(Volume.ts, 1:32)28 -8.312e-02 7.972e-02 -1.043 0.29850
## L(Volume.ts, 1:32)29 6.754e-02 7.660e-02 0.882 0.37910
## L(Volume.ts, 1:32)30 3.911e-02 8.053e-02 0.486 0.62783
## L(Volume.ts, 1:32)31 -6.293e-03 8.094e-02 -0.078 0.93812
## L(Volume.ts, 1:32)32 5.716e-02 7.646e-02 0.748 0.45571
## L(Volume.ts, 91:122)91 -6.240e-02 7.642e-02 -0.817 0.41527
## L(Volume.ts, 91:122)92 4.233e-02 8.076e-02 0.524 0.60089
## L(Volume.ts, 91:122)93 -2.370e-02 8.073e-02 -0.294 0.76940
## L(Volume.ts, 91:122)94 8.186e-03 7.669e-02 0.107 0.91512
## L(Volume.ts, 91:122)95 -5.600e-02 7.660e-02 -0.731 0.46568
## L(Volume.ts, 91:122)96 -1.704e-02 7.682e-02 -0.222 0.82472
## L(Volume.ts, 91:122)97 -4.758e-02 7.688e-02 -0.619 0.53682
## L(Volume.ts, 91:122)98 -8.314e-02 7.748e-02 -1.073 0.28473
## L(Volume.ts, 91:122)99 9.454e-02 7.752e-02 1.220 0.22427
## L(Volume.ts, 91:122)100 -6.465e-02 7.813e-02 -0.827 0.40911
## L(Volume.ts, 91:122)101 3.458e-02 7.846e-02 0.441 0.65994
## L(Volume.ts, 91:122)102 1.127e-03 7.769e-02 0.015 0.98845
## L(Volume.ts, 91:122)103 -1.182e-02 7.723e-02 -0.153 0.87857
## L(Volume.ts, 91:122)104 1.468e-02 7.909e-02 0.186 0.85299
## L(Volume.ts, 91:122)105 2.418e-02 7.766e-02 0.311 0.75592
## L(Volume.ts, 91:122)106 -5.411e-02 7.774e-02 -0.696 0.48731
## L(Volume.ts, 91:122)107 4.041e-02 7.773e-02 0.520 0.60375
## L(Volume.ts, 91:122)108 -4.923e-02 7.752e-02 -0.635 0.52616
## L(Volume.ts, 91:122)109 -5.262e-02 7.745e-02 -0.679 0.49774
## L(Volume.ts, 91:122)110 3.794e-02 7.718e-02 0.492 0.62360
## L(Volume.ts, 91:122)111 -1.403e-01 8.131e-02 -1.726 0.08617 .
## L(Volume.ts, 91:122)112 1.460e-02 8.154e-02 0.179 0.85807
## L(Volume.ts, 91:122)113 9.254e-02 8.117e-02 1.140 0.25585
## L(Volume.ts, 91:122)114 -9.978e-02 8.134e-02 -1.227 0.22156
## L(Volume.ts, 91:122)115 -8.866e-02 8.179e-02 -1.084 0.27983
## L(Volume.ts, 91:122)116 6.144e-02 7.700e-02 0.798 0.42600
## L(Volume.ts, 91:122)117 2.540e-01 7.742e-02 3.281 0.00124 **
## L(Volume.ts, 91:122)118 -1.302e-01 7.951e-02 -1.637 0.10333
## L(Volume.ts, 91:122)119 -6.888e-02 8.027e-02 -0.858 0.39197
## L(Volume.ts, 91:122)120 5.118e-02 7.974e-02 0.642 0.52186
## L(Volume.ts, 91:122)121 -2.605e-02 7.892e-02 -0.330 0.74174
## L(Volume.ts, 91:122)122 -5.801e-02 7.499e-02 -0.773 0.44028
## L(Close.ts.diff, 110) -2.788e+02 1.530e+03 -0.182 0.85563
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1890000 on 177 degrees of freedom
## Multiple R-squared: 0.3864, Adjusted R-squared: 0.161
## F-statistic: 1.715 on 65 and 177 DF, p-value: 0.002947plot_acf_pacf(residuals(ardl.volume.close.3), "ardl.volume.close.3")
The ACF graph shows residuals outside confidence bound between 0.05 and 0.06 lags meaning there is serial correlation there. The PACF graph shows this as well and also shows longer spikes than the other model, This means that the model is misspecified.
ardl.volume.close.4 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts, 91:122) + L(Close.ts.diff, 1:110), data = infy_stock)
summary(ardl.volume.close.4)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122) + L(Close.ts.diff, 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2450151 -629268 -161738 590886 5117462
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.953e+06 2.672e+06 1.854 0.068104 .
## L(Volume.ts, 1:32)1 3.387e-01 1.199e-01 2.825 0.006201 **
## L(Volume.ts, 1:32)2 1.105e-02 1.276e-01 0.087 0.931237
## L(Volume.ts, 1:32)3 -1.208e-01 1.309e-01 -0.923 0.359391
## L(Volume.ts, 1:32)4 1.092e-01 1.317e-01 0.829 0.410051
## L(Volume.ts, 1:32)5 -9.374e-02 1.292e-01 -0.726 0.470510
## L(Volume.ts, 1:32)6 2.617e-01 1.293e-01 2.024 0.046865 *
## L(Volume.ts, 1:32)7 5.899e-02 1.320e-01 0.447 0.656323
## L(Volume.ts, 1:32)8 5.241e-02 1.313e-01 0.399 0.691137
## L(Volume.ts, 1:32)9 6.382e-02 1.331e-01 0.479 0.633124
## L(Volume.ts, 1:32)10 -1.797e-03 1.353e-01 -0.013 0.989437
## L(Volume.ts, 1:32)11 -1.139e-01 1.336e-01 -0.853 0.396828
## L(Volume.ts, 1:32)12 -1.645e-02 1.347e-01 -0.122 0.903173
## L(Volume.ts, 1:32)13 -2.077e-02 1.302e-01 -0.160 0.873723
## L(Volume.ts, 1:32)14 -1.528e-01 1.303e-01 -1.173 0.244944
## L(Volume.ts, 1:32)15 8.337e-02 1.312e-01 0.636 0.527121
## L(Volume.ts, 1:32)16 -5.681e-02 1.311e-01 -0.433 0.666158
## L(Volume.ts, 1:32)17 -7.015e-02 1.317e-01 -0.533 0.595884
## L(Volume.ts, 1:32)18 5.269e-02 1.338e-01 0.394 0.694927
## L(Volume.ts, 1:32)19 -1.250e-01 1.323e-01 -0.945 0.348148
## L(Volume.ts, 1:32)20 2.338e-01 1.326e-01 1.764 0.082234 .
## L(Volume.ts, 1:32)21 -1.616e-01 1.365e-01 -1.184 0.240703
## L(Volume.ts, 1:32)22 -4.644e-02 1.363e-01 -0.341 0.734426
## L(Volume.ts, 1:32)23 -4.703e-02 1.345e-01 -0.350 0.727629
## L(Volume.ts, 1:32)24 -2.692e-02 1.318e-01 -0.204 0.838810
## L(Volume.ts, 1:32)25 7.401e-02 1.302e-01 0.569 0.571556
## L(Volume.ts, 1:32)26 -1.817e-01 1.294e-01 -1.404 0.164810
## L(Volume.ts, 1:32)27 1.197e-01 1.270e-01 0.943 0.349006
## L(Volume.ts, 1:32)28 -8.826e-02 1.288e-01 -0.685 0.495577
## L(Volume.ts, 1:32)29 -6.342e-02 1.180e-01 -0.538 0.592649
## L(Volume.ts, 1:32)30 6.081e-02 1.175e-01 0.518 0.606378
## L(Volume.ts, 1:32)31 -9.698e-02 1.190e-01 -0.815 0.417840
## L(Volume.ts, 1:32)32 1.413e-01 1.112e-01 1.271 0.208174
## L(Volume.ts, 91:122)91 5.711e-02 1.049e-01 0.545 0.587761
## L(Volume.ts, 91:122)92 -6.727e-02 1.103e-01 -0.610 0.543802
## L(Volume.ts, 91:122)93 6.234e-02 1.102e-01 0.566 0.573427
## L(Volume.ts, 91:122)94 -1.881e-01 1.103e-01 -1.705 0.092753 .
## L(Volume.ts, 91:122)95 1.742e-02 1.088e-01 0.160 0.873229
## L(Volume.ts, 91:122)96 -1.150e-01 1.097e-01 -1.048 0.298124
## L(Volume.ts, 91:122)97 -4.370e-02 1.105e-01 -0.395 0.693732
## L(Volume.ts, 91:122)98 -6.807e-02 1.100e-01 -0.619 0.538174
## L(Volume.ts, 91:122)99 4.654e-02 1.088e-01 0.428 0.670319
## L(Volume.ts, 91:122)100 -6.340e-02 1.094e-01 -0.580 0.564097
## L(Volume.ts, 91:122)101 -3.195e-02 1.095e-01 -0.292 0.771352
## L(Volume.ts, 91:122)102 8.306e-02 1.092e-01 0.760 0.449614
## L(Volume.ts, 91:122)103 -1.334e-01 1.087e-01 -1.228 0.223774
## L(Volume.ts, 91:122)104 5.985e-02 1.104e-01 0.542 0.589454
## L(Volume.ts, 91:122)105 9.617e-02 1.087e-01 0.885 0.379280
## L(Volume.ts, 91:122)106 -1.286e-01 1.120e-01 -1.149 0.254777
## L(Volume.ts, 91:122)107 1.112e-01 1.142e-01 0.974 0.333699
## L(Volume.ts, 91:122)108 -1.472e-01 1.151e-01 -1.279 0.205108
## L(Volume.ts, 91:122)109 -2.626e-02 1.171e-01 -0.224 0.823274
## L(Volume.ts, 91:122)110 1.753e-01 1.136e-01 1.544 0.127310
## L(Volume.ts, 91:122)111 -1.110e-01 1.191e-01 -0.932 0.354566
## L(Volume.ts, 91:122)112 1.189e-01 1.472e-01 0.808 0.422185
## L(Volume.ts, 91:122)113 -6.881e-02 1.438e-01 -0.478 0.633921
## L(Volume.ts, 91:122)114 -1.011e-02 1.408e-01 -0.072 0.942957
## L(Volume.ts, 91:122)115 -1.743e-01 1.404e-01 -1.241 0.218814
## L(Volume.ts, 91:122)116 6.476e-03 1.364e-01 0.047 0.962271
## L(Volume.ts, 91:122)117 1.531e-01 1.545e-01 0.991 0.325176
## L(Volume.ts, 91:122)118 -1.516e-01 1.534e-01 -0.988 0.326636
## L(Volume.ts, 91:122)119 -1.675e-01 1.559e-01 -1.074 0.286404
## L(Volume.ts, 91:122)120 -5.380e-02 1.554e-01 -0.346 0.730190
## L(Volume.ts, 91:122)121 -4.933e-02 1.532e-01 -0.322 0.748456
## L(Volume.ts, 91:122)122 -4.175e-02 1.295e-01 -0.322 0.748219
## L(Close.ts.diff, 1:110)1 -8.393e+02 2.191e+03 -0.383 0.702853
## L(Close.ts.diff, 1:110)2 2.256e+03 2.159e+03 1.045 0.299786
## L(Close.ts.diff, 1:110)3 -3.011e+02 2.212e+03 -0.136 0.892111
## L(Close.ts.diff, 1:110)4 5.762e+02 2.230e+03 0.258 0.796874
## L(Close.ts.diff, 1:110)5 1.705e+03 2.209e+03 0.772 0.442928
## L(Close.ts.diff, 1:110)6 5.648e+03 3.588e+03 1.574 0.120086
## L(Close.ts.diff, 1:110)7 -8.154e+02 3.695e+03 -0.221 0.825998
## L(Close.ts.diff, 1:110)8 3.707e+03 3.719e+03 0.997 0.322366
## L(Close.ts.diff, 1:110)9 1.053e+03 3.786e+03 0.278 0.781679
## L(Close.ts.diff, 1:110)10 2.840e+03 3.749e+03 0.758 0.451307
## L(Close.ts.diff, 1:110)11 3.009e+02 2.308e+03 0.130 0.896668
## L(Close.ts.diff, 1:110)12 7.292e+02 1.996e+03 0.365 0.715990
## L(Close.ts.diff, 1:110)13 1.733e+03 1.969e+03 0.880 0.381896
## L(Close.ts.diff, 1:110)14 1.099e+03 1.976e+03 0.556 0.579734
## L(Close.ts.diff, 1:110)15 7.498e+02 1.977e+03 0.379 0.705716
## L(Close.ts.diff, 1:110)16 9.805e+02 1.978e+03 0.496 0.621680
## L(Close.ts.diff, 1:110)17 1.407e+03 1.926e+03 0.731 0.467486
## L(Close.ts.diff, 1:110)18 -7.842e+01 1.816e+03 -0.043 0.965685
## L(Close.ts.diff, 1:110)19 9.498e+02 1.802e+03 0.527 0.599906
## L(Close.ts.diff, 1:110)20 1.458e+03 1.782e+03 0.818 0.416089
## L(Close.ts.diff, 1:110)21 -1.678e+02 1.763e+03 -0.095 0.924453
## L(Close.ts.diff, 1:110)22 -4.866e+01 1.759e+03 -0.028 0.978009
## L(Close.ts.diff, 1:110)23 -8.880e+02 1.759e+03 -0.505 0.615301
## L(Close.ts.diff, 1:110)24 6.887e+02 1.740e+03 0.396 0.693553
## L(Close.ts.diff, 1:110)25 1.736e+03 1.729e+03 1.004 0.318737
## L(Close.ts.diff, 1:110)26 -1.072e+04 1.754e+03 -6.114 5.36e-08 ***
## L(Close.ts.diff, 1:110)27 3.316e+03 2.238e+03 1.482 0.143002
## L(Close.ts.diff, 1:110)28 1.805e+02 2.250e+03 0.080 0.936286
## L(Close.ts.diff, 1:110)29 3.777e+02 2.289e+03 0.165 0.869408
## L(Close.ts.diff, 1:110)30 3.503e+02 2.299e+03 0.152 0.879333
## L(Close.ts.diff, 1:110)31 -1.687e+03 2.333e+03 -0.723 0.472175
## L(Close.ts.diff, 1:110)32 4.818e+03 2.356e+03 2.045 0.044730 *
## L(Close.ts.diff, 1:110)33 4.828e+02 2.422e+03 0.199 0.842624
## L(Close.ts.diff, 1:110)34 2.063e+03 2.425e+03 0.851 0.397778
## L(Close.ts.diff, 1:110)35 1.453e+03 2.419e+03 0.601 0.549904
## L(Close.ts.diff, 1:110)36 6.778e+01 2.506e+03 0.027 0.978505
## L(Close.ts.diff, 1:110)37 1.323e+03 2.457e+03 0.539 0.591836
## L(Close.ts.diff, 1:110)38 -7.929e+02 2.464e+03 -0.322 0.748629
## L(Close.ts.diff, 1:110)39 3.266e+03 2.283e+03 1.431 0.157074
## L(Close.ts.diff, 1:110)40 4.758e+02 2.264e+03 0.210 0.834196
## L(Close.ts.diff, 1:110)41 1.013e+03 2.284e+03 0.444 0.658740
## L(Close.ts.diff, 1:110)42 -3.978e+02 2.226e+03 -0.179 0.858720
## L(Close.ts.diff, 1:110)43 -1.148e+03 2.246e+03 -0.511 0.610983
## L(Close.ts.diff, 1:110)44 2.125e+03 2.231e+03 0.952 0.344290
## L(Close.ts.diff, 1:110)45 1.455e+02 2.225e+03 0.065 0.948048
## L(Close.ts.diff, 1:110)46 3.478e+03 2.207e+03 1.576 0.119756
## L(Close.ts.diff, 1:110)47 -1.565e+03 2.249e+03 -0.696 0.488791
## L(Close.ts.diff, 1:110)48 -2.593e+01 2.257e+03 -0.011 0.990867
## L(Close.ts.diff, 1:110)49 -8.677e+02 2.211e+03 -0.392 0.695994
## L(Close.ts.diff, 1:110)50 -1.951e+03 2.213e+03 -0.882 0.381134
## L(Close.ts.diff, 1:110)51 1.092e+03 2.193e+03 0.498 0.620204
## L(Close.ts.diff, 1:110)52 -4.137e+03 2.188e+03 -1.891 0.062924 .
## L(Close.ts.diff, 1:110)53 1.545e+02 2.249e+03 0.069 0.945451
## L(Close.ts.diff, 1:110)54 2.292e+02 2.243e+03 0.102 0.918898
## L(Close.ts.diff, 1:110)55 -2.372e+03 2.134e+03 -1.111 0.270272
## L(Close.ts.diff, 1:110)56 1.086e+03 2.198e+03 0.494 0.622696
## L(Close.ts.diff, 1:110)57 -2.077e+03 2.295e+03 -0.905 0.368713
## L(Close.ts.diff, 1:110)58 4.068e+03 2.145e+03 1.896 0.062180 .
## L(Close.ts.diff, 1:110)59 5.600e+02 1.971e+03 0.284 0.777210
## L(Close.ts.diff, 1:110)60 7.366e+02 1.956e+03 0.376 0.707721
## L(Close.ts.diff, 1:110)61 -3.065e+01 1.958e+03 -0.016 0.987556
## L(Close.ts.diff, 1:110)62 -2.949e+03 2.048e+03 -1.440 0.154403
## L(Close.ts.diff, 1:110)63 8.277e+02 2.085e+03 0.397 0.692555
## L(Close.ts.diff, 1:110)64 -1.286e+03 2.078e+03 -0.619 0.538137
## L(Close.ts.diff, 1:110)65 1.826e+02 2.051e+03 0.089 0.929314
## L(Close.ts.diff, 1:110)66 8.585e+02 2.035e+03 0.422 0.674460
## L(Close.ts.diff, 1:110)67 -2.610e+02 1.923e+03 -0.136 0.892437
## L(Close.ts.diff, 1:110)68 -1.806e+03 1.797e+03 -1.005 0.318505
## L(Close.ts.diff, 1:110)69 6.626e+02 1.802e+03 0.368 0.714226
## L(Close.ts.diff, 1:110)70 2.690e+02 1.792e+03 0.150 0.881140
## L(Close.ts.diff, 1:110)71 1.100e+03 1.766e+03 0.623 0.535463
## L(Close.ts.diff, 1:110)72 -1.234e+03 1.753e+03 -0.704 0.483730
## L(Close.ts.diff, 1:110)73 -1.026e+03 1.757e+03 -0.584 0.561082
## L(Close.ts.diff, 1:110)74 -4.279e+00 1.788e+03 -0.002 0.998098
## L(Close.ts.diff, 1:110)75 -2.122e+01 1.786e+03 -0.012 0.990553
## L(Close.ts.diff, 1:110)76 3.120e+03 1.776e+03 1.757 0.083411 .
## L(Close.ts.diff, 1:110)77 4.751e+02 1.818e+03 0.261 0.794631
## L(Close.ts.diff, 1:110)78 -7.639e+02 1.815e+03 -0.421 0.675254
## L(Close.ts.diff, 1:110)79 -8.090e+02 1.821e+03 -0.444 0.658203
## L(Close.ts.diff, 1:110)80 -3.270e+02 1.822e+03 -0.179 0.858080
## L(Close.ts.diff, 1:110)81 -1.701e+03 1.827e+03 -0.931 0.354968
## L(Close.ts.diff, 1:110)82 -6.581e+03 1.856e+03 -3.546 0.000713 ***
## L(Close.ts.diff, 1:110)83 -8.662e+02 2.020e+03 -0.429 0.669378
## L(Close.ts.diff, 1:110)84 -2.531e+03 2.020e+03 -1.253 0.214449
## L(Close.ts.diff, 1:110)85 -2.127e+03 2.015e+03 -1.056 0.294770
## L(Close.ts.diff, 1:110)86 -2.249e+01 2.025e+03 -0.011 0.991169
## L(Close.ts.diff, 1:110)87 -1.378e+03 2.002e+03 -0.688 0.493670
## L(Close.ts.diff, 1:110)88 2.165e+03 1.976e+03 1.096 0.276940
## L(Close.ts.diff, 1:110)89 9.805e+01 1.965e+03 0.050 0.960356
## L(Close.ts.diff, 1:110)90 1.031e+03 1.959e+03 0.526 0.600394
## L(Close.ts.diff, 1:110)91 1.291e+03 1.966e+03 0.657 0.513507
## L(Close.ts.diff, 1:110)92 1.087e+03 1.962e+03 0.554 0.581304
## L(Close.ts.diff, 1:110)93 1.606e+02 1.958e+03 0.082 0.934882
## L(Close.ts.diff, 1:110)94 -1.090e+03 2.002e+03 -0.544 0.587938
## L(Close.ts.diff, 1:110)95 1.053e+03 2.001e+03 0.526 0.600533
## L(Close.ts.diff, 1:110)96 -2.277e+03 1.995e+03 -1.142 0.257574
## L(Close.ts.diff, 1:110)97 1.128e+03 2.040e+03 0.553 0.582026
## L(Close.ts.diff, 1:110)98 -6.654e+02 2.001e+03 -0.333 0.740472
## L(Close.ts.diff, 1:110)99 1.019e+03 1.951e+03 0.522 0.603052
## L(Close.ts.diff, 1:110)100 2.804e+03 1.933e+03 1.451 0.151482
## L(Close.ts.diff, 1:110)101 -2.683e+03 1.892e+03 -1.418 0.160785
## L(Close.ts.diff, 1:110)102 1.914e+03 1.933e+03 0.990 0.325466
## L(Close.ts.diff, 1:110)103 -3.829e+00 1.938e+03 -0.002 0.998429
## L(Close.ts.diff, 1:110)104 -6.315e+02 1.932e+03 -0.327 0.744804
## L(Close.ts.diff, 1:110)105 -1.105e+03 1.876e+03 -0.589 0.557622
## L(Close.ts.diff, 1:110)106 -2.065e+03 1.883e+03 -1.097 0.276677
## L(Close.ts.diff, 1:110)107 -1.550e+03 1.909e+03 -0.812 0.419686
## L(Close.ts.diff, 1:110)108 -3.232e+03 1.901e+03 -1.700 0.093710 .
## L(Close.ts.diff, 1:110)109 3.884e+02 1.889e+03 0.206 0.837679
## L(Close.ts.diff, 1:110)110 -4.634e+02 1.891e+03 -0.245 0.807154
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1917000 on 68 degrees of freedom
## Multiple R-squared: 0.7575, Adjusted R-squared: 0.1369
## F-statistic: 1.221 on 174 and 68 DF, p-value: 0.1738plot_acf_pacf(residuals(ardl.volume.close.4), "ardl.volume.close.4")
Based on ALL 4 ACF and PACF graphs, model ardl.volume.close.1 represents the data the best.
Volume and Open
ACF and PACF graph shows that residuals are centered around 0 and within the confidence bound, and spikes are short. This means that the residuals are white noise and the model is successfully capturing the data.
ardl.volume.open.1 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.volume.open.1)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Open.ts.diff,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2622514 -846166 -262527 432638 16612825
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.486e+05 3.997e+05 1.372 0.1713
## L(Volume.ts, 1:32)1 3.214e-01 6.738e-02 4.770 3.35e-06 ***
## L(Volume.ts, 1:32)2 5.707e-02 7.077e-02 0.806 0.4209
## L(Volume.ts, 1:32)3 -4.049e-02 7.095e-02 -0.571 0.5688
## L(Volume.ts, 1:32)4 9.003e-02 7.044e-02 1.278 0.2026
## L(Volume.ts, 1:32)5 1.597e-03 7.047e-02 0.023 0.9819
## L(Volume.ts, 1:32)6 5.137e-02 7.042e-02 0.730 0.4664
## L(Volume.ts, 1:32)7 1.236e-01 7.070e-02 1.748 0.0819 .
## L(Volume.ts, 1:32)8 -3.481e-03 7.097e-02 -0.049 0.9609
## L(Volume.ts, 1:32)9 -6.644e-03 7.073e-02 -0.094 0.9252
## L(Volume.ts, 1:32)10 5.447e-02 7.128e-02 0.764 0.4456
## L(Volume.ts, 1:32)11 -7.348e-02 7.037e-02 -1.044 0.2975
## L(Volume.ts, 1:32)12 1.580e-02 7.049e-02 0.224 0.8228
## L(Volume.ts, 1:32)13 -3.200e-02 7.049e-02 -0.454 0.6503
## L(Volume.ts, 1:32)14 -3.337e-02 7.053e-02 -0.473 0.6366
## L(Volume.ts, 1:32)15 7.360e-02 7.050e-02 1.044 0.2977
## L(Volume.ts, 1:32)16 -3.783e-02 7.072e-02 -0.535 0.5933
## L(Volume.ts, 1:32)17 -1.469e-02 7.114e-02 -0.207 0.8366
## L(Volume.ts, 1:32)18 4.622e-02 7.096e-02 0.651 0.5155
## L(Volume.ts, 1:32)19 -1.960e-02 7.086e-02 -0.277 0.7823
## L(Volume.ts, 1:32)20 1.328e-02 7.083e-02 0.188 0.8514
## L(Volume.ts, 1:32)21 -2.454e-02 7.085e-02 -0.346 0.7294
## L(Volume.ts, 1:32)22 1.593e-02 7.067e-02 0.225 0.8219
## L(Volume.ts, 1:32)23 -7.492e-03 7.061e-02 -0.106 0.9156
## L(Volume.ts, 1:32)24 8.295e-02 7.074e-02 1.173 0.2422
## L(Volume.ts, 1:32)25 3.720e-02 7.103e-02 0.524 0.6010
## L(Volume.ts, 1:32)26 3.017e-02 7.044e-02 0.428 0.6689
## L(Volume.ts, 1:32)27 1.040e-02 7.040e-02 0.148 0.8827
## L(Volume.ts, 1:32)28 -9.240e-02 7.360e-02 -1.255 0.2107
## L(Volume.ts, 1:32)29 1.339e-01 7.065e-02 1.895 0.0594 .
## L(Volume.ts, 1:32)30 -2.942e-02 7.085e-02 -0.415 0.6784
## L(Volume.ts, 1:32)31 3.618e-02 7.081e-02 0.511 0.6099
## L(Volume.ts, 1:32)32 3.936e-02 6.740e-02 0.584 0.5599
## L(Open.ts.diff, 110) -3.881e+02 1.416e+03 -0.274 0.7843
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1854000 on 220 degrees of freedom
## Multiple R-squared: 0.2682, Adjusted R-squared: 0.1584
## F-statistic: 2.443 on 33 and 220 DF, p-value: 6.762e-05plot_acf_pacf(residuals(ardl.volume.open.1), "ardl.volume.open.1")
ACF and PACF graph shows that residuals are centered around 0 and within the confidence bound, and spikes are short. This means that the residuals are white noise and the model is successfully capturing the data.
ardl.volume.open.2 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Open.ts.diff, 35) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.volume.open.2)##
## Time series regression with "ts" data:
## Start = 2015(112), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Open.ts.diff,
## 35) + L(Open.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2548149 -798757 -270064 411072 16666155
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.674e+05 4.003e+05 1.418 0.1577
## L(Volume.ts, 1:32)1 3.202e-01 6.741e-02 4.750 3.67e-06 ***
## L(Volume.ts, 1:32)2 5.517e-02 7.081e-02 0.779 0.4367
## L(Volume.ts, 1:32)3 -3.899e-02 7.098e-02 -0.549 0.5833
## L(Volume.ts, 1:32)4 8.428e-02 7.070e-02 1.192 0.2346
## L(Volume.ts, 1:32)5 2.376e-03 7.049e-02 0.034 0.9731
## L(Volume.ts, 1:32)6 5.203e-02 7.043e-02 0.739 0.4608
## L(Volume.ts, 1:32)7 1.265e-01 7.078e-02 1.788 0.0752 .
## L(Volume.ts, 1:32)8 3.990e-04 7.109e-02 0.006 0.9955
## L(Volume.ts, 1:32)9 -4.135e-02 7.936e-02 -0.521 0.6029
## L(Volume.ts, 1:32)10 6.773e-02 7.261e-02 0.933 0.3519
## L(Volume.ts, 1:32)11 -6.702e-02 7.070e-02 -0.948 0.3442
## L(Volume.ts, 1:32)12 1.041e-02 7.073e-02 0.147 0.8832
## L(Volume.ts, 1:32)13 -2.987e-02 7.054e-02 -0.423 0.6724
## L(Volume.ts, 1:32)14 -3.572e-02 7.059e-02 -0.506 0.6133
## L(Volume.ts, 1:32)15 7.614e-02 7.057e-02 1.079 0.2818
## L(Volume.ts, 1:32)16 -3.192e-02 7.100e-02 -0.450 0.6535
## L(Volume.ts, 1:32)17 -1.889e-02 7.128e-02 -0.265 0.7912
## L(Volume.ts, 1:32)18 4.770e-02 7.099e-02 0.672 0.5024
## L(Volume.ts, 1:32)19 -1.582e-02 7.097e-02 -0.223 0.8238
## L(Volume.ts, 1:32)20 1.197e-02 7.086e-02 0.169 0.8660
## L(Volume.ts, 1:32)21 -2.325e-02 7.087e-02 -0.328 0.7432
## L(Volume.ts, 1:32)22 1.447e-02 7.069e-02 0.205 0.8380
## L(Volume.ts, 1:32)23 -1.235e-02 7.080e-02 -0.174 0.8617
## L(Volume.ts, 1:32)24 8.552e-02 7.080e-02 1.208 0.2284
## L(Volume.ts, 1:32)25 3.449e-02 7.109e-02 0.485 0.6281
## L(Volume.ts, 1:32)26 3.335e-02 7.053e-02 0.473 0.6368
## L(Volume.ts, 1:32)27 8.895e-03 7.042e-02 0.126 0.8996
## L(Volume.ts, 1:32)28 -9.694e-02 7.376e-02 -1.314 0.1902
## L(Volume.ts, 1:32)29 1.501e-01 7.262e-02 2.066 0.0400 *
## L(Volume.ts, 1:32)30 -3.257e-02 7.094e-02 -0.459 0.6466
## L(Volume.ts, 1:32)31 3.462e-02 7.083e-02 0.489 0.6255
## L(Volume.ts, 1:32)32 4.068e-02 6.743e-02 0.603 0.5469
## L(Open.ts.diff, 35) -1.474e+03 1.528e+03 -0.965 0.3358
## L(Open.ts.diff, 110) -4.603e+02 1.419e+03 -0.324 0.7459
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1854000 on 219 degrees of freedom
## Multiple R-squared: 0.2713, Adjusted R-squared: 0.1582
## F-statistic: 2.398 on 34 and 219 DF, p-value: 8.15e-05plot_acf_pacf(residuals(ardl.volume.open.2), "ardl.volume.open.2")
ACF and PACF graph shows that residuals are centered around 0 and within the confidence, and spikes are mostly short. In the PACF graph however there are longer spikes. This means that the residuals are white noise and the model is successfully capturing the data.
ardl.volume.open.3 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts, 91:122) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.volume.open.3)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122) + L(Open.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3154747 -835633 -192877 519592 15851812
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.081e+06 9.535e+05 2.182 0.03042 *
## L(Volume.ts, 1:32)1 3.085e-01 7.496e-02 4.116 5.91e-05 ***
## L(Volume.ts, 1:32)2 8.421e-02 7.870e-02 1.070 0.28602
## L(Volume.ts, 1:32)3 -7.088e-02 7.969e-02 -0.889 0.37497
## L(Volume.ts, 1:32)4 4.391e-02 7.981e-02 0.550 0.58290
## L(Volume.ts, 1:32)5 2.560e-02 7.914e-02 0.324 0.74670
## L(Volume.ts, 1:32)6 4.145e-02 7.702e-02 0.538 0.59115
## L(Volume.ts, 1:32)7 1.002e-01 7.704e-02 1.300 0.19520
## L(Volume.ts, 1:32)8 -1.237e-02 7.692e-02 -0.161 0.87241
## L(Volume.ts, 1:32)9 6.278e-03 7.643e-02 0.082 0.93463
## L(Volume.ts, 1:32)10 6.122e-02 7.703e-02 0.795 0.42779
## L(Volume.ts, 1:32)11 -1.055e-01 7.680e-02 -1.374 0.17119
## L(Volume.ts, 1:32)12 3.269e-02 7.708e-02 0.424 0.67204
## L(Volume.ts, 1:32)13 -7.063e-02 7.722e-02 -0.915 0.36165
## L(Volume.ts, 1:32)14 -3.175e-02 7.735e-02 -0.410 0.68199
## L(Volume.ts, 1:32)15 5.666e-02 7.727e-02 0.733 0.46439
## L(Volume.ts, 1:32)16 -3.639e-02 7.756e-02 -0.469 0.63949
## L(Volume.ts, 1:32)17 -3.313e-02 7.792e-02 -0.425 0.67121
## L(Volume.ts, 1:32)18 1.984e-02 7.759e-02 0.256 0.79850
## L(Volume.ts, 1:32)19 5.470e-03 7.742e-02 0.071 0.94376
## L(Volume.ts, 1:32)20 1.098e-02 7.732e-02 0.142 0.88728
## L(Volume.ts, 1:32)21 -2.210e-02 7.770e-02 -0.284 0.77640
## L(Volume.ts, 1:32)22 1.274e-02 7.806e-02 0.163 0.87056
## L(Volume.ts, 1:32)23 2.844e-03 7.783e-02 0.037 0.97089
## L(Volume.ts, 1:32)24 5.575e-02 7.759e-02 0.718 0.47340
## L(Volume.ts, 1:32)25 3.632e-02 7.744e-02 0.469 0.63960
## L(Volume.ts, 1:32)26 3.107e-02 7.673e-02 0.405 0.68604
## L(Volume.ts, 1:32)27 3.538e-02 7.678e-02 0.461 0.64551
## L(Volume.ts, 1:32)28 -8.622e-02 8.072e-02 -1.068 0.28691
## L(Volume.ts, 1:32)29 6.903e-02 7.691e-02 0.898 0.37061
## L(Volume.ts, 1:32)30 3.856e-02 8.045e-02 0.479 0.63234
## L(Volume.ts, 1:32)31 -5.650e-03 8.068e-02 -0.070 0.94425
## L(Volume.ts, 1:32)32 5.668e-02 7.637e-02 0.742 0.45897
## L(Volume.ts, 91:122)91 -6.199e-02 7.643e-02 -0.811 0.41844
## L(Volume.ts, 91:122)92 4.167e-02 8.080e-02 0.516 0.60673
## L(Volume.ts, 91:122)93 -2.367e-02 8.070e-02 -0.293 0.76963
## L(Volume.ts, 91:122)94 8.407e-03 7.663e-02 0.110 0.91277
## L(Volume.ts, 91:122)95 -5.569e-02 7.659e-02 -0.727 0.46816
## L(Volume.ts, 91:122)96 -1.711e-02 7.674e-02 -0.223 0.82384
## L(Volume.ts, 91:122)97 -4.800e-02 7.688e-02 -0.624 0.53320
## L(Volume.ts, 91:122)98 -8.314e-02 7.743e-02 -1.074 0.28436
## L(Volume.ts, 91:122)99 9.407e-02 7.750e-02 1.214 0.22644
## L(Volume.ts, 91:122)100 -6.515e-02 7.816e-02 -0.834 0.40562
## L(Volume.ts, 91:122)101 3.534e-02 7.853e-02 0.450 0.65325
## L(Volume.ts, 91:122)102 5.435e-04 7.773e-02 0.007 0.99443
## L(Volume.ts, 91:122)103 -1.191e-02 7.719e-02 -0.154 0.87752
## L(Volume.ts, 91:122)104 1.611e-02 7.897e-02 0.204 0.83857
## L(Volume.ts, 91:122)105 2.384e-02 7.765e-02 0.307 0.75919
## L(Volume.ts, 91:122)106 -5.431e-02 7.771e-02 -0.699 0.48555
## L(Volume.ts, 91:122)107 4.166e-02 7.789e-02 0.535 0.59336
## L(Volume.ts, 91:122)108 -5.032e-02 7.767e-02 -0.648 0.51795
## L(Volume.ts, 91:122)109 -5.208e-02 7.744e-02 -0.673 0.50212
## L(Volume.ts, 91:122)110 3.705e-02 7.729e-02 0.479 0.63225
## L(Volume.ts, 91:122)111 -1.404e-01 8.130e-02 -1.727 0.08591 .
## L(Volume.ts, 91:122)112 1.465e-02 8.150e-02 0.180 0.85756
## L(Volume.ts, 91:122)113 9.189e-02 8.120e-02 1.132 0.25930
## L(Volume.ts, 91:122)114 -9.942e-02 8.135e-02 -1.222 0.22330
## L(Volume.ts, 91:122)115 -8.935e-02 8.180e-02 -1.092 0.27619
## L(Volume.ts, 91:122)116 6.274e-02 7.722e-02 0.813 0.41755
## L(Volume.ts, 91:122)117 2.531e-01 7.752e-02 3.265 0.00132 **
## L(Volume.ts, 91:122)118 -1.304e-01 7.949e-02 -1.641 0.10264
## L(Volume.ts, 91:122)119 -6.804e-02 8.034e-02 -0.847 0.39820
## L(Volume.ts, 91:122)120 5.194e-02 7.980e-02 0.651 0.51594
## L(Volume.ts, 91:122)121 -2.678e-02 7.894e-02 -0.339 0.73488
## L(Volume.ts, 91:122)122 -5.760e-02 7.498e-02 -0.768 0.44339
## L(Open.ts.diff, 110) -4.233e+02 1.519e+03 -0.279 0.78090
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1890000 on 177 degrees of freedom
## Multiple R-squared: 0.3865, Adjusted R-squared: 0.1612
## F-statistic: 1.716 on 65 and 177 DF, p-value: 0.002916plot_acf_pacf(residuals(ardl.volume.open.3), "ardl.volume.open.3")
ACF and PACF graph shows that residuals are centered around 0 and within the confidence, and spikes are mostly short. In the PACF graph however there are longer spikes. This means that the residuals are white noise and the model is successfully capturing the data.
ardl.volume.open.4 <- dynlm(Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts, 91:122) + L(Open.ts.diff, 35) + L(Open.ts.diff, 110), data = infy_stock)
summary(ardl.volume.open.4)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = Volume.ts ~ L(Volume.ts, 1:32) + L(Volume.ts,
## 91:122) + L(Open.ts.diff, 35) + L(Open.ts.diff, 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3155009 -835609 -193015 519767 15851545
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.081e+06 9.638e+05 2.159 0.03218 *
## L(Volume.ts, 1:32)1 3.085e-01 7.520e-02 4.103 6.23e-05 ***
## L(Volume.ts, 1:32)2 8.422e-02 7.898e-02 1.066 0.28774
## L(Volume.ts, 1:32)3 -7.088e-02 7.993e-02 -0.887 0.37642
## L(Volume.ts, 1:32)4 4.392e-02 8.014e-02 0.548 0.58440
## L(Volume.ts, 1:32)5 2.560e-02 7.937e-02 0.323 0.74738
## L(Volume.ts, 1:32)6 4.145e-02 7.725e-02 0.537 0.59228
## L(Volume.ts, 1:32)7 1.002e-01 7.741e-02 1.294 0.19742
## L(Volume.ts, 1:32)8 -1.239e-02 7.740e-02 -0.160 0.87304
## L(Volume.ts, 1:32)9 6.385e-03 8.755e-02 0.073 0.94195
## L(Volume.ts, 1:32)10 6.118e-02 7.901e-02 0.774 0.43978
## L(Volume.ts, 1:32)11 -1.055e-01 7.747e-02 -1.362 0.17481
## L(Volume.ts, 1:32)12 3.270e-02 7.751e-02 0.422 0.67361
## L(Volume.ts, 1:32)13 -7.064e-02 7.769e-02 -0.909 0.36446
## L(Volume.ts, 1:32)14 -3.174e-02 7.763e-02 -0.409 0.68315
## L(Volume.ts, 1:32)15 5.665e-02 7.764e-02 0.730 0.46662
## L(Volume.ts, 1:32)16 -3.641e-02 7.792e-02 -0.467 0.64094
## L(Volume.ts, 1:32)17 -3.312e-02 7.825e-02 -0.423 0.67260
## L(Volume.ts, 1:32)18 1.983e-02 7.785e-02 0.255 0.79922
## L(Volume.ts, 1:32)19 5.455e-03 7.786e-02 0.070 0.94422
## L(Volume.ts, 1:32)20 1.098e-02 7.755e-02 0.142 0.88758
## L(Volume.ts, 1:32)21 -2.211e-02 7.795e-02 -0.284 0.77705
## L(Volume.ts, 1:32)22 1.274e-02 7.828e-02 0.163 0.87091
## L(Volume.ts, 1:32)23 2.859e-03 7.829e-02 0.037 0.97091
## L(Volume.ts, 1:32)24 5.574e-02 7.797e-02 0.715 0.47563
## L(Volume.ts, 1:32)25 3.633e-02 7.770e-02 0.468 0.64068
## L(Volume.ts, 1:32)26 3.106e-02 7.704e-02 0.403 0.68731
## L(Volume.ts, 1:32)27 3.539e-02 7.706e-02 0.459 0.64663
## L(Volume.ts, 1:32)28 -8.621e-02 8.105e-02 -1.064 0.28893
## L(Volume.ts, 1:32)29 6.899e-02 7.912e-02 0.872 0.38445
## L(Volume.ts, 1:32)30 3.857e-02 8.085e-02 0.477 0.63392
## L(Volume.ts, 1:32)31 -5.650e-03 8.091e-02 -0.070 0.94441
## L(Volume.ts, 1:32)32 5.668e-02 7.663e-02 0.740 0.46055
## L(Volume.ts, 91:122)91 -6.200e-02 7.678e-02 -0.807 0.42047
## L(Volume.ts, 91:122)92 4.168e-02 8.114e-02 0.514 0.60815
## L(Volume.ts, 91:122)93 -2.367e-02 8.094e-02 -0.292 0.77032
## L(Volume.ts, 91:122)94 8.405e-03 7.685e-02 0.109 0.91303
## L(Volume.ts, 91:122)95 -5.569e-02 7.684e-02 -0.725 0.46955
## L(Volume.ts, 91:122)96 -1.711e-02 7.696e-02 -0.222 0.82436
## L(Volume.ts, 91:122)97 -4.803e-02 7.797e-02 -0.616 0.53870
## L(Volume.ts, 91:122)98 -8.314e-02 7.767e-02 -1.070 0.28590
## L(Volume.ts, 91:122)99 9.408e-02 7.774e-02 1.210 0.22783
## L(Volume.ts, 91:122)100 -6.516e-02 7.847e-02 -0.830 0.40744
## L(Volume.ts, 91:122)101 3.535e-02 7.891e-02 0.448 0.65469
## L(Volume.ts, 91:122)102 5.372e-04 7.799e-02 0.007 0.99451
## L(Volume.ts, 91:122)103 -1.191e-02 7.746e-02 -0.154 0.87801
## L(Volume.ts, 91:122)104 1.611e-02 7.923e-02 0.203 0.83915
## L(Volume.ts, 91:122)105 2.384e-02 7.787e-02 0.306 0.75987
## L(Volume.ts, 91:122)106 -5.431e-02 7.794e-02 -0.697 0.48690
## L(Volume.ts, 91:122)107 4.167e-02 7.818e-02 0.533 0.59467
## L(Volume.ts, 91:122)108 -5.033e-02 7.804e-02 -0.645 0.51984
## L(Volume.ts, 91:122)109 -5.208e-02 7.766e-02 -0.671 0.50334
## L(Volume.ts, 91:122)110 3.705e-02 7.752e-02 0.478 0.63333
## L(Volume.ts, 91:122)111 -1.404e-01 8.161e-02 -1.720 0.08710 .
## L(Volume.ts, 91:122)112 1.466e-02 8.185e-02 0.179 0.85806
## L(Volume.ts, 91:122)113 9.190e-02 8.147e-02 1.128 0.26085
## L(Volume.ts, 91:122)114 -9.941e-02 8.158e-02 -1.219 0.22462
## L(Volume.ts, 91:122)115 -8.935e-02 8.204e-02 -1.089 0.27762
## L(Volume.ts, 91:122)116 6.273e-02 7.754e-02 0.809 0.41961
## L(Volume.ts, 91:122)117 2.531e-01 7.777e-02 3.254 0.00136 **
## L(Volume.ts, 91:122)118 -1.304e-01 7.972e-02 -1.636 0.10362
## L(Volume.ts, 91:122)119 -6.807e-02 8.131e-02 -0.837 0.40363
## L(Volume.ts, 91:122)120 5.195e-02 8.014e-02 0.648 0.51765
## L(Volume.ts, 91:122)121 -2.679e-02 7.926e-02 -0.338 0.73582
## L(Volume.ts, 91:122)122 -5.762e-02 7.548e-02 -0.763 0.44626
## L(Open.ts.diff, 35) 4.193e+00 1.658e+03 0.003 0.99799
## L(Open.ts.diff, 110) -4.230e+02 1.527e+03 -0.277 0.78209
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1895000 on 176 degrees of freedom
## Multiple R-squared: 0.3865, Adjusted R-squared: 0.1565
## F-statistic: 1.68 on 66 and 176 DF, p-value: 0.003931plot_acf_pacf(residuals(ardl.volume.open.4), "ardl.volume.open.4")
Based on all 4 ACF and PACF graphs, models ardl.volume.open.1 and ardl.volume.open.2 are the best fits for the data.
Training and Testing for ARDL models
Turnover and Close
Size
train_size.Turnover.ardl <- floor (2/3 * length(Turnover.ts))
train_size.Close.diff.ardl <- floor (2/3 * length(Close.ts.diff))Data
train_data.Turnover.ardl <- Turnover.ts[1:train_size.Turnover.ardl]
train_data.Turnover.ardl = ts(train_data.Turnover.ardl,
start=c(2015,1),
end=c(2015,365),
frequency=365)
train_data.Close.diff.ardl <- Close.ts.diff[1:train_size.Close.diff.ardl]
train_data.Close.diff.ardl = ts(train_data.Close.diff.ardl,
start=c(2015,1),
end=c(2015,365),
frequency=365)Test
test_data.Turnover.ardl <- Turnover.ts[(train_size.Turnover.ardl + 1):length(Turnover.ts)]
test_data.Turnover.ardl = ts(test_data.Turnover.ardl, start=c(2015,1), end=c(2015,365), frequency=365)
test_data.Close.diff.ardl <- Close.ts.diff[(train_size.Close.diff.ardl + 1):length(Close.ts.diff)]
test_data.Close.diff.ardl = ts(test_data.Close.diff.ardl, start=c(2015,1), end=c(2015,365), frequency=365)
length(train_data.Turnover.ardl) ## [1] 365length(test_data.Close.diff.ardl)## [1] 365Training and Testing for Turnover with lag (1:4) and Close with lag (110)
Turnover.Close.training.1 <- dynlm(train_data.Turnover.ardl ~ L(train_data.Turnover.ardl, 1:4) + L(train_data.Close.diff.ardl, 110))
summary(Turnover.Close.training.1)##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover.ardl ~ L(train_data.Turnover.ardl,
## 1:4) + L(train_data.Close.diff.ardl, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.824e+14 -1.182e+14 -4.393e+13 5.605e+13 1.779e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.421e+14 4.189e+13 5.779 2.24e-08 ***
## L(train_data.Turnover.ardl, 1:4)1 3.317e-01 6.312e-02 5.255 3.19e-07 ***
## L(train_data.Turnover.ardl, 1:4)2 3.212e-02 6.655e-02 0.483 0.630
## L(train_data.Turnover.ardl, 1:4)3 -2.603e-02 6.653e-02 -0.391 0.696
## L(train_data.Turnover.ardl, 1:4)4 8.752e-02 6.315e-02 1.386 0.167
## L(train_data.Close.diff.ardl, 110) 7.216e+10 2.355e+11 0.306 0.760
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.521e+14 on 249 degrees of freedom
## Multiple R-squared: 0.1263, Adjusted R-squared: 0.1088
## F-statistic: 7.2 on 5 and 249 DF, p-value: 2.582e-06Turnover.Close.testing.1 <- predict(Turnover.Close.training.1, n.ahead = length(test_data.Turnover.ardl, test_data.Close.diff.ardl))
head(Turnover.Close.testing.1)## 2015(111) 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## 4.261698e+14 4.430394e+14 3.568575e+14 3.651518e+14 3.938898e+14 3.333381e+14Turnover.Close.fitted_training.1 <- fitted(Turnover.Close.training.1)
head(Turnover.Close.fitted_training.1)## Time Series:
## Start = c(2015, 111)
## End = c(2015, 116)
## Frequency = 365
## [1] 4.261698e+14 4.430394e+14 3.568575e+14 3.651518e+14 3.938898e+14
## [6] 3.333381e+14Turnover.Close.1.training.mse_value <- mse(train_data.Turnover.ardl, Turnover.Close.fitted_training.1)
Turnover.Close.1.training.rmse_value <- rmse(train_data.Turnover.ardl, Turnover.Close.fitted_training.1)
Turnover.testing.n.1 = as.numeric(Turnover.Close.testing.1)
Turnover.Close.1.testing.mse_value <- mse(test_data.Turnover.ardl, Turnover.testing.n.1)
Turnover.Close.1.testing.rmse_value <- rmse(test_data.Turnover.ardl, Turnover.testing.n.1)
cat("Training Model MSE:", Turnover.Close.1.training.mse_value, "\n Training Model RMSE:", Turnover.Close.1.training.rmse_value , "\n Testing Model MSE:", Turnover.Close.1.testing.mse_value, "\n Testing Model RMSE:", Turnover.Close.1.testing.rmse_value , "\n")## Training Model MSE: 6.206749e+28
## Training Model RMSE: 2.491335e+14
## Testing Model MSE: 9.040994e+28
## Testing Model RMSE: 3.006825e+14cat(" Training Model AIC:", AIC(Turnover.Close.training.1), "\n Training Model BIC:", BIC(Turnover.Close.training.1), "\n")## Training Model AIC: 17643.65
## Training Model BIC: 17668.44The MSE and RMSE of the training model are extremely high, which suggest a bad model fit. This is further supported by its R-squared values of 0.1263. It is relatively low, meaning only a small percentage of the variance in the dependent variable can be explained by the independent variable, in this case, Close on Turnover. The MSE and RMSE of the testing model are also extremely high, so we can conclude that the ARDL model of Turnover with lag(1:4) and Close with lag (110) is a bad fit.
Training and Testing for Turnover with lag (1:4) and Close with lag (1:110)
Turnover.Close.training.2 <- dynlm(train_data.Turnover.ardl ~ L(train_data.Turnover.ardl, 1:4) + L(train_data.Close.diff.ardl, 1:110), data = infy_stock)
summary(Turnover.Close.training.2)##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover.ardl ~ L(train_data.Turnover.ardl,
## 1:4) + L(train_data.Close.diff.ardl, 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.776e+14 -7.744e+13 -1.566e+13 5.255e+13 1.700e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.394e+14 5.528e+13 4.330 2.82e-05
## L(train_data.Turnover.ardl, 1:4)1 3.509e-01 8.423e-02 4.166 5.39e-05
## L(train_data.Turnover.ardl, 1:4)2 2.883e-02 8.919e-02 0.323 0.7469
## L(train_data.Turnover.ardl, 1:4)3 -2.155e-02 8.900e-02 -0.242 0.8090
## L(train_data.Turnover.ardl, 1:4)4 8.805e-02 8.383e-02 1.050 0.2954
## L(train_data.Close.diff.ardl, 1:110)1 9.013e+10 1.997e+11 0.451 0.6525
## L(train_data.Close.diff.ardl, 1:110)2 -3.013e+10 1.998e+11 -0.151 0.8803
## L(train_data.Close.diff.ardl, 1:110)3 1.983e+11 1.998e+11 0.993 0.3226
## L(train_data.Close.diff.ardl, 1:110)4 5.280e+10 2.004e+11 0.264 0.7925
## L(train_data.Close.diff.ardl, 1:110)5 7.057e+10 2.001e+11 0.353 0.7249
## L(train_data.Close.diff.ardl, 1:110)6 -1.131e+11 1.989e+11 -0.569 0.5705
## L(train_data.Close.diff.ardl, 1:110)7 3.572e+10 1.988e+11 0.180 0.8577
## L(train_data.Close.diff.ardl, 1:110)8 4.864e+10 1.981e+11 0.246 0.8064
## L(train_data.Close.diff.ardl, 1:110)9 -9.270e+09 1.978e+11 -0.047 0.9627
## L(train_data.Close.diff.ardl, 1:110)10 1.835e+11 1.976e+11 0.929 0.3547
## L(train_data.Close.diff.ardl, 1:110)11 8.119e+10 1.980e+11 0.410 0.6823
## L(train_data.Close.diff.ardl, 1:110)12 9.412e+10 1.978e+11 0.476 0.6350
## L(train_data.Close.diff.ardl, 1:110)13 1.112e+11 2.615e+11 0.425 0.6713
## L(train_data.Close.diff.ardl, 1:110)14 1.833e+11 2.619e+11 0.700 0.4851
## L(train_data.Close.diff.ardl, 1:110)15 2.826e+11 2.620e+11 1.079 0.2826
## L(train_data.Close.diff.ardl, 1:110)16 1.255e+11 2.629e+11 0.477 0.6338
## L(train_data.Close.diff.ardl, 1:110)17 1.295e+11 2.623e+11 0.493 0.6224
## L(train_data.Close.diff.ardl, 1:110)18 5.773e+10 2.624e+11 0.220 0.8262
## L(train_data.Close.diff.ardl, 1:110)19 -4.479e+09 2.623e+11 -0.017 0.9864
## L(train_data.Close.diff.ardl, 1:110)20 -5.977e+10 2.611e+11 -0.229 0.8193
## L(train_data.Close.diff.ardl, 1:110)21 6.963e+10 2.612e+11 0.267 0.7902
## L(train_data.Close.diff.ardl, 1:110)22 4.073e+10 2.613e+11 0.156 0.8763
## L(train_data.Close.diff.ardl, 1:110)23 1.491e+11 2.605e+11 0.572 0.5680
## L(train_data.Close.diff.ardl, 1:110)24 1.125e+11 2.604e+11 0.432 0.6665
## L(train_data.Close.diff.ardl, 1:110)25 2.180e+11 2.604e+11 0.837 0.4039
## L(train_data.Close.diff.ardl, 1:110)26 1.474e+11 2.612e+11 0.564 0.5734
## L(train_data.Close.diff.ardl, 1:110)27 -1.595e+12 2.636e+11 -6.053 1.24e-08
## L(train_data.Close.diff.ardl, 1:110)28 4.188e+11 2.952e+11 1.419 0.1582
## L(train_data.Close.diff.ardl, 1:110)29 1.290e+11 2.976e+11 0.433 0.6654
## L(train_data.Close.diff.ardl, 1:110)30 2.311e+11 2.961e+11 0.780 0.4365
## L(train_data.Close.diff.ardl, 1:110)31 7.227e+10 2.907e+11 0.249 0.8040
## L(train_data.Close.diff.ardl, 1:110)32 -3.334e+11 2.636e+11 -1.264 0.2082
## L(train_data.Close.diff.ardl, 1:110)33 -8.523e+10 2.651e+11 -0.322 0.7483
## L(train_data.Close.diff.ardl, 1:110)34 -1.451e+11 2.652e+11 -0.547 0.5851
## L(train_data.Close.diff.ardl, 1:110)35 7.130e+10 2.629e+11 0.271 0.7867
## L(train_data.Close.diff.ardl, 1:110)36 -2.464e+10 2.650e+11 -0.093 0.9261
## L(train_data.Close.diff.ardl, 1:110)37 -1.438e+11 2.637e+11 -0.545 0.5865
## L(train_data.Close.diff.ardl, 1:110)38 2.433e+11 2.634e+11 0.923 0.3574
## L(train_data.Close.diff.ardl, 1:110)39 -3.398e+10 2.636e+11 -0.129 0.8976
## L(train_data.Close.diff.ardl, 1:110)40 7.051e+10 2.639e+11 0.267 0.7897
## L(train_data.Close.diff.ardl, 1:110)41 3.442e+11 2.640e+11 1.304 0.1945
## L(train_data.Close.diff.ardl, 1:110)42 8.468e+10 2.647e+11 0.320 0.7495
## L(train_data.Close.diff.ardl, 1:110)43 -2.397e+11 2.646e+11 -0.906 0.3666
## L(train_data.Close.diff.ardl, 1:110)44 -1.951e+11 2.653e+11 -0.735 0.4633
## L(train_data.Close.diff.ardl, 1:110)45 2.619e+11 2.656e+11 0.986 0.3258
## L(train_data.Close.diff.ardl, 1:110)46 2.136e+11 2.655e+11 0.805 0.4224
## L(train_data.Close.diff.ardl, 1:110)47 8.741e+10 2.657e+11 0.329 0.7427
## L(train_data.Close.diff.ardl, 1:110)48 6.426e+10 2.654e+11 0.242 0.8091
## L(train_data.Close.diff.ardl, 1:110)49 6.881e+10 2.638e+11 0.261 0.7946
## L(train_data.Close.diff.ardl, 1:110)50 -1.032e+11 2.637e+11 -0.391 0.6961
## L(train_data.Close.diff.ardl, 1:110)51 -2.194e+11 2.629e+11 -0.835 0.4053
## L(train_data.Close.diff.ardl, 1:110)52 -4.618e+09 2.629e+11 -0.018 0.9860
## L(train_data.Close.diff.ardl, 1:110)53 -2.095e+11 2.628e+11 -0.797 0.4266
## L(train_data.Close.diff.ardl, 1:110)54 -4.779e+10 2.637e+11 -0.181 0.8564
## L(train_data.Close.diff.ardl, 1:110)55 1.635e+11 2.636e+11 0.620 0.5360
## L(train_data.Close.diff.ardl, 1:110)56 -2.263e+11 2.638e+11 -0.858 0.3925
## L(train_data.Close.diff.ardl, 1:110)57 -1.074e+11 2.645e+11 -0.406 0.6852
## L(train_data.Close.diff.ardl, 1:110)58 -1.639e+11 2.639e+11 -0.621 0.5357
## L(train_data.Close.diff.ardl, 1:110)59 -4.400e+09 2.639e+11 -0.017 0.9867
## L(train_data.Close.diff.ardl, 1:110)60 1.265e+11 2.634e+11 0.480 0.6318
## L(train_data.Close.diff.ardl, 1:110)61 -1.790e+10 2.637e+11 -0.068 0.9460
## L(train_data.Close.diff.ardl, 1:110)62 1.371e+11 2.637e+11 0.520 0.6039
## L(train_data.Close.diff.ardl, 1:110)63 -2.068e+11 2.632e+11 -0.786 0.4332
## L(train_data.Close.diff.ardl, 1:110)64 4.602e+10 2.644e+11 0.174 0.8621
## L(train_data.Close.diff.ardl, 1:110)65 -1.427e+11 2.638e+11 -0.541 0.5895
## L(train_data.Close.diff.ardl, 1:110)66 -5.698e+10 2.639e+11 -0.216 0.8294
## L(train_data.Close.diff.ardl, 1:110)67 2.544e+11 2.638e+11 0.964 0.3365
## L(train_data.Close.diff.ardl, 1:110)68 1.718e+10 2.641e+11 0.065 0.9482
## L(train_data.Close.diff.ardl, 1:110)69 -1.505e+11 2.640e+11 -0.570 0.5696
## L(train_data.Close.diff.ardl, 1:110)70 2.174e+11 2.643e+11 0.823 0.4122
## L(train_data.Close.diff.ardl, 1:110)71 -5.526e+10 2.643e+11 -0.209 0.8347
## L(train_data.Close.diff.ardl, 1:110)72 4.425e+11 2.641e+11 1.675 0.0961
## L(train_data.Close.diff.ardl, 1:110)73 -3.332e+11 2.662e+11 -1.252 0.2127
## L(train_data.Close.diff.ardl, 1:110)74 1.726e+10 2.677e+11 0.064 0.9487
## L(train_data.Close.diff.ardl, 1:110)75 4.689e+10 2.680e+11 0.175 0.8614
## L(train_data.Close.diff.ardl, 1:110)76 -1.784e+11 2.669e+11 -0.668 0.5050
## L(train_data.Close.diff.ardl, 1:110)77 5.522e+10 2.635e+11 0.210 0.8343
## L(train_data.Close.diff.ardl, 1:110)78 1.205e+11 2.631e+11 0.458 0.6475
## L(train_data.Close.diff.ardl, 1:110)79 -1.194e+11 2.631e+11 -0.454 0.6506
## L(train_data.Close.diff.ardl, 1:110)80 -1.512e+11 2.632e+11 -0.575 0.5664
## L(train_data.Close.diff.ardl, 1:110)81 -8.688e+10 2.634e+11 -0.330 0.7420
## L(train_data.Close.diff.ardl, 1:110)82 -1.030e+11 2.633e+11 -0.391 0.6963
## L(train_data.Close.diff.ardl, 1:110)83 -1.139e+12 2.629e+11 -4.332 2.80e-05
## L(train_data.Close.diff.ardl, 1:110)84 1.495e+10 2.797e+11 0.053 0.9574
## L(train_data.Close.diff.ardl, 1:110)85 1.217e+11 2.768e+11 0.439 0.6610
## L(train_data.Close.diff.ardl, 1:110)86 5.108e+10 2.763e+11 0.185 0.8536
## L(train_data.Close.diff.ardl, 1:110)87 1.838e+11 2.752e+11 0.668 0.5054
## L(train_data.Close.diff.ardl, 1:110)88 -2.690e+10 2.623e+11 -0.103 0.9185
## L(train_data.Close.diff.ardl, 1:110)89 -1.765e+11 2.608e+11 -0.677 0.4996
## L(train_data.Close.diff.ardl, 1:110)90 3.346e+10 2.610e+11 0.128 0.8982
## L(train_data.Close.diff.ardl, 1:110)91 -7.053e+10 2.606e+11 -0.271 0.7871
## L(train_data.Close.diff.ardl, 1:110)92 1.912e+11 2.604e+11 0.734 0.4640
## L(train_data.Close.diff.ardl, 1:110)93 1.268e+11 2.609e+11 0.486 0.6278
## L(train_data.Close.diff.ardl, 1:110)94 2.602e+10 2.606e+11 0.100 0.9206
## L(train_data.Close.diff.ardl, 1:110)95 4.596e+10 2.613e+11 0.176 0.8606
## L(train_data.Close.diff.ardl, 1:110)96 2.413e+11 2.613e+11 0.923 0.3574
## L(train_data.Close.diff.ardl, 1:110)97 1.352e+11 2.619e+11 0.516 0.6066
## L(train_data.Close.diff.ardl, 1:110)98 1.365e+11 2.619e+11 0.521 0.6029
## L(train_data.Close.diff.ardl, 1:110)99 1.939e+10 2.617e+11 0.074 0.9410
## L(train_data.Close.diff.ardl, 1:110)100 2.368e+11 2.619e+11 0.904 0.3674
## L(train_data.Close.diff.ardl, 1:110)101 1.444e+11 2.622e+11 0.551 0.5827
## L(train_data.Close.diff.ardl, 1:110)102 -1.191e+11 2.619e+11 -0.455 0.6498
## L(train_data.Close.diff.ardl, 1:110)103 2.703e+10 2.618e+11 0.103 0.9179
## L(train_data.Close.diff.ardl, 1:110)104 1.834e+11 2.618e+11 0.700 0.4849
## L(train_data.Close.diff.ardl, 1:110)105 3.790e+10 2.606e+11 0.145 0.8846
## L(train_data.Close.diff.ardl, 1:110)106 -3.272e+10 2.618e+11 -0.125 0.9007
## L(train_data.Close.diff.ardl, 1:110)107 -1.475e+11 2.617e+11 -0.564 0.5738
## L(train_data.Close.diff.ardl, 1:110)108 -2.665e+11 2.618e+11 -1.018 0.3105
## L(train_data.Close.diff.ardl, 1:110)109 -9.164e+10 2.620e+11 -0.350 0.7271
## L(train_data.Close.diff.ardl, 1:110)110 1.593e+11 2.619e+11 0.608 0.5440
##
## (Intercept) ***
## L(train_data.Turnover.ardl, 1:4)1 ***
## L(train_data.Turnover.ardl, 1:4)2
## L(train_data.Turnover.ardl, 1:4)3
## L(train_data.Turnover.ardl, 1:4)4
## L(train_data.Close.diff.ardl, 1:110)1
## L(train_data.Close.diff.ardl, 1:110)2
## L(train_data.Close.diff.ardl, 1:110)3
## L(train_data.Close.diff.ardl, 1:110)4
## L(train_data.Close.diff.ardl, 1:110)5
## L(train_data.Close.diff.ardl, 1:110)6
## L(train_data.Close.diff.ardl, 1:110)7
## L(train_data.Close.diff.ardl, 1:110)8
## L(train_data.Close.diff.ardl, 1:110)9
## L(train_data.Close.diff.ardl, 1:110)10
## L(train_data.Close.diff.ardl, 1:110)11
## L(train_data.Close.diff.ardl, 1:110)12
## L(train_data.Close.diff.ardl, 1:110)13
## L(train_data.Close.diff.ardl, 1:110)14
## L(train_data.Close.diff.ardl, 1:110)15
## L(train_data.Close.diff.ardl, 1:110)16
## L(train_data.Close.diff.ardl, 1:110)17
## L(train_data.Close.diff.ardl, 1:110)18
## L(train_data.Close.diff.ardl, 1:110)19
## L(train_data.Close.diff.ardl, 1:110)20
## L(train_data.Close.diff.ardl, 1:110)21
## L(train_data.Close.diff.ardl, 1:110)22
## L(train_data.Close.diff.ardl, 1:110)23
## L(train_data.Close.diff.ardl, 1:110)24
## L(train_data.Close.diff.ardl, 1:110)25
## L(train_data.Close.diff.ardl, 1:110)26
## L(train_data.Close.diff.ardl, 1:110)27 ***
## L(train_data.Close.diff.ardl, 1:110)28
## L(train_data.Close.diff.ardl, 1:110)29
## L(train_data.Close.diff.ardl, 1:110)30
## L(train_data.Close.diff.ardl, 1:110)31
## L(train_data.Close.diff.ardl, 1:110)32
## L(train_data.Close.diff.ardl, 1:110)33
## L(train_data.Close.diff.ardl, 1:110)34
## L(train_data.Close.diff.ardl, 1:110)35
## L(train_data.Close.diff.ardl, 1:110)36
## L(train_data.Close.diff.ardl, 1:110)37
## L(train_data.Close.diff.ardl, 1:110)38
## L(train_data.Close.diff.ardl, 1:110)39
## L(train_data.Close.diff.ardl, 1:110)40
## L(train_data.Close.diff.ardl, 1:110)41
## L(train_data.Close.diff.ardl, 1:110)42
## L(train_data.Close.diff.ardl, 1:110)43
## L(train_data.Close.diff.ardl, 1:110)44
## L(train_data.Close.diff.ardl, 1:110)45
## L(train_data.Close.diff.ardl, 1:110)46
## L(train_data.Close.diff.ardl, 1:110)47
## L(train_data.Close.diff.ardl, 1:110)48
## L(train_data.Close.diff.ardl, 1:110)49
## L(train_data.Close.diff.ardl, 1:110)50
## L(train_data.Close.diff.ardl, 1:110)51
## L(train_data.Close.diff.ardl, 1:110)52
## L(train_data.Close.diff.ardl, 1:110)53
## L(train_data.Close.diff.ardl, 1:110)54
## L(train_data.Close.diff.ardl, 1:110)55
## L(train_data.Close.diff.ardl, 1:110)56
## L(train_data.Close.diff.ardl, 1:110)57
## L(train_data.Close.diff.ardl, 1:110)58
## L(train_data.Close.diff.ardl, 1:110)59
## L(train_data.Close.diff.ardl, 1:110)60
## L(train_data.Close.diff.ardl, 1:110)61
## L(train_data.Close.diff.ardl, 1:110)62
## L(train_data.Close.diff.ardl, 1:110)63
## L(train_data.Close.diff.ardl, 1:110)64
## L(train_data.Close.diff.ardl, 1:110)65
## L(train_data.Close.diff.ardl, 1:110)66
## L(train_data.Close.diff.ardl, 1:110)67
## L(train_data.Close.diff.ardl, 1:110)68
## L(train_data.Close.diff.ardl, 1:110)69
## L(train_data.Close.diff.ardl, 1:110)70
## L(train_data.Close.diff.ardl, 1:110)71
## L(train_data.Close.diff.ardl, 1:110)72 .
## L(train_data.Close.diff.ardl, 1:110)73
## L(train_data.Close.diff.ardl, 1:110)74
## L(train_data.Close.diff.ardl, 1:110)75
## L(train_data.Close.diff.ardl, 1:110)76
## L(train_data.Close.diff.ardl, 1:110)77
## L(train_data.Close.diff.ardl, 1:110)78
## L(train_data.Close.diff.ardl, 1:110)79
## L(train_data.Close.diff.ardl, 1:110)80
## L(train_data.Close.diff.ardl, 1:110)81
## L(train_data.Close.diff.ardl, 1:110)82
## L(train_data.Close.diff.ardl, 1:110)83 ***
## L(train_data.Close.diff.ardl, 1:110)84
## L(train_data.Close.diff.ardl, 1:110)85
## L(train_data.Close.diff.ardl, 1:110)86
## L(train_data.Close.diff.ardl, 1:110)87
## L(train_data.Close.diff.ardl, 1:110)88
## L(train_data.Close.diff.ardl, 1:110)89
## L(train_data.Close.diff.ardl, 1:110)90
## L(train_data.Close.diff.ardl, 1:110)91
## L(train_data.Close.diff.ardl, 1:110)92
## L(train_data.Close.diff.ardl, 1:110)93
## L(train_data.Close.diff.ardl, 1:110)94
## L(train_data.Close.diff.ardl, 1:110)95
## L(train_data.Close.diff.ardl, 1:110)96
## L(train_data.Close.diff.ardl, 1:110)97
## L(train_data.Close.diff.ardl, 1:110)98
## L(train_data.Close.diff.ardl, 1:110)99
## L(train_data.Close.diff.ardl, 1:110)100
## L(train_data.Close.diff.ardl, 1:110)101
## L(train_data.Close.diff.ardl, 1:110)102
## L(train_data.Close.diff.ardl, 1:110)103
## L(train_data.Close.diff.ardl, 1:110)104
## L(train_data.Close.diff.ardl, 1:110)105
## L(train_data.Close.diff.ardl, 1:110)106
## L(train_data.Close.diff.ardl, 1:110)107
## L(train_data.Close.diff.ardl, 1:110)108
## L(train_data.Close.diff.ardl, 1:110)109
## L(train_data.Close.diff.ardl, 1:110)110
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.6e+14 on 140 degrees of freedom
## Multiple R-squared: 0.4777, Adjusted R-squared: 0.05231
## F-statistic: 1.123 on 114 and 140 DF, p-value: 0.2559Turnover.Close.testing.2 <- predict(Turnover.Close.training.2, n.ahead = length(test_data.Turnover.ardl, test_data.Close.diff.ardl))
head(Turnover.Close.testing.2)## 2015(111) 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## 4.467430e+14 3.122180e+14 2.610087e+14 3.198778e+14 3.008239e+14 2.760999e+14Turnover.Close.fitted_training.2 <- fitted(Turnover.Close.training.2)
head(Turnover.Close.fitted_training.2)## Time Series:
## Start = c(2015, 111)
## End = c(2015, 116)
## Frequency = 365
## [1] 4.467430e+14 3.122180e+14 2.610087e+14 3.198778e+14 3.008239e+14
## [6] 2.760999e+14Turnover.Close.2.training.mse_value <- mse(train_data.Turnover.ardl, Turnover.Close.fitted_training.2)
Turnover.Close.2.training.rmse_value <- rmse(train_data.Turnover.ardl, Turnover.Close.fitted_training.2)
Turnover.testing.n.2 = as.numeric(Turnover.Close.testing.2)
Turnover.Close.2.testing.mse_value <- mse(test_data.Turnover.ardl, Turnover.testing.n.2)
Turnover.Close.2.testing.rmse_value <- rmse(test_data.Turnover.ardl, Turnover.testing.n.2)
cat("Training Model MSE:", Turnover.Close.2.training.mse_value, "\n Training Model RMSE:", Turnover.Close.2.training.rmse_value , "\n Testing Model MSE:", Turnover.Close.2.testing.mse_value, "\n Testing Model RMSE:", Turnover.Close.2.testing.rmse_value , "\n")## Training Model MSE: 3.710815e+28
## Training Model RMSE: 1.926348e+14
## Testing Model MSE: 1.250564e+29
## Testing Model RMSE: 3.536331e+14cat(" Training Model AIC:", AIC(Turnover.Close.training.2), "\n Training Model BIC:", BIC(Turnover.Close.training.2), "\n")## Training Model AIC: 17730.49
## Training Model BIC: 18141.27The R-squared of this training model is 0.4777. This value is better compared to the previous model and might hint at a moderate fit, but looking at the high values of MSE and RMSE of both training and testing models, it is to be observed that the ARDL model is not a good fit. Looking at the AIC and BIC of this model are also higher than that of the previous model despite its R-squared value being better suited. We can conclude that this ARDL model is also not a good fit.
Training and Testing for Turnover with lag (2)n(61)n(75)n(117) and Close with lag (110)
Turnover.Close.training.3 <- dynlm(train_data.Turnover.ardl ~ L(train_data.Turnover.ardl, 2) + L(train_data.Turnover.ardl, 61) + L(train_data.Turnover.ardl, 75) + L(train_data.Turnover.ardl, 117) + L(train_data.Close.diff.ardl, 110), data = infy_stock)
summary(Turnover.Close.training.3)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover.ardl ~ L(train_data.Turnover.ardl,
## 2) + L(train_data.Turnover.ardl, 61) + L(train_data.Turnover.ardl,
## 75) + L(train_data.Turnover.ardl, 117) + L(train_data.Close.diff.ardl,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.274e+14 -1.325e+14 -4.685e+13 7.484e+13 1.888e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.593e+14 5.492e+13 4.721 3.98e-06 ***
## L(train_data.Turnover.ardl, 2) 1.464e-01 6.264e-02 2.337 0.0203 *
## L(train_data.Turnover.ardl, 61) 1.464e-01 6.453e-02 2.268 0.0242 *
## L(train_data.Turnover.ardl, 75) 1.242e-02 6.266e-02 0.198 0.8431
## L(train_data.Turnover.ardl, 117) 8.348e-02 6.501e-02 1.284 0.2003
## L(train_data.Close.diff.ardl, 110) 4.366e+10 2.495e+11 0.175 0.8613
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.646e+14 on 242 degrees of freedom
## Multiple R-squared: 0.05654, Adjusted R-squared: 0.03705
## F-statistic: 2.901 on 5 and 242 DF, p-value: 0.01455Turnover.Close.testing.3 <- predict(Turnover.Close.training.3, n.ahead = length(test_data.Turnover.ardl, test_data.Close.diff.ardl))
head(Turnover.Close.testing.3)## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 3.734164e+14 3.847273e+14 4.804043e+14 4.365705e+14 3.818708e+14 4.250643e+14Turnover.Close.fitted_training.3 <- fitted(Turnover.Close.training.3)
head(Turnover.Close.fitted_training.3)## Time Series:
## Start = c(2015, 118)
## End = c(2015, 123)
## Frequency = 365
## [1] 3.734164e+14 3.847273e+14 4.804043e+14 4.365705e+14 3.818708e+14
## [6] 4.250643e+14Turnover.Close.3.training.mse_value <- mse(train_data.Turnover.ardl, Turnover.Close.fitted_training.3)
Turnover.Close.3.training.rmse_value <- rmse(train_data.Turnover.ardl, Turnover.Close.fitted_training.3)
Turnover.testing.n.3 = as.numeric(Turnover.Close.testing.3)
Turnover.Close.3.testing.mse_value <- mse(test_data.Turnover.ardl, Turnover.testing.n.3)
Turnover.Close.3.testing.rmse_value <- rmse(test_data.Turnover.ardl, Turnover.testing.n.3)
cat("Training Model MSE:", Turnover.Close.3.training.mse_value, "\n Training Model RMSE:", Turnover.Close.3.training.rmse_value , "\n Testing Model MSE:", Turnover.Close.3.testing.mse_value, "\n Testing Model RMSE:", Turnover.Close.3.testing.rmse_value , "\n")## Training Model MSE: 6.832031e+28
## Training Model RMSE: 2.613815e+14
## Testing Model MSE: 7.532087e+28
## Testing Model RMSE: 2.744465e+14cat(" Training Model AIC:", AIC(Turnover.Close.training.3), "\n Training Model BIC:", BIC(Turnover.Close.training.3), "\n")## Training Model AIC: 17183.51
## Training Model BIC: 17208.1For this model too, the MSE and RMSE of both training and testing models are high, suggesting a bad fit. The R-squared value of 0.05654 also further supports that conclusion. And though the AIC and BIC of this model seems to be lower than the previous two, it is still high and thus, can be concluded to not be a good fit.
Training and Testing for Turnover with lag (2)n(61)n(75)n(117) and Close with lag (1:110)
Turnover.Close.training.4 <- dynlm(train_data.Turnover.ardl ~ L(train_data.Turnover.ardl, 2) + L(train_data.Turnover.ardl, 61) + L(train_data.Turnover.ardl, 75) + L(train_data.Turnover.ardl, 117) + L(train_data.Close.diff.ardl, 1:110))
summary(Turnover.Close.training.4) ##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover.ardl ~ L(train_data.Turnover.ardl,
## 2) + L(train_data.Turnover.ardl, 61) + L(train_data.Turnover.ardl,
## 75) + L(train_data.Turnover.ardl, 117) + L(train_data.Close.diff.ardl,
## 1:110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.517e+14 -9.168e+13 -2.370e+13 6.036e+13 1.752e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.299e+14 7.520e+13 4.386 2.32e-05
## L(train_data.Turnover.ardl, 2) 1.462e-01 8.618e-02 1.696 0.092167
## L(train_data.Turnover.ardl, 61) 1.247e-01 1.078e-01 1.157 0.249333
## L(train_data.Turnover.ardl, 75) 6.533e-02 9.535e-02 0.685 0.494466
## L(train_data.Turnover.ardl, 117) -1.028e-01 1.103e-01 -0.932 0.353053
## L(train_data.Close.diff.ardl, 1:110)1 -7.166e+10 2.837e+11 -0.253 0.800986
## L(train_data.Close.diff.ardl, 1:110)2 -2.801e+10 2.844e+11 -0.098 0.921687
## L(train_data.Close.diff.ardl, 1:110)3 1.666e+11 2.844e+11 0.586 0.559061
## L(train_data.Close.diff.ardl, 1:110)4 -1.370e+10 2.834e+11 -0.048 0.961500
## L(train_data.Close.diff.ardl, 1:110)5 1.006e+11 2.828e+11 0.356 0.722701
## L(train_data.Close.diff.ardl, 1:110)6 -1.667e+11 2.862e+11 -0.583 0.561182
## L(train_data.Close.diff.ardl, 1:110)7 6.876e+10 2.215e+11 0.310 0.756747
## L(train_data.Close.diff.ardl, 1:110)8 8.633e+10 2.164e+11 0.399 0.690530
## L(train_data.Close.diff.ardl, 1:110)9 3.122e+10 2.160e+11 0.145 0.885310
## L(train_data.Close.diff.ardl, 1:110)10 2.066e+11 2.171e+11 0.951 0.343104
## L(train_data.Close.diff.ardl, 1:110)11 1.649e+11 2.142e+11 0.770 0.442730
## L(train_data.Close.diff.ardl, 1:110)12 1.083e+11 2.146e+11 0.505 0.614650
## L(train_data.Close.diff.ardl, 1:110)13 -2.945e+10 3.313e+11 -0.089 0.929302
## L(train_data.Close.diff.ardl, 1:110)14 2.229e+11 2.837e+11 0.786 0.433515
## L(train_data.Close.diff.ardl, 1:110)15 3.817e+11 2.828e+11 1.350 0.179295
## L(train_data.Close.diff.ardl, 1:110)16 2.522e+11 2.830e+11 0.891 0.374371
## L(train_data.Close.diff.ardl, 1:110)17 2.151e+11 2.861e+11 0.752 0.453409
## L(train_data.Close.diff.ardl, 1:110)18 1.147e+11 2.825e+11 0.406 0.685297
## L(train_data.Close.diff.ardl, 1:110)19 6.083e+10 2.828e+11 0.215 0.830033
## L(train_data.Close.diff.ardl, 1:110)20 -4.189e+10 2.818e+11 -0.149 0.882069
## L(train_data.Close.diff.ardl, 1:110)21 6.689e+10 2.825e+11 0.237 0.813190
## L(train_data.Close.diff.ardl, 1:110)22 4.812e+10 2.833e+11 0.170 0.865391
## L(train_data.Close.diff.ardl, 1:110)23 2.160e+11 2.851e+11 0.758 0.449947
## L(train_data.Close.diff.ardl, 1:110)24 1.851e+11 2.831e+11 0.654 0.514323
## L(train_data.Close.diff.ardl, 1:110)25 2.594e+11 2.856e+11 0.908 0.365324
## L(train_data.Close.diff.ardl, 1:110)26 2.210e+11 2.849e+11 0.776 0.439344
## L(train_data.Close.diff.ardl, 1:110)27 -1.351e+12 3.373e+11 -4.004 0.000103
## L(train_data.Close.diff.ardl, 1:110)28 -4.384e+10 2.924e+11 -0.150 0.881052
## L(train_data.Close.diff.ardl, 1:110)29 3.095e+11 3.125e+11 0.991 0.323677
## L(train_data.Close.diff.ardl, 1:110)30 3.587e+11 2.890e+11 1.241 0.216672
## L(train_data.Close.diff.ardl, 1:110)31 8.525e+10 2.867e+11 0.297 0.766691
## L(train_data.Close.diff.ardl, 1:110)32 -3.379e+11 2.871e+11 -1.177 0.241188
## L(train_data.Close.diff.ardl, 1:110)33 -1.893e+11 2.849e+11 -0.664 0.507540
## L(train_data.Close.diff.ardl, 1:110)34 -1.183e+11 2.859e+11 -0.414 0.679721
## L(train_data.Close.diff.ardl, 1:110)35 5.111e+10 2.844e+11 0.180 0.857638
## L(train_data.Close.diff.ardl, 1:110)36 -8.316e+09 2.865e+11 -0.029 0.976887
## L(train_data.Close.diff.ardl, 1:110)37 -1.630e+11 2.858e+11 -0.570 0.569369
## L(train_data.Close.diff.ardl, 1:110)38 1.923e+11 2.850e+11 0.675 0.500934
## L(train_data.Close.diff.ardl, 1:110)39 4.405e+10 2.880e+11 0.153 0.878667
## L(train_data.Close.diff.ardl, 1:110)40 6.279e+10 2.866e+11 0.219 0.826941
## L(train_data.Close.diff.ardl, 1:110)41 4.606e+11 3.310e+11 1.392 0.166357
## L(train_data.Close.diff.ardl, 1:110)42 2.717e+11 2.914e+11 0.932 0.352810
## L(train_data.Close.diff.ardl, 1:110)43 -1.898e+11 2.872e+11 -0.661 0.509776
## L(train_data.Close.diff.ardl, 1:110)44 -2.759e+11 2.861e+11 -0.964 0.336579
## L(train_data.Close.diff.ardl, 1:110)45 2.412e+11 2.873e+11 0.840 0.402659
## L(train_data.Close.diff.ardl, 1:110)46 3.245e+11 2.867e+11 1.132 0.259659
## L(train_data.Close.diff.ardl, 1:110)47 1.544e+11 2.860e+11 0.540 0.590245
## L(train_data.Close.diff.ardl, 1:110)48 8.503e+10 2.864e+11 0.297 0.766972
## L(train_data.Close.diff.ardl, 1:110)49 1.271e+11 2.860e+11 0.444 0.657502
## L(train_data.Close.diff.ardl, 1:110)50 -3.109e+10 2.847e+11 -0.109 0.913201
## L(train_data.Close.diff.ardl, 1:110)51 -1.426e+11 2.938e+11 -0.485 0.628143
## L(train_data.Close.diff.ardl, 1:110)52 -5.165e+10 2.844e+11 -0.182 0.856183
## L(train_data.Close.diff.ardl, 1:110)53 -2.169e+11 2.849e+11 -0.761 0.447786
## L(train_data.Close.diff.ardl, 1:110)54 -1.350e+11 2.856e+11 -0.473 0.637246
## L(train_data.Close.diff.ardl, 1:110)55 9.666e+10 2.869e+11 0.337 0.736720
## L(train_data.Close.diff.ardl, 1:110)56 -1.758e+11 2.852e+11 -0.616 0.538712
## L(train_data.Close.diff.ardl, 1:110)57 -2.202e+11 2.851e+11 -0.772 0.441375
## L(train_data.Close.diff.ardl, 1:110)58 -2.306e+11 2.847e+11 -0.810 0.419235
## L(train_data.Close.diff.ardl, 1:110)59 -6.470e+10 2.849e+11 -0.227 0.820674
## L(train_data.Close.diff.ardl, 1:110)60 9.474e+10 2.859e+11 0.331 0.740907
## L(train_data.Close.diff.ardl, 1:110)61 2.369e+10 2.846e+11 0.083 0.933803
## L(train_data.Close.diff.ardl, 1:110)62 7.429e+10 2.847e+11 0.261 0.794506
## L(train_data.Close.diff.ardl, 1:110)63 -2.086e+11 2.859e+11 -0.730 0.466882
## L(train_data.Close.diff.ardl, 1:110)64 -2.993e+10 2.854e+11 -0.105 0.916653
## L(train_data.Close.diff.ardl, 1:110)65 -1.674e+11 2.995e+11 -0.559 0.577093
## L(train_data.Close.diff.ardl, 1:110)66 -1.265e+11 2.873e+11 -0.440 0.660537
## L(train_data.Close.diff.ardl, 1:110)67 2.059e+11 2.856e+11 0.721 0.472222
## L(train_data.Close.diff.ardl, 1:110)68 7.855e+10 2.856e+11 0.275 0.783720
## L(train_data.Close.diff.ardl, 1:110)69 -1.664e+11 2.857e+11 -0.582 0.561263
## L(train_data.Close.diff.ardl, 1:110)70 1.509e+11 2.851e+11 0.529 0.597583
## L(train_data.Close.diff.ardl, 1:110)71 -1.249e+10 2.863e+11 -0.044 0.965281
## L(train_data.Close.diff.ardl, 1:110)72 4.188e+11 2.851e+11 1.469 0.144220
## L(train_data.Close.diff.ardl, 1:110)73 -2.404e+11 2.864e+11 -0.839 0.402773
## L(train_data.Close.diff.ardl, 1:110)74 -9.235e+10 2.882e+11 -0.320 0.749180
## L(train_data.Close.diff.ardl, 1:110)75 1.336e+10 2.890e+11 0.046 0.963185
## L(train_data.Close.diff.ardl, 1:110)76 -1.681e+11 2.866e+11 -0.587 0.558492
## L(train_data.Close.diff.ardl, 1:110)77 -6.560e+10 2.877e+11 -0.228 0.819967
## L(train_data.Close.diff.ardl, 1:110)78 1.011e+11 2.853e+11 0.354 0.723681
## L(train_data.Close.diff.ardl, 1:110)79 -1.256e+11 2.860e+11 -0.439 0.661232
## L(train_data.Close.diff.ardl, 1:110)80 -2.278e+11 2.850e+11 -0.799 0.425500
## L(train_data.Close.diff.ardl, 1:110)81 -1.863e+11 2.857e+11 -0.652 0.515551
## L(train_data.Close.diff.ardl, 1:110)82 -1.635e+11 2.859e+11 -0.572 0.568326
## L(train_data.Close.diff.ardl, 1:110)83 -1.376e+12 3.483e+11 -3.950 0.000126
## L(train_data.Close.diff.ardl, 1:110)84 -4.828e+11 2.957e+11 -1.633 0.104926
## L(train_data.Close.diff.ardl, 1:110)85 6.079e+10 3.000e+11 0.203 0.839705
## L(train_data.Close.diff.ardl, 1:110)86 3.801e+10 2.875e+11 0.132 0.895025
## L(train_data.Close.diff.ardl, 1:110)87 1.727e+10 2.887e+11 0.060 0.952383
## L(train_data.Close.diff.ardl, 1:110)88 1.028e+11 3.155e+11 0.326 0.745105
## L(train_data.Close.diff.ardl, 1:110)89 -2.298e+11 2.859e+11 -0.804 0.423049
## L(train_data.Close.diff.ardl, 1:110)90 -6.132e+10 2.833e+11 -0.216 0.828932
## L(train_data.Close.diff.ardl, 1:110)91 -8.693e+10 2.832e+11 -0.307 0.759361
## L(train_data.Close.diff.ardl, 1:110)92 1.575e+11 2.822e+11 0.558 0.577648
## L(train_data.Close.diff.ardl, 1:110)93 2.015e+11 2.829e+11 0.712 0.477404
## L(train_data.Close.diff.ardl, 1:110)94 6.543e+10 2.819e+11 0.232 0.816819
## L(train_data.Close.diff.ardl, 1:110)95 8.842e+10 2.845e+11 0.311 0.756451
## L(train_data.Close.diff.ardl, 1:110)96 2.833e+11 2.831e+11 1.000 0.318889
## L(train_data.Close.diff.ardl, 1:110)97 2.464e+11 2.844e+11 0.866 0.387950
## L(train_data.Close.diff.ardl, 1:110)98 2.116e+11 2.846e+11 0.744 0.458426
## L(train_data.Close.diff.ardl, 1:110)99 3.565e+10 2.832e+11 0.126 0.900016
## L(train_data.Close.diff.ardl, 1:110)100 2.561e+11 2.845e+11 0.900 0.369558
## L(train_data.Close.diff.ardl, 1:110)101 1.885e+11 2.855e+11 0.660 0.510286
## L(train_data.Close.diff.ardl, 1:110)102 3.838e+10 3.156e+11 0.122 0.903389
## L(train_data.Close.diff.ardl, 1:110)103 2.821e+10 2.837e+11 0.099 0.920938
## L(train_data.Close.diff.ardl, 1:110)104 2.596e+11 2.835e+11 0.916 0.361505
## L(train_data.Close.diff.ardl, 1:110)105 1.344e+11 2.830e+11 0.475 0.635600
## L(train_data.Close.diff.ardl, 1:110)106 -6.070e+10 2.847e+11 -0.213 0.831503
## L(train_data.Close.diff.ardl, 1:110)107 -2.314e+11 2.923e+11 -0.791 0.430104
## L(train_data.Close.diff.ardl, 1:110)108 -3.045e+11 2.826e+11 -1.077 0.283242
## L(train_data.Close.diff.ardl, 1:110)109 -1.599e+11 2.837e+11 -0.564 0.573917
## L(train_data.Close.diff.ardl, 1:110)110 1.436e+11 2.835e+11 0.506 0.613471
##
## (Intercept) ***
## L(train_data.Turnover.ardl, 2) .
## L(train_data.Turnover.ardl, 61)
## L(train_data.Turnover.ardl, 75)
## L(train_data.Turnover.ardl, 117)
## L(train_data.Close.diff.ardl, 1:110)1
## L(train_data.Close.diff.ardl, 1:110)2
## L(train_data.Close.diff.ardl, 1:110)3
## L(train_data.Close.diff.ardl, 1:110)4
## L(train_data.Close.diff.ardl, 1:110)5
## L(train_data.Close.diff.ardl, 1:110)6
## L(train_data.Close.diff.ardl, 1:110)7
## L(train_data.Close.diff.ardl, 1:110)8
## L(train_data.Close.diff.ardl, 1:110)9
## L(train_data.Close.diff.ardl, 1:110)10
## L(train_data.Close.diff.ardl, 1:110)11
## L(train_data.Close.diff.ardl, 1:110)12
## L(train_data.Close.diff.ardl, 1:110)13
## L(train_data.Close.diff.ardl, 1:110)14
## L(train_data.Close.diff.ardl, 1:110)15
## L(train_data.Close.diff.ardl, 1:110)16
## L(train_data.Close.diff.ardl, 1:110)17
## L(train_data.Close.diff.ardl, 1:110)18
## L(train_data.Close.diff.ardl, 1:110)19
## L(train_data.Close.diff.ardl, 1:110)20
## L(train_data.Close.diff.ardl, 1:110)21
## L(train_data.Close.diff.ardl, 1:110)22
## L(train_data.Close.diff.ardl, 1:110)23
## L(train_data.Close.diff.ardl, 1:110)24
## L(train_data.Close.diff.ardl, 1:110)25
## L(train_data.Close.diff.ardl, 1:110)26
## L(train_data.Close.diff.ardl, 1:110)27 ***
## L(train_data.Close.diff.ardl, 1:110)28
## L(train_data.Close.diff.ardl, 1:110)29
## L(train_data.Close.diff.ardl, 1:110)30
## L(train_data.Close.diff.ardl, 1:110)31
## L(train_data.Close.diff.ardl, 1:110)32
## L(train_data.Close.diff.ardl, 1:110)33
## L(train_data.Close.diff.ardl, 1:110)34
## L(train_data.Close.diff.ardl, 1:110)35
## L(train_data.Close.diff.ardl, 1:110)36
## L(train_data.Close.diff.ardl, 1:110)37
## L(train_data.Close.diff.ardl, 1:110)38
## L(train_data.Close.diff.ardl, 1:110)39
## L(train_data.Close.diff.ardl, 1:110)40
## L(train_data.Close.diff.ardl, 1:110)41
## L(train_data.Close.diff.ardl, 1:110)42
## L(train_data.Close.diff.ardl, 1:110)43
## L(train_data.Close.diff.ardl, 1:110)44
## L(train_data.Close.diff.ardl, 1:110)45
## L(train_data.Close.diff.ardl, 1:110)46
## L(train_data.Close.diff.ardl, 1:110)47
## L(train_data.Close.diff.ardl, 1:110)48
## L(train_data.Close.diff.ardl, 1:110)49
## L(train_data.Close.diff.ardl, 1:110)50
## L(train_data.Close.diff.ardl, 1:110)51
## L(train_data.Close.diff.ardl, 1:110)52
## L(train_data.Close.diff.ardl, 1:110)53
## L(train_data.Close.diff.ardl, 1:110)54
## L(train_data.Close.diff.ardl, 1:110)55
## L(train_data.Close.diff.ardl, 1:110)56
## L(train_data.Close.diff.ardl, 1:110)57
## L(train_data.Close.diff.ardl, 1:110)58
## L(train_data.Close.diff.ardl, 1:110)59
## L(train_data.Close.diff.ardl, 1:110)60
## L(train_data.Close.diff.ardl, 1:110)61
## L(train_data.Close.diff.ardl, 1:110)62
## L(train_data.Close.diff.ardl, 1:110)63
## L(train_data.Close.diff.ardl, 1:110)64
## L(train_data.Close.diff.ardl, 1:110)65
## L(train_data.Close.diff.ardl, 1:110)66
## L(train_data.Close.diff.ardl, 1:110)67
## L(train_data.Close.diff.ardl, 1:110)68
## L(train_data.Close.diff.ardl, 1:110)69
## L(train_data.Close.diff.ardl, 1:110)70
## L(train_data.Close.diff.ardl, 1:110)71
## L(train_data.Close.diff.ardl, 1:110)72
## L(train_data.Close.diff.ardl, 1:110)73
## L(train_data.Close.diff.ardl, 1:110)74
## L(train_data.Close.diff.ardl, 1:110)75
## L(train_data.Close.diff.ardl, 1:110)76
## L(train_data.Close.diff.ardl, 1:110)77
## L(train_data.Close.diff.ardl, 1:110)78
## L(train_data.Close.diff.ardl, 1:110)79
## L(train_data.Close.diff.ardl, 1:110)80
## L(train_data.Close.diff.ardl, 1:110)81
## L(train_data.Close.diff.ardl, 1:110)82
## L(train_data.Close.diff.ardl, 1:110)83 ***
## L(train_data.Close.diff.ardl, 1:110)84
## L(train_data.Close.diff.ardl, 1:110)85
## L(train_data.Close.diff.ardl, 1:110)86
## L(train_data.Close.diff.ardl, 1:110)87
## L(train_data.Close.diff.ardl, 1:110)88
## L(train_data.Close.diff.ardl, 1:110)89
## L(train_data.Close.diff.ardl, 1:110)90
## L(train_data.Close.diff.ardl, 1:110)91
## L(train_data.Close.diff.ardl, 1:110)92
## L(train_data.Close.diff.ardl, 1:110)93
## L(train_data.Close.diff.ardl, 1:110)94
## L(train_data.Close.diff.ardl, 1:110)95
## L(train_data.Close.diff.ardl, 1:110)96
## L(train_data.Close.diff.ardl, 1:110)97
## L(train_data.Close.diff.ardl, 1:110)98
## L(train_data.Close.diff.ardl, 1:110)99
## L(train_data.Close.diff.ardl, 1:110)100
## L(train_data.Close.diff.ardl, 1:110)101
## L(train_data.Close.diff.ardl, 1:110)102
## L(train_data.Close.diff.ardl, 1:110)103
## L(train_data.Close.diff.ardl, 1:110)104
## L(train_data.Close.diff.ardl, 1:110)105
## L(train_data.Close.diff.ardl, 1:110)106
## L(train_data.Close.diff.ardl, 1:110)107
## L(train_data.Close.diff.ardl, 1:110)108
## L(train_data.Close.diff.ardl, 1:110)109
## L(train_data.Close.diff.ardl, 1:110)110
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.81e+14 on 133 degrees of freedom
## Multiple R-squared: 0.4152, Adjusted R-squared: -0.08608
## F-statistic: 0.8283 on 114 and 133 DF, p-value: 0.8494Turnover.Close.testing.4 <- predict(Turnover.Close.training.4, n.ahead = length(test_data.Turnover.ardl, test_data.Close.diff.ardl))
head(Turnover.Close.testing.4)## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 3.024653e+14 3.231393e+14 4.290379e+14 2.608829e+14 2.236482e+14 2.309187e+14Turnover.Close.fitted_training.4 <- fitted(Turnover.Close.training.4)
head(Turnover.Close.fitted_training.4)## Time Series:
## Start = c(2015, 118)
## End = c(2015, 123)
## Frequency = 365
## [1] 3.024653e+14 3.231393e+14 4.290379e+14 2.608829e+14 2.236482e+14
## [6] 2.309187e+14Turnover.Close.4.training.mse_value <- mse(train_data.Turnover.ardl, Turnover.Close.fitted_training.4)
Turnover.Close.4.training.rmse_value <- rmse(train_data.Turnover.ardl, Turnover.Close.fitted_training.4)
Turnover.testing.n.4 = as.numeric(Turnover.Close.testing.4)
Turnover.Close.4.testing.mse_value <- mse(test_data.Turnover.ardl, Turnover.testing.n.4)
Turnover.Close.4.testing.rmse_value <- rmse(test_data.Turnover.ardl, Turnover.testing.n.4)
cat("Training Model MSE:", Turnover.Close.4.training.mse_value, "\n Training Model RMSE:", Turnover.Close.4.training.rmse_value , "\n Testing Model MSE:", Turnover.Close.4.testing.mse_value, "\n Testing Model RMSE:", Turnover.Close.4.testing.rmse_value , "\n")## Training Model MSE: 4.234901e+28
## Training Model RMSE: 2.057888e+14
## Testing Model MSE: 1.050948e+29
## Testing Model RMSE: 3.241834e+14cat(" Training Model AIC:", AIC(Turnover.Close.training.4), "\n Training Model BIC:", BIC(Turnover.Close.training.4), "\n")## Training Model AIC: 17282.9
## Training Model BIC: 17690.46The R-squared of this training model is 0.4152, relatively better compared to that of the other models. A decent percent of the model seems to be explained by stock closing price. The AIC model seems to be lower than the BIC model, thus it might be better compared to BIC model. However, both the training model and the testing model result in high MSE and RMSE values suggesting a bad fit.
Turnover and Open
Size
train_size.Turnover.ardl <- floor (2/3 * length(Turnover.ts))
train_size.Open.diff.ardl <- floor (2/3 * length(Open.ts.diff))Data
train_data.Turnover.ardl <- Turnover.ts[1:train_size.Turnover.ardl]
train_data.Turnover.ardl = ts(train_data.Turnover.ardl,
start=c(2015,1),
end=c(2015,365),
frequency=365)
train_data.Open.diff.ardl <- Open.ts.diff[1:train_size.Open.diff.ardl]
train_data.Open.diff.ardl = ts(train_data.Open.diff.ardl,
start=c(2015,1),
end=c(2015,365),
frequency=365)Test
test_data.Turnover.ardl <- Turnover.ts[(train_size.Turnover.ardl + 1):length(Turnover.ts)]
test_data.Turnover.ardl = ts(test_data.Turnover.ardl, start=c(2015,1), end=c(2015,365), frequency=365)
test_data.Open.diff.ardl <- Open.ts.diff[(train_size.Open.diff.ardl + 1):length(Open.ts.diff)]
test_data.Open.diff.ardl = ts(test_data.Open.diff.ardl, start=c(2015,1), end=c(2015,365), frequency=365)
length(train_data.Turnover.ardl) ## [1] 365length(test_data.Open.diff.ardl)## [1] 365Training and Testing for Turnover with lag (1:4) and Close with lag (110)
Turnover.open.training.1 <- dynlm(train_data.Turnover.ardl ~ L(train_data.Turnover.ardl, 1:4) + L(train_data.Open.diff.ardl, 110))
summary(Turnover.open.training.1)##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover.ardl ~ L(train_data.Turnover.ardl,
## 1:4) + L(train_data.Open.diff.ardl, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.836e+14 -1.171e+14 -4.466e+13 5.824e+13 1.779e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.420e+14 4.189e+13 5.777 2.27e-08 ***
## L(train_data.Turnover.ardl, 1:4)1 3.317e-01 6.312e-02 5.256 3.16e-07 ***
## L(train_data.Turnover.ardl, 1:4)2 3.215e-02 6.654e-02 0.483 0.629
## L(train_data.Turnover.ardl, 1:4)3 -2.656e-02 6.649e-02 -0.400 0.690
## L(train_data.Turnover.ardl, 1:4)4 8.819e-02 6.312e-02 1.397 0.164
## L(train_data.Open.diff.ardl, 110) 7.830e+10 2.278e+11 0.344 0.731
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.521e+14 on 249 degrees of freedom
## Multiple R-squared: 0.1264, Adjusted R-squared: 0.1089
## F-statistic: 7.205 on 5 and 249 DF, p-value: 2.554e-06Turnover.open.testing.1 <- predict(Turnover.open.training.1, n.ahead = length(test_data.Turnover.ardl, test_data.Open.diff.ardl))
head(Turnover.open.testing.1)## 2015(111) 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## 4.235781e+14 4.473081e+14 3.574453e+14 3.632945e+14 3.949272e+14 3.255934e+14Turnover.open.fitted_training.1 <- fitted(Turnover.open.training.1)
head(Turnover.open.fitted_training.1)## Time Series:
## Start = c(2015, 111)
## End = c(2015, 116)
## Frequency = 365
## [1] 4.235781e+14 4.473081e+14 3.574453e+14 3.632945e+14 3.949272e+14
## [6] 3.255934e+14Turnover.open.1.training.mse_value <- mse(train_data.Turnover.ardl, Turnover.open.fitted_training.1)
Turnover.open.1.training.rmse_value <- rmse(train_data.Turnover.ardl, Turnover.open.fitted_training.1)
Turnover.testing.n.1 = as.numeric(Turnover.open.testing.1)
Turnover.open.1.testing.mse_value <- mse(test_data.Turnover.ardl, Turnover.testing.n.1)
Turnover.open.1.testing.rmse_value <- rmse(test_data.Turnover.ardl, Turnover.testing.n.1)
cat("Training Model MSE:", Turnover.open.1.training.mse_value, "\n Training Model RMSE:", Turnover.open.1.training.rmse_value , "\n Testing Model MSE:", Turnover.open.1.testing.mse_value, "\n Testing Model RMSE:", Turnover.open.1.testing.rmse_value , "\n")## Training Model MSE: 6.206145e+28
## Training Model RMSE: 2.491214e+14
## Testing Model MSE: 9.034831e+28
## Testing Model RMSE: 3.0058e+14cat(" Training Model AIC:", AIC(Turnover.open.training.1), "\n Training Model BIC:", BIC(Turnover.open.training.1), "\n")## Training Model AIC: 17643.63
## Training Model BIC: 17668.42For the ARDL model with Turnover with lag (1:4) and Close with lag (110), the training model has a R-squared value of 0.1264, a relatively low value. The closing price might not have much explanation for the model. And the MSE and RMSE of the training and testing models are also very high, again suggesting a bad fit. The AIC of this model is only slightly lower than the BIC, so it is not that much better than BIC.
Training and Testing for Turnover with lag (1:4) and Close with lag (35)n(110)
Turnover.open.training.2 <- dynlm(train_data.Turnover.ardl ~ L(train_data.Turnover.ardl, 1:4) + L(train_data.Open.diff.ardl, 110))
summary(Turnover.open.training.2)##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover.ardl ~ L(train_data.Turnover.ardl,
## 1:4) + L(train_data.Open.diff.ardl, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.836e+14 -1.171e+14 -4.466e+13 5.824e+13 1.779e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.420e+14 4.189e+13 5.777 2.27e-08 ***
## L(train_data.Turnover.ardl, 1:4)1 3.317e-01 6.312e-02 5.256 3.16e-07 ***
## L(train_data.Turnover.ardl, 1:4)2 3.215e-02 6.654e-02 0.483 0.629
## L(train_data.Turnover.ardl, 1:4)3 -2.656e-02 6.649e-02 -0.400 0.690
## L(train_data.Turnover.ardl, 1:4)4 8.819e-02 6.312e-02 1.397 0.164
## L(train_data.Open.diff.ardl, 110) 7.830e+10 2.278e+11 0.344 0.731
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.521e+14 on 249 degrees of freedom
## Multiple R-squared: 0.1264, Adjusted R-squared: 0.1089
## F-statistic: 7.205 on 5 and 249 DF, p-value: 2.554e-06Turnover.open.testing.2 <- predict(Turnover.open.training.2, n.ahead = length(test_data.Turnover.ardl, test_data.Open.diff.ardl))
head(Turnover.open.testing.2)## 2015(111) 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## 4.235781e+14 4.473081e+14 3.574453e+14 3.632945e+14 3.949272e+14 3.255934e+14Turnover.open.fitted_training.2 <- fitted(Turnover.open.training.2)
head(Turnover.open.fitted_training.2)## Time Series:
## Start = c(2015, 111)
## End = c(2015, 116)
## Frequency = 365
## [1] 4.235781e+14 4.473081e+14 3.574453e+14 3.632945e+14 3.949272e+14
## [6] 3.255934e+14Turnover.open.2.training.mse_value <- mse(train_data.Turnover.ardl, Turnover.open.fitted_training.2)
Turnover.open.2.training.rmse_value <- rmse(train_data.Turnover.ardl, Turnover.open.fitted_training.2)
Turnover.testing.n.2 = as.numeric(Turnover.open.testing.2)
Turnover.open.2.testing.mse_value <- mse(test_data.Turnover.ardl, Turnover.testing.n.2)
Turnover.open.2.testing.rmse_value <- rmse(test_data.Turnover.ardl, Turnover.testing.n.2)
cat("Training Model MSE:", Turnover.open.2.training.mse_value, "\n Training Model RMSE:", Turnover.open.2.training.rmse_value , "\n Testing Model MSE:", Turnover.open.2.testing.mse_value, "\n Testing Model RMSE:", Turnover.open.2.testing.rmse_value , "\n")## Training Model MSE: 6.206145e+28
## Training Model RMSE: 2.491214e+14
## Testing Model MSE: 9.034831e+28
## Testing Model RMSE: 3.0058e+14cat(" Training Model AIC:", AIC(Turnover.open.training.2), "\n Training Model BIC:", BIC(Turnover.open.training.2), "\n")## Training Model AIC: 17643.63
## Training Model BIC: 17668.42The R-squared value of this training model is not much different from the previous one, suggesting a similarly unfit model. Its AIC and BIC are also of similar values, with AIC being slightly lower than BIC. The MSE and RMSE of both the training and the testing models are also relatively high, so we can concluded that the ARDL model with Turnover with lag (1:4) and Close with lag 35 and lag 110 is a not a good fit.
Training and Testing for Turnover with lag (2)n(61)n(75)n(117) and Close with lag (110)
Turnover.open.training.3 <- dynlm(train_data.Turnover.ardl ~ L(train_data.Turnover.ardl, 2) + L(train_data.Turnover.ardl, 61) + L(train_data.Turnover.ardl, 75) + L(train_data.Turnover.ardl, 117) + L(train_data.Open.diff.ardl, 110), data = infy_stock)
summary(Turnover.open.training.3)##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover.ardl ~ L(train_data.Turnover.ardl,
## 2) + L(train_data.Turnover.ardl, 61) + L(train_data.Turnover.ardl,
## 75) + L(train_data.Turnover.ardl, 117) + L(train_data.Open.diff.ardl,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.278e+14 -1.336e+14 -4.820e+13 7.673e+13 1.888e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.591e+14 5.491e+13 4.718 4.03e-06 ***
## L(train_data.Turnover.ardl, 2) 1.465e-01 6.262e-02 2.339 0.0201 *
## L(train_data.Turnover.ardl, 61) 1.460e-01 6.453e-02 2.263 0.0245 *
## L(train_data.Turnover.ardl, 75) 1.275e-02 6.269e-02 0.203 0.8390
## L(train_data.Turnover.ardl, 117) 8.398e-02 6.481e-02 1.296 0.1963
## L(train_data.Open.diff.ardl, 110) 5.634e+10 2.409e+11 0.234 0.8153
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.646e+14 on 242 degrees of freedom
## Multiple R-squared: 0.05664, Adjusted R-squared: 0.03715
## F-statistic: 2.906 on 5 and 242 DF, p-value: 0.01441Turnover.open.testing.3 <- predict(Turnover.open.training.3, n.ahead = length(test_data.Turnover.ardl, test_data.Open.diff.ardl))
head(Turnover.open.testing.3)## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 3.753256e+14 3.824230e+14 4.821168e+14 4.380066e+14 3.810161e+14 4.235079e+14Turnover.open.fitted_training.3 <- fitted(Turnover.open.training.3)
head(Turnover.open.fitted_training.3)## Time Series:
## Start = c(2015, 118)
## End = c(2015, 123)
## Frequency = 365
## [1] 3.753256e+14 3.824230e+14 4.821168e+14 4.380066e+14 3.810161e+14
## [6] 4.235079e+14Turnover.open.3.training.mse_value <- mse(train_data.Turnover.ardl, Turnover.open.fitted_training.3)
Turnover.open.3.training.rmse_value <- rmse(train_data.Turnover.ardl, Turnover.open.fitted_training.3)
Turnover.testing.n.3 = as.numeric(Turnover.open.testing.3)
Turnover.open.3.testing.mse_value <- mse(test_data.Turnover.ardl, Turnover.testing.n.3)
Turnover.open.3.testing.rmse_value <- rmse(test_data.Turnover.ardl, Turnover.testing.n.3)
cat("Training Model MSE:", Turnover.open.3.training.mse_value, "\n Training Model RMSE:", Turnover.open.3.training.rmse_value , "\n Testing Model MSE:", Turnover.open.3.testing.mse_value, "\n Testing Model RMSE:", Turnover.open.3.testing.rmse_value , "\n")## Training Model MSE: 6.831351e+28
## Training Model RMSE: 2.613685e+14
## Testing Model MSE: 7.528142e+28
## Testing Model RMSE: 2.743746e+14cat(" Training Model AIC:", AIC(Turnover.open.training.3), "\n Training Model BIC:", BIC(Turnover.open.training.3), "\n")## Training Model AIC: 17183.48
## Training Model BIC: 17208.08Looking at the high value of MSE and RMSE of the training and testing models, they are suggesting a bad fit. The R-squared value of 0.05664 also supports this sentiment. The AIC and BIC are though lower than those of other ARDL model, with the AIC model having a slightly smaller value than the BIC model.
Training and Testing for Turnover with lag (2)n(61)n(75)n(117) and Close with lag (35)n(110)
Turnover.open.training.4 <- dynlm(train_data.Turnover.ardl ~ L(train_data.Turnover.ardl, 2) + L(train_data.Turnover.ardl, 61) + L(train_data.Turnover.ardl, 75) + L(train_data.Turnover.ardl, 117) + L(train_data.Open.diff.ardl, 35) + L(train_data.Open.diff.ardl, 110))
summary(Turnover.open.training.4) ##
## Time series regression with "ts" data:
## Start = 2015(118), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Turnover.ardl ~ L(train_data.Turnover.ardl,
## 2) + L(train_data.Turnover.ardl, 61) + L(train_data.Turnover.ardl,
## 75) + L(train_data.Turnover.ardl, 117) + L(train_data.Open.diff.ardl,
## 35) + L(train_data.Open.diff.ardl, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.253e+14 -1.379e+14 -4.640e+13 7.651e+13 1.886e+15
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.571e+14 5.502e+13 4.673 4.95e-06 ***
## L(train_data.Turnover.ardl, 2) 1.469e-01 6.267e-02 2.344 0.0199 *
## L(train_data.Turnover.ardl, 61) 1.460e-01 6.458e-02 2.261 0.0247 *
## L(train_data.Turnover.ardl, 75) 1.198e-02 6.275e-02 0.191 0.8488
## L(train_data.Turnover.ardl, 117) 8.736e-02 6.501e-02 1.344 0.1803
## L(train_data.Open.diff.ardl, 35) -1.866e+11 2.408e+11 -0.775 0.4393
## L(train_data.Open.diff.ardl, 110) 5.331e+10 2.411e+11 0.221 0.8252
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.648e+14 on 241 degrees of freedom
## Multiple R-squared: 0.05898, Adjusted R-squared: 0.03555
## F-statistic: 2.518 on 6 and 241 DF, p-value: 0.02211Turnover.open.testing.4 <- predict(Turnover.open.training.4, n.ahead = length(test_data.Turnover.ardl, test_data.Open.diff.ardl))
head(Turnover.open.testing.4)## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 3.782094e+14 3.914244e+14 4.748761e+14 4.360750e+14 3.748475e+14 4.314554e+14Turnover.open.fitted_training.4 <- fitted(Turnover.open.training.4)
head(Turnover.open.fitted_training.4)## Time Series:
## Start = c(2015, 118)
## End = c(2015, 123)
## Frequency = 365
## [1] 3.782094e+14 3.914244e+14 4.748761e+14 4.360750e+14 3.748475e+14
## [6] 4.314554e+14Turnover.open.4.training.mse_value <- mse(train_data.Turnover.ardl, Turnover.open.fitted_training.4)
Turnover.open.4.training.rmse_value <- rmse(train_data.Turnover.ardl, Turnover.open.fitted_training.4)
Turnover.testing.n.4 = as.numeric(Turnover.open.testing.4)
Turnover.open.4.testing.mse_value <- mse(test_data.Turnover.ardl, Turnover.testing.n.4)
Turnover.open.4.testing.rmse_value <- rmse(test_data.Turnover.ardl, Turnover.testing.n.4)
cat("Training Model MSE:", Turnover.open.4.training.mse_value, "\n Training Model RMSE:", Turnover.open.4.training.rmse_value , "\n Testing Model MSE:", Turnover.open.4.testing.mse_value, "\n Testing Model RMSE:", Turnover.open.4.testing.rmse_value , "\n")## Training Model MSE: 6.814379e+28
## Training Model RMSE: 2.610437e+14
## Testing Model MSE: 7.544455e+28
## Testing Model RMSE: 2.746717e+14cat(" Training Model AIC:", AIC(Turnover.open.training.4), "\n Training Model BIC:", BIC(Turnover.open.training.4), "\n")## Training Model AIC: 17184.87
## Training Model BIC: 17212.97This last ARDL model for turnover is also observed to be not a good fit. The R-squared value of 0.05898, and the relatively high values of MSE and RMSE of both the training and the testing model supports this conclusion. The AIC and BIC of this model are not much different from the previous one too, with AIC being lower than BIC.
Volume and Close
Size
train_size.Volume.ardl <- floor (2/3 * length(Volume.ts))
train_size.Close.diff.ardl <- floor (2/3 * length(Close.ts.diff))Data
train_data.Volume.ardl <- Volume.ts[1:train_size.Volume.ardl]
train_data.Volume.ardl = ts(train_data.Volume.ardl,
start=c(2015,1),
end=c(2015,365),
frequency=365)
train_data.Close.diff.ardl <- Close.ts.diff[1:train_size.Close.diff.ardl]
train_data.Close.diff.ardl = ts(train_data.Close.diff.ardl,
start=c(2015,1),
end=c(2015,365),
frequency=365)Test
test_data.Volume.ardl <- Volume.ts[(train_size.Volume.ardl + 1):length(Volume.ts)]
test_data.Volume.ardl = ts(test_data.Volume.ardl, start=c(2015,1), end=c(2015,365), frequency=365)
test_data.Close.diff.ardl <- Close.ts.diff[(train_size.Close.diff.ardl + 1):length(Close.ts.diff)]
test_data.Close.diff.ardl = ts(test_data.Close.diff.ardl, start=c(2015,1), end=c(2015,365), frequency=365)
length(train_data.Volume.ardl) ## [1] 365length(test_data.Close.diff.ardl)## [1] 365Testing and Training for Volume with lag (1:32) and Close lag (110)
Volume.Close.training.1 <- dynlm(train_data.Volume.ardl ~ L(train_data.Volume.ardl, 1:32) + L(train_data.Close.diff.ardl, 110))
summary(Volume.Close.training.1)##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Volume.ardl ~ L(train_data.Volume.ardl,
## 1:32) + L(train_data.Close.diff.ardl, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2243794 -859961 -208859 410699 16614502
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.634e+05 3.911e+05 1.440 0.151
## L(train_data.Volume.ardl, 1:32)1 3.213e-01 6.714e-02 4.786 3.11e-06 ***
## L(train_data.Volume.ardl, 1:32)2 6.593e-02 7.066e-02 0.933 0.352
## L(train_data.Volume.ardl, 1:32)3 -4.245e-02 7.065e-02 -0.601 0.549
## L(train_data.Volume.ardl, 1:32)4 1.058e-01 7.054e-02 1.500 0.135
## L(train_data.Volume.ardl, 1:32)5 -6.789e-04 7.052e-02 -0.010 0.992
## L(train_data.Volume.ardl, 1:32)6 4.269e-02 7.055e-02 0.605 0.546
## L(train_data.Volume.ardl, 1:32)7 9.498e-02 7.051e-02 1.347 0.179
## L(train_data.Volume.ardl, 1:32)8 -3.525e-03 7.091e-02 -0.050 0.960
## L(train_data.Volume.ardl, 1:32)9 -3.928e-04 7.033e-02 -0.006 0.996
## L(train_data.Volume.ardl, 1:32)10 5.399e-02 6.966e-02 0.775 0.439
## L(train_data.Volume.ardl, 1:32)11 -5.194e-02 6.975e-02 -0.745 0.457
## L(train_data.Volume.ardl, 1:32)12 1.638e-02 6.983e-02 0.235 0.815
## L(train_data.Volume.ardl, 1:32)13 -2.872e-02 6.974e-02 -0.412 0.681
## L(train_data.Volume.ardl, 1:32)14 -2.790e-02 6.975e-02 -0.400 0.690
## L(train_data.Volume.ardl, 1:32)15 4.999e-02 6.977e-02 0.717 0.474
## L(train_data.Volume.ardl, 1:32)16 -4.025e-02 6.983e-02 -0.576 0.565
## L(train_data.Volume.ardl, 1:32)17 -6.026e-03 6.979e-02 -0.086 0.931
## L(train_data.Volume.ardl, 1:32)18 1.925e-02 6.973e-02 0.276 0.783
## L(train_data.Volume.ardl, 1:32)19 -2.659e-02 6.971e-02 -0.382 0.703
## L(train_data.Volume.ardl, 1:32)20 3.286e-02 6.980e-02 0.471 0.638
## L(train_data.Volume.ardl, 1:32)21 -3.366e-02 6.983e-02 -0.482 0.630
## L(train_data.Volume.ardl, 1:32)22 4.264e-04 7.007e-02 0.006 0.995
## L(train_data.Volume.ardl, 1:32)23 1.993e-02 6.999e-02 0.285 0.776
## L(train_data.Volume.ardl, 1:32)24 1.580e-01 7.004e-02 2.256 0.025 *
## L(train_data.Volume.ardl, 1:32)25 -1.511e-02 7.080e-02 -0.213 0.831
## L(train_data.Volume.ardl, 1:32)26 4.845e-02 7.047e-02 0.687 0.492
## L(train_data.Volume.ardl, 1:32)27 1.936e-02 7.484e-02 0.259 0.796
## L(train_data.Volume.ardl, 1:32)28 -1.139e-01 7.055e-02 -1.615 0.108
## L(train_data.Volume.ardl, 1:32)29 7.090e-02 7.063e-02 1.004 0.317
## L(train_data.Volume.ardl, 1:32)30 1.127e-02 7.100e-02 0.159 0.874
## L(train_data.Volume.ardl, 1:32)31 2.085e-02 7.057e-02 0.295 0.768
## L(train_data.Volume.ardl, 1:32)32 5.764e-02 6.718e-02 0.858 0.392
## L(train_data.Close.diff.ardl, 110) 6.742e+02 1.874e+03 0.360 0.719
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1837000 on 221 degrees of freedom
## Multiple R-squared: 0.2737, Adjusted R-squared: 0.1652
## F-statistic: 2.523 on 33 and 221 DF, p-value: 3.628e-05Volume.Close.testing.1 <- predict(Volume.Close.training.1, n.ahead = length(test_data.Volume.ardl, test_data.Close.diff.ardl))
head(Volume.Close.testing.1)## 2015(111) 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## 2324120 2136256 2417843 2347545 2609755 2266470Volume.Close.fitted_training.1 <- fitted(Volume.Close.training.1)
head(Volume.Close.fitted_training.1)## Time Series:
## Start = c(2015, 111)
## End = c(2015, 116)
## Frequency = 365
## [1] 2324120 2136256 2417843 2347545 2609755 2266470Volume.Close.1.training.mse_value <- mse(train_data.Volume.ardl, Volume.Close.fitted_training.1)
Volume.Close.1.training.rmse_value <- rmse(train_data.Volume.ardl, Volume.Close.fitted_training.1)
Volume.testing.n.1 = as.numeric(Volume.Close.testing.1)
Volume.Close.1.testing.mse_value <- mse(test_data.Volume.ardl, Volume.testing.n.1)
Volume.Close.1.testing.rmse_value <- rmse(test_data.Volume.ardl, Volume.testing.n.1)
cat("Training Model MSE:", Volume.Close.1.training.mse_value, "\n Training Model RMSE:", Volume.Close.1.training.rmse_value , "\n Testing Model MSE:", Volume.Close.1.testing.mse_value, "\n Testing Model RMSE:", Volume.Close.1.testing.rmse_value , "\n")## Training Model MSE: 2.92334e+12
## Training Model RMSE: 1709778
## Testing Model MSE: 4.253261e+12
## Testing Model RMSE: 2062344cat(" Training Model AIC:", AIC(Volume.Close.training.1), "\n Training Model BIC:", BIC(Volume.Close.training.1), "\n")## Training Model AIC: 8113.114
## Training Model BIC: 8237.059The R-squared value of this training model is 0.2737. Not a high enough value to suggest that a good percent of this model can be explained by the independent variable. The MSE and RMSE values are also extremely high for both the training and the testing models. However, it has AIC of 8113.114 and BIC of 8237.059, the lowest out of all the ARDL models so far. The AIC model results in lower value than BIC model, suggesting a better fit. However, the low R-squared value and the high MSE and RMSE values still point to a not well fit model.
Testing and Training for Volume with lag (1:32) and Close lag (1:110)
Volume.Close.training.2 <- dynlm(train_data.Volume.ardl ~ L(train_data.Volume.ardl, 1:32) + L(train_data.Close.diff.ardl, 1:110), data = infy_stock)
summary(Volume.Close.training.2)##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Volume.ardl ~ L(train_data.Volume.ardl,
## 1:32) + L(train_data.Close.diff.ardl, 1:110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2643542 -453755 -44404 325441 7176538
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.845e+05 6.564e+05 1.500 0.136479
## L(train_data.Volume.ardl, 1:32)1 3.288e-01 9.298e-02 3.537 0.000591
## L(train_data.Volume.ardl, 1:32)2 5.529e-02 9.839e-02 0.562 0.575273
## L(train_data.Volume.ardl, 1:32)3 -2.603e-02 9.650e-02 -0.270 0.787874
## L(train_data.Volume.ardl, 1:32)4 1.201e-01 9.633e-02 1.246 0.215253
## L(train_data.Volume.ardl, 1:32)5 -4.472e-02 9.696e-02 -0.461 0.645513
## L(train_data.Volume.ardl, 1:32)6 -9.591e-02 9.646e-02 -0.994 0.322220
## L(train_data.Volume.ardl, 1:32)7 1.167e-01 9.601e-02 1.216 0.226707
## L(train_data.Volume.ardl, 1:32)8 -6.744e-02 9.703e-02 -0.695 0.488454
## L(train_data.Volume.ardl, 1:32)9 4.914e-02 9.647e-02 0.509 0.611459
## L(train_data.Volume.ardl, 1:32)10 2.459e-02 9.705e-02 0.253 0.800464
## L(train_data.Volume.ardl, 1:32)11 1.288e-02 9.737e-02 0.132 0.895019
## L(train_data.Volume.ardl, 1:32)12 9.877e-02 9.553e-02 1.034 0.303361
## L(train_data.Volume.ardl, 1:32)13 -6.219e-04 9.580e-02 -0.006 0.994832
## L(train_data.Volume.ardl, 1:32)14 -2.204e-03 9.571e-02 -0.023 0.981671
## L(train_data.Volume.ardl, 1:32)15 5.302e-02 9.539e-02 0.556 0.579474
## L(train_data.Volume.ardl, 1:32)16 -1.096e-01 9.525e-02 -1.151 0.252195
## L(train_data.Volume.ardl, 1:32)17 -3.885e-02 9.554e-02 -0.407 0.685015
## L(train_data.Volume.ardl, 1:32)18 1.066e-01 9.544e-02 1.117 0.266212
## L(train_data.Volume.ardl, 1:32)19 -5.254e-02 9.588e-02 -0.548 0.584791
## L(train_data.Volume.ardl, 1:32)20 2.381e-02 9.570e-02 0.249 0.803945
## L(train_data.Volume.ardl, 1:32)21 -8.342e-02 9.536e-02 -0.875 0.383601
## L(train_data.Volume.ardl, 1:32)22 -6.954e-02 9.564e-02 -0.727 0.468678
## L(train_data.Volume.ardl, 1:32)23 -9.116e-03 9.640e-02 -0.095 0.924835
## L(train_data.Volume.ardl, 1:32)24 2.173e-01 9.654e-02 2.250 0.026371
## L(train_data.Volume.ardl, 1:32)25 -1.916e-01 9.825e-02 -1.950 0.053684
## L(train_data.Volume.ardl, 1:32)26 1.220e-01 9.863e-02 1.237 0.218676
## L(train_data.Volume.ardl, 1:32)27 -7.113e-02 9.898e-02 -0.719 0.473865
## L(train_data.Volume.ardl, 1:32)28 -5.399e-02 8.739e-02 -0.618 0.537958
## L(train_data.Volume.ardl, 1:32)29 -1.435e-02 8.588e-02 -0.167 0.867607
## L(train_data.Volume.ardl, 1:32)30 5.938e-02 8.652e-02 0.686 0.493903
## L(train_data.Volume.ardl, 1:32)31 -3.617e-02 8.682e-02 -0.417 0.677750
## L(train_data.Volume.ardl, 1:32)32 1.641e-01 8.057e-02 2.037 0.044001
## L(train_data.Close.diff.ardl, 1:110)1 -4.702e+02 1.250e+03 -0.376 0.707505
## L(train_data.Close.diff.ardl, 1:110)2 -1.014e+03 1.249e+03 -0.812 0.418481
## L(train_data.Close.diff.ardl, 1:110)3 6.938e+02 1.250e+03 0.555 0.579908
## L(train_data.Close.diff.ardl, 1:110)4 -6.864e+02 1.249e+03 -0.550 0.583698
## L(train_data.Close.diff.ardl, 1:110)5 -3.784e+01 1.249e+03 -0.030 0.975888
## L(train_data.Close.diff.ardl, 1:110)6 -2.044e+03 1.241e+03 -1.646 0.102484
## L(train_data.Close.diff.ardl, 1:110)7 -1.321e+03 1.253e+03 -1.055 0.293893
## L(train_data.Close.diff.ardl, 1:110)8 -8.086e+02 1.256e+03 -0.644 0.521170
## L(train_data.Close.diff.ardl, 1:110)9 -3.992e+02 1.255e+03 -0.318 0.751033
## L(train_data.Close.diff.ardl, 1:110)10 -1.503e+02 1.253e+03 -0.120 0.904743
## L(train_data.Close.diff.ardl, 1:110)11 -3.898e+02 1.247e+03 -0.313 0.755196
## L(train_data.Close.diff.ardl, 1:110)12 -9.358e+02 1.243e+03 -0.753 0.453245
## L(train_data.Close.diff.ardl, 1:110)13 -1.923e+01 1.594e+03 -0.012 0.990397
## L(train_data.Close.diff.ardl, 1:110)14 2.498e+03 1.607e+03 1.555 0.122726
## L(train_data.Close.diff.ardl, 1:110)15 1.714e+03 1.622e+03 1.057 0.292844
## L(train_data.Close.diff.ardl, 1:110)16 4.548e+01 1.624e+03 0.028 0.977712
## L(train_data.Close.diff.ardl, 1:110)17 3.234e+02 1.620e+03 0.200 0.842068
## L(train_data.Close.diff.ardl, 1:110)18 -7.526e+02 1.614e+03 -0.466 0.641866
## L(train_data.Close.diff.ardl, 1:110)19 -1.324e+03 1.613e+03 -0.821 0.413409
## L(train_data.Close.diff.ardl, 1:110)20 -4.963e+02 1.600e+03 -0.310 0.756924
## L(train_data.Close.diff.ardl, 1:110)21 1.182e+02 1.593e+03 0.074 0.940998
## L(train_data.Close.diff.ardl, 1:110)22 -4.765e+02 1.597e+03 -0.298 0.766021
## L(train_data.Close.diff.ardl, 1:110)23 1.179e+03 1.585e+03 0.744 0.458708
## L(train_data.Close.diff.ardl, 1:110)24 -3.499e+02 1.565e+03 -0.224 0.823536
## L(train_data.Close.diff.ardl, 1:110)25 2.223e+02 1.564e+03 0.142 0.887195
## L(train_data.Close.diff.ardl, 1:110)26 4.432e+02 1.553e+03 0.285 0.775863
## L(train_data.Close.diff.ardl, 1:110)27 -1.609e+04 1.556e+03 -10.341 < 2e-16
## L(train_data.Close.diff.ardl, 1:110)28 1.435e+03 2.143e+03 0.670 0.504500
## L(train_data.Close.diff.ardl, 1:110)29 9.862e+02 2.157e+03 0.457 0.648365
## L(train_data.Close.diff.ardl, 1:110)30 1.048e+03 2.115e+03 0.495 0.621317
## L(train_data.Close.diff.ardl, 1:110)31 4.887e+02 2.118e+03 0.231 0.817959
## L(train_data.Close.diff.ardl, 1:110)32 -3.509e+03 2.118e+03 -1.657 0.100414
## L(train_data.Close.diff.ardl, 1:110)33 -2.740e+03 2.137e+03 -1.282 0.202480
## L(train_data.Close.diff.ardl, 1:110)34 -9.223e+02 2.142e+03 -0.431 0.667586
## L(train_data.Close.diff.ardl, 1:110)35 -4.674e+02 2.137e+03 -0.219 0.827288
## L(train_data.Close.diff.ardl, 1:110)36 -1.827e+02 2.176e+03 -0.084 0.933247
## L(train_data.Close.diff.ardl, 1:110)37 -1.698e+03 2.167e+03 -0.784 0.434891
## L(train_data.Close.diff.ardl, 1:110)38 1.532e+03 2.183e+03 0.702 0.484158
## L(train_data.Close.diff.ardl, 1:110)39 6.252e+02 2.140e+03 0.292 0.770758
## L(train_data.Close.diff.ardl, 1:110)40 1.041e+03 2.151e+03 0.484 0.629258
## L(train_data.Close.diff.ardl, 1:110)41 2.489e+03 2.158e+03 1.153 0.251218
## L(train_data.Close.diff.ardl, 1:110)42 3.472e+02 2.164e+03 0.160 0.872830
## L(train_data.Close.diff.ardl, 1:110)43 -3.518e+03 2.160e+03 -1.629 0.106194
## L(train_data.Close.diff.ardl, 1:110)44 -2.054e+03 2.180e+03 -0.942 0.348249
## L(train_data.Close.diff.ardl, 1:110)45 2.850e+03 2.186e+03 1.304 0.194941
## L(train_data.Close.diff.ardl, 1:110)46 1.394e+03 2.201e+03 0.634 0.527638
## L(train_data.Close.diff.ardl, 1:110)47 8.080e+02 2.211e+03 0.365 0.715450
## L(train_data.Close.diff.ardl, 1:110)48 -1.859e+03 2.204e+03 -0.843 0.400752
## L(train_data.Close.diff.ardl, 1:110)49 -1.876e+03 2.207e+03 -0.850 0.397148
## L(train_data.Close.diff.ardl, 1:110)50 -2.337e+03 2.221e+03 -1.052 0.295105
## L(train_data.Close.diff.ardl, 1:110)51 4.878e+02 2.240e+03 0.218 0.827994
## L(train_data.Close.diff.ardl, 1:110)52 -3.453e+03 2.244e+03 -1.539 0.126738
## L(train_data.Close.diff.ardl, 1:110)53 -2.075e+03 2.243e+03 -0.925 0.356868
## L(train_data.Close.diff.ardl, 1:110)54 -3.297e+03 2.248e+03 -1.466 0.145397
## L(train_data.Close.diff.ardl, 1:110)55 6.574e+02 2.135e+03 0.308 0.758739
## L(train_data.Close.diff.ardl, 1:110)56 -3.018e+03 2.140e+03 -1.411 0.161130
## L(train_data.Close.diff.ardl, 1:110)57 -8.027e+02 2.162e+03 -0.371 0.711081
## L(train_data.Close.diff.ardl, 1:110)58 -2.789e+03 2.139e+03 -1.304 0.194937
## L(train_data.Close.diff.ardl, 1:110)59 5.202e+02 2.028e+03 0.256 0.798075
## L(train_data.Close.diff.ardl, 1:110)60 1.028e+03 1.725e+03 0.596 0.552272
## L(train_data.Close.diff.ardl, 1:110)61 5.337e+02 1.732e+03 0.308 0.758498
## L(train_data.Close.diff.ardl, 1:110)62 -4.217e+02 1.725e+03 -0.244 0.807390
## L(train_data.Close.diff.ardl, 1:110)63 -1.436e+03 1.710e+03 -0.840 0.402787
## L(train_data.Close.diff.ardl, 1:110)64 -1.080e+03 1.720e+03 -0.628 0.531233
## L(train_data.Close.diff.ardl, 1:110)65 -1.810e+03 1.705e+03 -1.061 0.290780
## L(train_data.Close.diff.ardl, 1:110)66 6.732e+02 1.715e+03 0.393 0.695358
## L(train_data.Close.diff.ardl, 1:110)67 2.290e+03 1.728e+03 1.325 0.187829
## L(train_data.Close.diff.ardl, 1:110)68 3.111e+01 1.742e+03 0.018 0.985781
## L(train_data.Close.diff.ardl, 1:110)69 -2.388e+03 1.737e+03 -1.375 0.171811
## L(train_data.Close.diff.ardl, 1:110)70 1.028e+03 1.735e+03 0.592 0.554848
## L(train_data.Close.diff.ardl, 1:110)71 -1.778e+03 1.736e+03 -1.024 0.308189
## L(train_data.Close.diff.ardl, 1:110)72 2.232e+03 1.744e+03 1.280 0.203271
## L(train_data.Close.diff.ardl, 1:110)73 -4.107e+03 1.747e+03 -2.351 0.020495
## L(train_data.Close.diff.ardl, 1:110)74 -1.251e+03 1.769e+03 -0.707 0.481097
## L(train_data.Close.diff.ardl, 1:110)75 -2.820e+01 1.775e+03 -0.016 0.987354
## L(train_data.Close.diff.ardl, 1:110)76 -1.683e+03 1.770e+03 -0.951 0.343692
## L(train_data.Close.diff.ardl, 1:110)77 -2.880e+02 1.760e+03 -0.164 0.870286
## L(train_data.Close.diff.ardl, 1:110)78 3.260e+02 1.761e+03 0.185 0.853463
## L(train_data.Close.diff.ardl, 1:110)79 -3.509e+03 1.743e+03 -2.014 0.046449
## L(train_data.Close.diff.ardl, 1:110)80 -1.471e+03 1.754e+03 -0.838 0.403559
## L(train_data.Close.diff.ardl, 1:110)81 -1.727e+03 1.739e+03 -0.994 0.322593
## L(train_data.Close.diff.ardl, 1:110)82 -1.786e+03 1.738e+03 -1.027 0.306447
## L(train_data.Close.diff.ardl, 1:110)83 -9.794e+03 1.742e+03 -5.621 1.41e-07
## L(train_data.Close.diff.ardl, 1:110)84 -5.250e+02 1.960e+03 -0.268 0.789343
## L(train_data.Close.diff.ardl, 1:110)85 3.342e+02 1.916e+03 0.174 0.861852
## L(train_data.Close.diff.ardl, 1:110)86 3.141e+02 1.872e+03 0.168 0.867047
## L(train_data.Close.diff.ardl, 1:110)87 1.745e+03 1.861e+03 0.937 0.350605
## L(train_data.Close.diff.ardl, 1:110)88 -9.548e+02 1.867e+03 -0.511 0.610118
## L(train_data.Close.diff.ardl, 1:110)89 -1.957e+03 1.863e+03 -1.051 0.295615
## L(train_data.Close.diff.ardl, 1:110)90 -2.826e+02 1.865e+03 -0.151 0.879855
## L(train_data.Close.diff.ardl, 1:110)91 -6.853e+02 1.846e+03 -0.371 0.711084
## L(train_data.Close.diff.ardl, 1:110)92 1.766e+03 1.865e+03 0.947 0.345918
## L(train_data.Close.diff.ardl, 1:110)93 1.346e+03 1.870e+03 0.720 0.473214
## L(train_data.Close.diff.ardl, 1:110)94 -8.379e+02 1.881e+03 -0.445 0.656868
## L(train_data.Close.diff.ardl, 1:110)95 1.143e+03 1.893e+03 0.604 0.547330
## L(train_data.Close.diff.ardl, 1:110)96 -8.062e+01 1.890e+03 -0.043 0.966055
## L(train_data.Close.diff.ardl, 1:110)97 1.426e+03 1.889e+03 0.755 0.451846
## L(train_data.Close.diff.ardl, 1:110)98 7.780e+02 1.885e+03 0.413 0.680563
## L(train_data.Close.diff.ardl, 1:110)99 -1.123e+03 1.881e+03 -0.597 0.551894
## L(train_data.Close.diff.ardl, 1:110)100 7.495e+02 1.886e+03 0.397 0.691890
## L(train_data.Close.diff.ardl, 1:110)101 1.590e+03 1.870e+03 0.850 0.397161
## L(train_data.Close.diff.ardl, 1:110)102 -2.155e+03 1.864e+03 -1.156 0.250024
## L(train_data.Close.diff.ardl, 1:110)103 3.016e+02 1.871e+03 0.161 0.872203
## L(train_data.Close.diff.ardl, 1:110)104 8.460e+01 1.873e+03 0.045 0.964058
## L(train_data.Close.diff.ardl, 1:110)105 -1.500e+03 1.832e+03 -0.819 0.414620
## L(train_data.Close.diff.ardl, 1:110)106 -7.017e+02 1.844e+03 -0.381 0.704278
## L(train_data.Close.diff.ardl, 1:110)107 9.518e+00 1.841e+03 0.005 0.995884
## L(train_data.Close.diff.ardl, 1:110)108 -4.561e+03 1.821e+03 -2.504 0.013722
## L(train_data.Close.diff.ardl, 1:110)109 -6.035e+02 1.869e+03 -0.323 0.747319
## L(train_data.Close.diff.ardl, 1:110)110 1.364e+02 1.869e+03 0.073 0.941955
##
## (Intercept)
## L(train_data.Volume.ardl, 1:32)1 ***
## L(train_data.Volume.ardl, 1:32)2
## L(train_data.Volume.ardl, 1:32)3
## L(train_data.Volume.ardl, 1:32)4
## L(train_data.Volume.ardl, 1:32)5
## L(train_data.Volume.ardl, 1:32)6
## L(train_data.Volume.ardl, 1:32)7
## L(train_data.Volume.ardl, 1:32)8
## L(train_data.Volume.ardl, 1:32)9
## L(train_data.Volume.ardl, 1:32)10
## L(train_data.Volume.ardl, 1:32)11
## L(train_data.Volume.ardl, 1:32)12
## L(train_data.Volume.ardl, 1:32)13
## L(train_data.Volume.ardl, 1:32)14
## L(train_data.Volume.ardl, 1:32)15
## L(train_data.Volume.ardl, 1:32)16
## L(train_data.Volume.ardl, 1:32)17
## L(train_data.Volume.ardl, 1:32)18
## L(train_data.Volume.ardl, 1:32)19
## L(train_data.Volume.ardl, 1:32)20
## L(train_data.Volume.ardl, 1:32)21
## L(train_data.Volume.ardl, 1:32)22
## L(train_data.Volume.ardl, 1:32)23
## L(train_data.Volume.ardl, 1:32)24 *
## L(train_data.Volume.ardl, 1:32)25 .
## L(train_data.Volume.ardl, 1:32)26
## L(train_data.Volume.ardl, 1:32)27
## L(train_data.Volume.ardl, 1:32)28
## L(train_data.Volume.ardl, 1:32)29
## L(train_data.Volume.ardl, 1:32)30
## L(train_data.Volume.ardl, 1:32)31
## L(train_data.Volume.ardl, 1:32)32 *
## L(train_data.Close.diff.ardl, 1:110)1
## L(train_data.Close.diff.ardl, 1:110)2
## L(train_data.Close.diff.ardl, 1:110)3
## L(train_data.Close.diff.ardl, 1:110)4
## L(train_data.Close.diff.ardl, 1:110)5
## L(train_data.Close.diff.ardl, 1:110)6
## L(train_data.Close.diff.ardl, 1:110)7
## L(train_data.Close.diff.ardl, 1:110)8
## L(train_data.Close.diff.ardl, 1:110)9
## L(train_data.Close.diff.ardl, 1:110)10
## L(train_data.Close.diff.ardl, 1:110)11
## L(train_data.Close.diff.ardl, 1:110)12
## L(train_data.Close.diff.ardl, 1:110)13
## L(train_data.Close.diff.ardl, 1:110)14
## L(train_data.Close.diff.ardl, 1:110)15
## L(train_data.Close.diff.ardl, 1:110)16
## L(train_data.Close.diff.ardl, 1:110)17
## L(train_data.Close.diff.ardl, 1:110)18
## L(train_data.Close.diff.ardl, 1:110)19
## L(train_data.Close.diff.ardl, 1:110)20
## L(train_data.Close.diff.ardl, 1:110)21
## L(train_data.Close.diff.ardl, 1:110)22
## L(train_data.Close.diff.ardl, 1:110)23
## L(train_data.Close.diff.ardl, 1:110)24
## L(train_data.Close.diff.ardl, 1:110)25
## L(train_data.Close.diff.ardl, 1:110)26
## L(train_data.Close.diff.ardl, 1:110)27 ***
## L(train_data.Close.diff.ardl, 1:110)28
## L(train_data.Close.diff.ardl, 1:110)29
## L(train_data.Close.diff.ardl, 1:110)30
## L(train_data.Close.diff.ardl, 1:110)31
## L(train_data.Close.diff.ardl, 1:110)32
## L(train_data.Close.diff.ardl, 1:110)33
## L(train_data.Close.diff.ardl, 1:110)34
## L(train_data.Close.diff.ardl, 1:110)35
## L(train_data.Close.diff.ardl, 1:110)36
## L(train_data.Close.diff.ardl, 1:110)37
## L(train_data.Close.diff.ardl, 1:110)38
## L(train_data.Close.diff.ardl, 1:110)39
## L(train_data.Close.diff.ardl, 1:110)40
## L(train_data.Close.diff.ardl, 1:110)41
## L(train_data.Close.diff.ardl, 1:110)42
## L(train_data.Close.diff.ardl, 1:110)43
## L(train_data.Close.diff.ardl, 1:110)44
## L(train_data.Close.diff.ardl, 1:110)45
## L(train_data.Close.diff.ardl, 1:110)46
## L(train_data.Close.diff.ardl, 1:110)47
## L(train_data.Close.diff.ardl, 1:110)48
## L(train_data.Close.diff.ardl, 1:110)49
## L(train_data.Close.diff.ardl, 1:110)50
## L(train_data.Close.diff.ardl, 1:110)51
## L(train_data.Close.diff.ardl, 1:110)52
## L(train_data.Close.diff.ardl, 1:110)53
## L(train_data.Close.diff.ardl, 1:110)54
## L(train_data.Close.diff.ardl, 1:110)55
## L(train_data.Close.diff.ardl, 1:110)56
## L(train_data.Close.diff.ardl, 1:110)57
## L(train_data.Close.diff.ardl, 1:110)58
## L(train_data.Close.diff.ardl, 1:110)59
## L(train_data.Close.diff.ardl, 1:110)60
## L(train_data.Close.diff.ardl, 1:110)61
## L(train_data.Close.diff.ardl, 1:110)62
## L(train_data.Close.diff.ardl, 1:110)63
## L(train_data.Close.diff.ardl, 1:110)64
## L(train_data.Close.diff.ardl, 1:110)65
## L(train_data.Close.diff.ardl, 1:110)66
## L(train_data.Close.diff.ardl, 1:110)67
## L(train_data.Close.diff.ardl, 1:110)68
## L(train_data.Close.diff.ardl, 1:110)69
## L(train_data.Close.diff.ardl, 1:110)70
## L(train_data.Close.diff.ardl, 1:110)71
## L(train_data.Close.diff.ardl, 1:110)72
## L(train_data.Close.diff.ardl, 1:110)73 *
## L(train_data.Close.diff.ardl, 1:110)74
## L(train_data.Close.diff.ardl, 1:110)75
## L(train_data.Close.diff.ardl, 1:110)76
## L(train_data.Close.diff.ardl, 1:110)77
## L(train_data.Close.diff.ardl, 1:110)78
## L(train_data.Close.diff.ardl, 1:110)79 *
## L(train_data.Close.diff.ardl, 1:110)80
## L(train_data.Close.diff.ardl, 1:110)81
## L(train_data.Close.diff.ardl, 1:110)82
## L(train_data.Close.diff.ardl, 1:110)83 ***
## L(train_data.Close.diff.ardl, 1:110)84
## L(train_data.Close.diff.ardl, 1:110)85
## L(train_data.Close.diff.ardl, 1:110)86
## L(train_data.Close.diff.ardl, 1:110)87
## L(train_data.Close.diff.ardl, 1:110)88
## L(train_data.Close.diff.ardl, 1:110)89
## L(train_data.Close.diff.ardl, 1:110)90
## L(train_data.Close.diff.ardl, 1:110)91
## L(train_data.Close.diff.ardl, 1:110)92
## L(train_data.Close.diff.ardl, 1:110)93
## L(train_data.Close.diff.ardl, 1:110)94
## L(train_data.Close.diff.ardl, 1:110)95
## L(train_data.Close.diff.ardl, 1:110)96
## L(train_data.Close.diff.ardl, 1:110)97
## L(train_data.Close.diff.ardl, 1:110)98
## L(train_data.Close.diff.ardl, 1:110)99
## L(train_data.Close.diff.ardl, 1:110)100
## L(train_data.Close.diff.ardl, 1:110)101
## L(train_data.Close.diff.ardl, 1:110)102
## L(train_data.Close.diff.ardl, 1:110)103
## L(train_data.Close.diff.ardl, 1:110)104
## L(train_data.Close.diff.ardl, 1:110)105
## L(train_data.Close.diff.ardl, 1:110)106
## L(train_data.Close.diff.ardl, 1:110)107
## L(train_data.Close.diff.ardl, 1:110)108 *
## L(train_data.Close.diff.ardl, 1:110)109
## L(train_data.Close.diff.ardl, 1:110)110
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1490000 on 112 degrees of freedom
## Multiple R-squared: 0.7579, Adjusted R-squared: 0.4509
## F-statistic: 2.469 on 142 and 112 DF, p-value: 5.41e-07Volume.Close.testing.2 <- predict(Volume.Close.training.2, n.ahead = length(test_data.Volume.ardl, test_data.Close.diff.ardl))
head(Volume.Close.testing.2)## 2015(111) 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## 2188815 2396618 3021395 2967878 2630902 2670640Volume.Close.fitted_training.2 <- fitted(Volume.Close.training.2)
head(Volume.Close.fitted_training.2)## Time Series:
## Start = c(2015, 111)
## End = c(2015, 116)
## Frequency = 365
## [1] 2188815 2396618 3021395 2967878 2630902 2670640Volume.Close.2.training.mse_value <- mse(train_data.Volume.ardl, Volume.Close.fitted_training.2)
Volume.Close.2.training.rmse_value <- rmse(train_data.Volume.ardl, Volume.Close.fitted_training.2)
Volume.testing.n.2 = as.numeric(Volume.Close.testing.2)
Volume.Close.2.testing.mse_value <- mse(test_data.Volume.ardl, Volume.testing.n.2)
Volume.Close.2.testing.rmse_value <- rmse(test_data.Volume.ardl, Volume.testing.n.2)
cat("Training Model MSE:", Volume.Close.2.training.mse_value, "\n Training Model RMSE:", Volume.Close.2.training.rmse_value , "\n Testing Model MSE:", Volume.Close.2.testing.mse_value, "\n Testing Model RMSE:", Volume.Close.2.testing.rmse_value , "\n")## Training Model MSE: 974451842772
## Training Model RMSE: 987143.3
## Testing Model MSE: 6.898777e+12
## Testing Model RMSE: 2626552cat(" Training Model AIC:", AIC(Volume.Close.training.2), "\n Training Model BIC:", BIC(Volume.Close.training.2), "\n")## Training Model AIC: 8050.97
## Training Model BIC: 8560.912This training model has a R-squared value of 0.7579, meaning a large portion of the model can be attributed to and explained by the independent variable. The MSE of the models are still high, but the RMSE of both the training and testing models are significantly lower when compared to the other models, suggesting that this model might be a better fit. The AIC and BIC are also lower than that of the previous model.
Testing and Training for Volume with lag (1:32)n(91:122) and Close lag (110)
Volume.Close.training.3 <- dynlm(train_data.Volume.ardl ~ L(train_data.Volume.ardl, 1:32) + L(train_data.Volume.ardl, 91:122) + L(train_data.Close.diff.ardl, 110), data = infy_stock)
summary(Volume.Close.training.3)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Volume.ardl ~ L(train_data.Volume.ardl,
## 1:32) + L(train_data.Volume.ardl, 91:122) + L(train_data.Close.diff.ardl,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2783386 -861150 -134581 490754 16159831
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.500e+06 1.021e+06 2.449 0.0153 *
## L(train_data.Volume.ardl, 1:32)1 3.030e-01 7.499e-02 4.041 7.92e-05 ***
## L(train_data.Volume.ardl, 1:32)2 4.374e-02 7.842e-02 0.558 0.5777
## L(train_data.Volume.ardl, 1:32)3 -3.848e-02 7.907e-02 -0.487 0.6271
## L(train_data.Volume.ardl, 1:32)4 6.283e-02 7.894e-02 0.796 0.4271
## L(train_data.Volume.ardl, 1:32)5 -1.749e-02 7.893e-02 -0.222 0.8249
## L(train_data.Volume.ardl, 1:32)6 2.295e-02 7.872e-02 0.292 0.7710
## L(train_data.Volume.ardl, 1:32)7 1.091e-01 7.861e-02 1.388 0.1669
## L(train_data.Volume.ardl, 1:32)8 -3.501e-02 7.914e-02 -0.442 0.6588
## L(train_data.Volume.ardl, 1:32)9 -5.269e-03 7.901e-02 -0.067 0.9469
## L(train_data.Volume.ardl, 1:32)10 5.887e-02 7.863e-02 0.749 0.4550
## L(train_data.Volume.ardl, 1:32)11 -7.503e-02 7.807e-02 -0.961 0.3379
## L(train_data.Volume.ardl, 1:32)12 4.801e-02 7.836e-02 0.613 0.5409
## L(train_data.Volume.ardl, 1:32)13 -9.118e-02 7.848e-02 -1.162 0.2469
## L(train_data.Volume.ardl, 1:32)14 -2.186e-03 7.892e-02 -0.028 0.9779
## L(train_data.Volume.ardl, 1:32)15 1.101e-02 7.893e-02 0.140 0.8892
## L(train_data.Volume.ardl, 1:32)16 -4.078e-02 7.884e-02 -0.517 0.6056
## L(train_data.Volume.ardl, 1:32)17 -7.596e-03 7.859e-02 -0.097 0.9231
## L(train_data.Volume.ardl, 1:32)18 -5.021e-03 7.866e-02 -0.064 0.9492
## L(train_data.Volume.ardl, 1:32)19 -2.395e-02 7.852e-02 -0.305 0.7607
## L(train_data.Volume.ardl, 1:32)20 2.615e-02 7.858e-02 0.333 0.7397
## L(train_data.Volume.ardl, 1:32)21 -3.462e-02 7.903e-02 -0.438 0.6618
## L(train_data.Volume.ardl, 1:32)22 3.908e-03 7.969e-02 0.049 0.9609
## L(train_data.Volume.ardl, 1:32)23 3.326e-02 7.949e-02 0.418 0.6761
## L(train_data.Volume.ardl, 1:32)24 9.474e-02 7.943e-02 1.193 0.2345
## L(train_data.Volume.ardl, 1:32)25 3.407e-02 7.975e-02 0.427 0.6698
## L(train_data.Volume.ardl, 1:32)26 1.819e-02 7.943e-02 0.229 0.8191
## L(train_data.Volume.ardl, 1:32)27 5.483e-02 8.550e-02 0.641 0.5222
## L(train_data.Volume.ardl, 1:32)28 -1.163e-01 7.950e-02 -1.463 0.1453
## L(train_data.Volume.ardl, 1:32)29 3.809e-02 7.935e-02 0.480 0.6318
## L(train_data.Volume.ardl, 1:32)30 5.844e-02 8.035e-02 0.727 0.4680
## L(train_data.Volume.ardl, 1:32)31 8.024e-03 8.030e-02 0.100 0.9205
## L(train_data.Volume.ardl, 1:32)32 7.073e-02 7.557e-02 0.936 0.3506
## L(train_data.Volume.ardl, 91:122)91 -7.663e-02 7.571e-02 -1.012 0.3128
## L(train_data.Volume.ardl, 91:122)92 1.525e-02 8.029e-02 0.190 0.8496
## L(train_data.Volume.ardl, 91:122)93 -1.169e-01 8.000e-02 -1.461 0.1457
## L(train_data.Volume.ardl, 91:122)94 8.934e-02 7.934e-02 1.126 0.2616
## L(train_data.Volume.ardl, 91:122)95 -6.091e-02 7.964e-02 -0.765 0.4454
## L(train_data.Volume.ardl, 91:122)96 1.598e-02 7.943e-02 0.201 0.8407
## L(train_data.Volume.ardl, 91:122)97 -3.957e-02 7.944e-02 -0.498 0.6191
## L(train_data.Volume.ardl, 91:122)98 -2.785e-02 7.979e-02 -0.349 0.7275
## L(train_data.Volume.ardl, 91:122)99 5.709e-02 7.940e-02 0.719 0.4731
## L(train_data.Volume.ardl, 91:122)100 -5.484e-02 7.947e-02 -0.690 0.4910
## L(train_data.Volume.ardl, 91:122)101 1.211e-02 7.968e-02 0.152 0.8794
## L(train_data.Volume.ardl, 91:122)102 -1.998e-03 7.902e-02 -0.025 0.9799
## L(train_data.Volume.ardl, 91:122)103 9.043e-03 7.840e-02 0.115 0.9083
## L(train_data.Volume.ardl, 91:122)104 -5.065e-02 7.858e-02 -0.645 0.5200
## L(train_data.Volume.ardl, 91:122)105 -1.324e-02 7.872e-02 -0.168 0.8666
## L(train_data.Volume.ardl, 91:122)106 -9.372e-02 7.859e-02 -1.192 0.2347
## L(train_data.Volume.ardl, 91:122)107 6.061e-02 7.902e-02 0.767 0.4440
## L(train_data.Volume.ardl, 91:122)108 -3.755e-02 7.899e-02 -0.475 0.6351
## L(train_data.Volume.ardl, 91:122)109 -3.825e-02 7.893e-02 -0.485 0.6286
## L(train_data.Volume.ardl, 91:122)110 -4.305e-02 7.849e-02 -0.548 0.5840
## L(train_data.Volume.ardl, 91:122)111 -2.868e-02 7.834e-02 -0.366 0.7147
## L(train_data.Volume.ardl, 91:122)112 1.563e-01 7.812e-02 2.001 0.0470 *
## L(train_data.Volume.ardl, 91:122)113 -8.047e-02 7.863e-02 -1.023 0.3075
## L(train_data.Volume.ardl, 91:122)114 -5.862e-02 7.883e-02 -0.744 0.4581
## L(train_data.Volume.ardl, 91:122)115 -8.955e-03 7.951e-02 -0.113 0.9105
## L(train_data.Volume.ardl, 91:122)116 1.852e-02 7.865e-02 0.235 0.8141
## L(train_data.Volume.ardl, 91:122)117 8.373e-02 7.873e-02 1.064 0.2890
## L(train_data.Volume.ardl, 91:122)118 -3.248e-02 7.902e-02 -0.411 0.6815
## L(train_data.Volume.ardl, 91:122)119 -1.058e-01 7.889e-02 -1.341 0.1815
## L(train_data.Volume.ardl, 91:122)120 7.376e-02 7.992e-02 0.923 0.3573
## L(train_data.Volume.ardl, 91:122)121 -4.995e-02 7.829e-02 -0.638 0.5242
## L(train_data.Volume.ardl, 91:122)122 -1.182e-02 7.499e-02 -0.158 0.8749
## L(train_data.Close.diff.ardl, 110) 1.042e+03 2.065e+03 0.504 0.6146
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1932000 on 177 degrees of freedom
## Multiple R-squared: 0.354, Adjusted R-squared: 0.1167
## F-statistic: 1.492 on 65 and 177 DF, p-value: 0.02095Volume.Close.testing.3 <- predict(Volume.Close.training.3, n.ahead = length(test_data.Volume.ardl, test_data.Close.diff.ardl))
head(Volume.Close.testing.3)## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128)
## 3465236 4155716 3050391 2200056 3056388 2565630Volume.Close.fitted_training.3 <- fitted(Volume.Close.training.3)
head(Volume.Close.fitted_training.3)## Time Series:
## Start = c(2015, 123)
## End = c(2015, 128)
## Frequency = 365
## [1] 3465236 4155716 3050391 2200056 3056388 2565630Volume.Close.3.training.mse_value <- mse(train_data.Volume.ardl, Volume.Close.fitted_training.3)
Volume.Close.3.training.rmse_value <- rmse(train_data.Volume.ardl, Volume.Close.fitted_training.3)
Volume.testing.n.3 = as.numeric(Volume.Close.testing.3)
Volume.Close.3.testing.mse_value <- mse(test_data.Volume.ardl, Volume.testing.n.3)
Volume.Close.3.testing.rmse_value <- rmse(test_data.Volume.ardl, Volume.testing.n.3)
cat("Training Model MSE:", Volume.Close.3.training.mse_value, "\n Training Model RMSE:", Volume.Close.3.training.rmse_value , "\n Testing Model MSE:", Volume.Close.3.testing.mse_value, "\n Testing Model RMSE:", Volume.Close.3.testing.rmse_value , "\n")## Training Model MSE: 2.71972e+12
## Training Model RMSE: 1649158
## Testing Model MSE: 4.671199e+12
## Testing Model RMSE: 2161296cat(" Training Model AIC:", AIC(Volume.Close.training.3), "\n Training Model BIC:", BIC(Volume.Close.training.3), "\n")## Training Model AIC: 7781.071
## Training Model BIC: 8015.106The R-squared of this training model is 0.354, not a high enough value to suggest a good fit. But although the MSE of the models are high, the RMSE of both models are not that high compared to others. The AIC and BIC models also result in lower values, with AIC being a slightly better fit than the BIC.
Testing and Training for Volume with lag (1:32)n(91:122) and Close lag (1:110)
Volume.Close.training.4 <- dynlm(train_data.Volume.ardl ~ L(train_data.Volume.ardl, 1:32) + L(train_data.Volume.ardl, 91:122) + L(train_data.Close.diff.ardl, 1:110))
summary(Volume.Close.training.4) ##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Volume.ardl ~ L(train_data.Volume.ardl,
## 1:32) + L(train_data.Volume.ardl, 91:122) + L(train_data.Close.diff.ardl,
## 1:110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2541601 -372924 -24793 374553 5313139
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.000e+06 2.198e+06 1.820 0.073209
## L(train_data.Volume.ardl, 1:32)1 4.292e-01 1.195e-01 3.591 0.000618
## L(train_data.Volume.ardl, 1:32)2 -2.411e-02 1.295e-01 -0.186 0.852804
## L(train_data.Volume.ardl, 1:32)3 -2.397e-02 1.323e-01 -0.181 0.856795
## L(train_data.Volume.ardl, 1:32)4 9.798e-02 1.273e-01 0.769 0.444300
## L(train_data.Volume.ardl, 1:32)5 -2.345e-02 1.303e-01 -0.180 0.857725
## L(train_data.Volume.ardl, 1:32)6 -2.264e-01 1.293e-01 -1.751 0.084519
## L(train_data.Volume.ardl, 1:32)7 2.531e-01 1.314e-01 1.926 0.058227
## L(train_data.Volume.ardl, 1:32)8 -2.333e-01 1.355e-01 -1.722 0.089695
## L(train_data.Volume.ardl, 1:32)9 5.345e-02 1.424e-01 0.375 0.708538
## L(train_data.Volume.ardl, 1:32)10 1.191e-02 1.418e-01 0.084 0.933356
## L(train_data.Volume.ardl, 1:32)11 7.074e-03 1.316e-01 0.054 0.957289
## L(train_data.Volume.ardl, 1:32)12 4.239e-02 1.268e-01 0.334 0.739125
## L(train_data.Volume.ardl, 1:32)13 -8.582e-02 1.265e-01 -0.678 0.499958
## L(train_data.Volume.ardl, 1:32)14 3.596e-02 1.297e-01 0.277 0.782433
## L(train_data.Volume.ardl, 1:32)15 -6.102e-02 1.310e-01 -0.466 0.642947
## L(train_data.Volume.ardl, 1:32)16 -9.215e-02 1.345e-01 -0.685 0.495446
## L(train_data.Volume.ardl, 1:32)17 8.074e-02 1.335e-01 0.605 0.547266
## L(train_data.Volume.ardl, 1:32)18 1.103e-01 1.332e-01 0.828 0.410526
## L(train_data.Volume.ardl, 1:32)19 -7.908e-02 1.324e-01 -0.597 0.552191
## L(train_data.Volume.ardl, 1:32)20 4.696e-02 1.323e-01 0.355 0.723622
## L(train_data.Volume.ardl, 1:32)21 -1.577e-01 1.331e-01 -1.185 0.240287
## L(train_data.Volume.ardl, 1:32)22 2.474e-04 1.336e-01 0.002 0.998528
## L(train_data.Volume.ardl, 1:32)23 6.768e-02 1.345e-01 0.503 0.616515
## L(train_data.Volume.ardl, 1:32)24 -1.704e-02 1.333e-01 -0.128 0.898702
## L(train_data.Volume.ardl, 1:32)25 -6.091e-02 1.325e-01 -0.460 0.647294
## L(train_data.Volume.ardl, 1:32)26 3.312e-02 1.321e-01 0.251 0.802772
## L(train_data.Volume.ardl, 1:32)27 -1.608e-01 1.316e-01 -1.222 0.225817
## L(train_data.Volume.ardl, 1:32)28 2.240e-02 1.115e-01 0.201 0.841372
## L(train_data.Volume.ardl, 1:32)29 -1.239e-01 1.090e-01 -1.136 0.259756
## L(train_data.Volume.ardl, 1:32)30 8.851e-02 1.094e-01 0.809 0.421096
## L(train_data.Volume.ardl, 1:32)31 -3.509e-02 1.092e-01 -0.321 0.748931
## L(train_data.Volume.ardl, 1:32)32 1.358e-01 1.011e-01 1.344 0.183472
## L(train_data.Volume.ardl, 91:122)91 2.392e-02 8.426e-02 0.284 0.777389
## L(train_data.Volume.ardl, 91:122)92 -6.513e-02 8.549e-02 -0.762 0.448826
## L(train_data.Volume.ardl, 91:122)93 -4.418e-02 8.611e-02 -0.513 0.609512
## L(train_data.Volume.ardl, 91:122)94 1.814e-01 8.629e-02 2.102 0.039263
## L(train_data.Volume.ardl, 91:122)95 -6.623e-02 8.921e-02 -0.742 0.460440
## L(train_data.Volume.ardl, 91:122)96 7.434e-02 8.838e-02 0.841 0.403254
## L(train_data.Volume.ardl, 91:122)97 4.150e-02 8.684e-02 0.478 0.634317
## L(train_data.Volume.ardl, 91:122)98 -1.046e-01 8.850e-02 -1.182 0.241254
## L(train_data.Volume.ardl, 91:122)99 4.530e-02 8.940e-02 0.507 0.614042
## L(train_data.Volume.ardl, 91:122)100 -3.760e-04 8.924e-02 -0.004 0.996650
## L(train_data.Volume.ardl, 91:122)101 -4.087e-02 8.981e-02 -0.455 0.650533
## L(train_data.Volume.ardl, 91:122)102 -4.015e-03 8.715e-02 -0.046 0.963387
## L(train_data.Volume.ardl, 91:122)103 -2.044e-02 8.539e-02 -0.239 0.811558
## L(train_data.Volume.ardl, 91:122)104 -1.014e-01 9.194e-02 -1.102 0.274215
## L(train_data.Volume.ardl, 91:122)105 -3.503e-02 9.144e-02 -0.383 0.702794
## L(train_data.Volume.ardl, 91:122)106 -1.317e-01 9.240e-02 -1.425 0.158765
## L(train_data.Volume.ardl, 91:122)107 3.751e-02 9.327e-02 0.402 0.688811
## L(train_data.Volume.ardl, 91:122)108 6.157e-02 9.226e-02 0.667 0.506798
## L(train_data.Volume.ardl, 91:122)109 -5.158e-02 9.193e-02 -0.561 0.576545
## L(train_data.Volume.ardl, 91:122)110 8.279e-03 8.939e-02 0.093 0.926473
## L(train_data.Volume.ardl, 91:122)111 -5.627e-02 8.957e-02 -0.628 0.531938
## L(train_data.Volume.ardl, 91:122)112 2.979e-01 8.906e-02 3.345 0.001341
## L(train_data.Volume.ardl, 91:122)113 -2.036e-01 9.520e-02 -2.139 0.036048
## L(train_data.Volume.ardl, 91:122)114 -5.171e-03 9.798e-02 -0.053 0.958068
## L(train_data.Volume.ardl, 91:122)115 2.620e-02 8.967e-02 0.292 0.771078
## L(train_data.Volume.ardl, 91:122)116 -6.009e-02 8.775e-02 -0.685 0.495818
## L(train_data.Volume.ardl, 91:122)117 -3.109e-02 9.120e-02 -0.341 0.734228
## L(train_data.Volume.ardl, 91:122)118 -2.455e-02 9.223e-02 -0.266 0.790886
## L(train_data.Volume.ardl, 91:122)119 -2.338e-01 9.247e-02 -2.528 0.013789
## L(train_data.Volume.ardl, 91:122)120 6.854e-02 9.496e-02 0.722 0.472916
## L(train_data.Volume.ardl, 91:122)121 -7.957e-02 9.380e-02 -0.848 0.399216
## L(train_data.Volume.ardl, 91:122)122 -9.246e-03 9.278e-02 -0.100 0.920909
## L(train_data.Close.diff.ardl, 1:110)1 -1.864e+02 2.138e+03 -0.087 0.930780
## L(train_data.Close.diff.ardl, 1:110)2 -8.623e+02 2.094e+03 -0.412 0.681747
## L(train_data.Close.diff.ardl, 1:110)3 -3.295e+01 2.083e+03 -0.016 0.987425
## L(train_data.Close.diff.ardl, 1:110)4 4.613e+01 2.083e+03 0.022 0.982394
## L(train_data.Close.diff.ardl, 1:110)5 2.470e+03 2.078e+03 1.189 0.238720
## L(train_data.Close.diff.ardl, 1:110)6 -2.226e+03 2.078e+03 -1.071 0.287851
## L(train_data.Close.diff.ardl, 1:110)7 1.855e+01 2.120e+03 0.009 0.993044
## L(train_data.Close.diff.ardl, 1:110)8 -5.544e+01 2.111e+03 -0.026 0.979124
## L(train_data.Close.diff.ardl, 1:110)9 4.047e+03 2.105e+03 1.923 0.058710
## L(train_data.Close.diff.ardl, 1:110)10 -2.293e+03 2.178e+03 -1.053 0.296018
## L(train_data.Close.diff.ardl, 1:110)11 1.293e+03 2.187e+03 0.591 0.556418
## L(train_data.Close.diff.ardl, 1:110)12 -6.345e+02 1.665e+03 -0.381 0.704421
## L(train_data.Close.diff.ardl, 1:110)13 1.967e+02 2.011e+03 0.098 0.922363
## L(train_data.Close.diff.ardl, 1:110)14 1.941e+03 2.017e+03 0.962 0.339377
## L(train_data.Close.diff.ardl, 1:110)15 -2.669e+02 2.030e+03 -0.131 0.895771
## L(train_data.Close.diff.ardl, 1:110)16 1.797e+03 2.026e+03 0.887 0.378123
## L(train_data.Close.diff.ardl, 1:110)17 5.709e+02 2.033e+03 0.281 0.779766
## L(train_data.Close.diff.ardl, 1:110)18 1.703e+02 2.020e+03 0.084 0.933082
## L(train_data.Close.diff.ardl, 1:110)19 3.298e+02 1.894e+03 0.174 0.862258
## L(train_data.Close.diff.ardl, 1:110)20 7.297e+02 1.872e+03 0.390 0.697898
## L(train_data.Close.diff.ardl, 1:110)21 7.410e+02 1.872e+03 0.396 0.693529
## L(train_data.Close.diff.ardl, 1:110)22 4.823e+02 1.903e+03 0.253 0.800660
## L(train_data.Close.diff.ardl, 1:110)23 2.391e+03 1.881e+03 1.272 0.207872
## L(train_data.Close.diff.ardl, 1:110)24 -1.293e+02 1.876e+03 -0.069 0.945252
## L(train_data.Close.diff.ardl, 1:110)25 8.300e+02 1.856e+03 0.447 0.656107
## L(train_data.Close.diff.ardl, 1:110)26 1.083e+03 1.856e+03 0.584 0.561272
## L(train_data.Close.diff.ardl, 1:110)27 -1.635e+04 1.882e+03 -8.687 1.24e-12
## L(train_data.Close.diff.ardl, 1:110)28 3.695e+03 2.680e+03 1.379 0.172376
## L(train_data.Close.diff.ardl, 1:110)29 8.454e+02 2.691e+03 0.314 0.754346
## L(train_data.Close.diff.ardl, 1:110)30 2.065e+03 2.718e+03 0.760 0.449992
## L(train_data.Close.diff.ardl, 1:110)31 1.418e+03 2.696e+03 0.526 0.600485
## L(train_data.Close.diff.ardl, 1:110)32 -2.006e+03 2.699e+03 -0.743 0.459892
## L(train_data.Close.diff.ardl, 1:110)33 -4.036e+03 2.717e+03 -1.485 0.142124
## L(train_data.Close.diff.ardl, 1:110)34 2.189e+03 2.740e+03 0.799 0.427205
## L(train_data.Close.diff.ardl, 1:110)35 -1.552e+03 2.735e+03 -0.568 0.572231
## L(train_data.Close.diff.ardl, 1:110)36 1.622e+02 2.779e+03 0.058 0.953625
## L(train_data.Close.diff.ardl, 1:110)37 -1.178e+03 2.807e+03 -0.420 0.675957
## L(train_data.Close.diff.ardl, 1:110)38 3.017e+03 2.716e+03 1.111 0.270691
## L(train_data.Close.diff.ardl, 1:110)39 -6.022e+01 2.710e+03 -0.022 0.982334
## L(train_data.Close.diff.ardl, 1:110)40 -2.035e+02 2.718e+03 -0.075 0.940543
## L(train_data.Close.diff.ardl, 1:110)41 3.367e+03 2.751e+03 1.224 0.225260
## L(train_data.Close.diff.ardl, 1:110)42 -8.092e+02 2.797e+03 -0.289 0.773266
## L(train_data.Close.diff.ardl, 1:110)43 -2.715e+03 2.833e+03 -0.958 0.341410
## L(train_data.Close.diff.ardl, 1:110)44 1.512e+03 2.839e+03 0.532 0.596234
## L(train_data.Close.diff.ardl, 1:110)45 3.607e+03 2.837e+03 1.271 0.207996
## L(train_data.Close.diff.ardl, 1:110)46 1.565e+03 2.848e+03 0.549 0.584476
## L(train_data.Close.diff.ardl, 1:110)47 1.458e+03 2.907e+03 0.501 0.617762
## L(train_data.Close.diff.ardl, 1:110)48 -2.255e+03 2.836e+03 -0.795 0.429320
## L(train_data.Close.diff.ardl, 1:110)49 1.033e+02 2.845e+03 0.036 0.971140
## L(train_data.Close.diff.ardl, 1:110)50 2.800e+02 2.842e+03 0.099 0.921810
## L(train_data.Close.diff.ardl, 1:110)51 -1.380e+03 2.818e+03 -0.490 0.625962
## L(train_data.Close.diff.ardl, 1:110)52 -1.696e+03 2.833e+03 -0.599 0.551485
## L(train_data.Close.diff.ardl, 1:110)53 -2.296e+03 2.826e+03 -0.812 0.419383
## L(train_data.Close.diff.ardl, 1:110)54 -3.790e+03 2.809e+03 -1.349 0.181750
## L(train_data.Close.diff.ardl, 1:110)55 1.982e+03 2.554e+03 0.776 0.440371
## L(train_data.Close.diff.ardl, 1:110)56 -3.814e+03 2.581e+03 -1.478 0.144134
## L(train_data.Close.diff.ardl, 1:110)57 5.306e+02 2.665e+03 0.199 0.842788
## L(train_data.Close.diff.ardl, 1:110)58 -3.314e+03 2.604e+03 -1.273 0.207484
## L(train_data.Close.diff.ardl, 1:110)59 -4.520e+02 2.486e+03 -0.182 0.856252
## L(train_data.Close.diff.ardl, 1:110)60 3.302e+03 2.063e+03 1.601 0.114108
## L(train_data.Close.diff.ardl, 1:110)61 5.937e+02 2.103e+03 0.282 0.778602
## L(train_data.Close.diff.ardl, 1:110)62 6.651e+01 2.089e+03 0.032 0.974698
## L(train_data.Close.diff.ardl, 1:110)63 -1.414e+03 2.058e+03 -0.687 0.494469
## L(train_data.Close.diff.ardl, 1:110)64 -2.271e+03 2.077e+03 -1.093 0.278187
## L(train_data.Close.diff.ardl, 1:110)65 -1.340e+03 2.068e+03 -0.648 0.519139
## L(train_data.Close.diff.ardl, 1:110)66 3.765e+02 2.080e+03 0.181 0.856927
## L(train_data.Close.diff.ardl, 1:110)67 1.266e+03 2.111e+03 0.600 0.550815
## L(train_data.Close.diff.ardl, 1:110)68 -5.516e+02 2.097e+03 -0.263 0.793355
## L(train_data.Close.diff.ardl, 1:110)69 -3.151e+03 2.111e+03 -1.492 0.140234
## L(train_data.Close.diff.ardl, 1:110)70 1.034e+03 2.167e+03 0.477 0.634870
## L(train_data.Close.diff.ardl, 1:110)71 -2.791e+03 2.138e+03 -1.306 0.196120
## L(train_data.Close.diff.ardl, 1:110)72 1.434e+03 2.164e+03 0.663 0.509867
## L(train_data.Close.diff.ardl, 1:110)73 -4.576e+03 2.134e+03 -2.144 0.035580
## L(train_data.Close.diff.ardl, 1:110)74 4.076e+02 2.210e+03 0.184 0.854215
## L(train_data.Close.diff.ardl, 1:110)75 -6.363e+02 2.193e+03 -0.290 0.772597
## L(train_data.Close.diff.ardl, 1:110)76 -3.382e+02 2.192e+03 -0.154 0.877868
## L(train_data.Close.diff.ardl, 1:110)77 -2.239e+03 2.133e+03 -1.050 0.297510
## L(train_data.Close.diff.ardl, 1:110)78 2.598e+03 2.145e+03 1.211 0.230036
## L(train_data.Close.diff.ardl, 1:110)79 -4.744e+03 2.151e+03 -2.205 0.030836
## L(train_data.Close.diff.ardl, 1:110)80 -1.698e+03 2.168e+03 -0.783 0.436203
## L(train_data.Close.diff.ardl, 1:110)81 -1.734e+03 2.118e+03 -0.819 0.415812
## L(train_data.Close.diff.ardl, 1:110)82 -2.664e+03 2.147e+03 -1.241 0.218965
## L(train_data.Close.diff.ardl, 1:110)83 -1.014e+04 2.127e+03 -4.767 1.03e-05
## L(train_data.Close.diff.ardl, 1:110)84 8.292e+01 2.456e+03 0.034 0.973169
## L(train_data.Close.diff.ardl, 1:110)85 -2.393e+03 2.391e+03 -1.001 0.320477
## L(train_data.Close.diff.ardl, 1:110)86 2.911e+02 2.429e+03 0.120 0.904969
## L(train_data.Close.diff.ardl, 1:110)87 6.290e+02 2.383e+03 0.264 0.792636
## L(train_data.Close.diff.ardl, 1:110)88 -1.739e+03 2.400e+03 -0.724 0.471265
## L(train_data.Close.diff.ardl, 1:110)89 -3.828e+03 2.268e+03 -1.688 0.096077
## L(train_data.Close.diff.ardl, 1:110)90 3.149e+02 2.275e+03 0.138 0.890323
## L(train_data.Close.diff.ardl, 1:110)91 -1.414e+03 2.234e+03 -0.633 0.528845
## L(train_data.Close.diff.ardl, 1:110)92 5.441e+02 2.294e+03 0.237 0.813209
## L(train_data.Close.diff.ardl, 1:110)93 9.802e+02 2.230e+03 0.440 0.661675
## L(train_data.Close.diff.ardl, 1:110)94 -2.523e+02 2.240e+03 -0.113 0.910676
## L(train_data.Close.diff.ardl, 1:110)95 -7.200e+02 2.245e+03 -0.321 0.749438
## L(train_data.Close.diff.ardl, 1:110)96 1.301e+02 2.235e+03 0.058 0.953774
## L(train_data.Close.diff.ardl, 1:110)97 1.145e+03 2.253e+03 0.508 0.612873
## L(train_data.Close.diff.ardl, 1:110)98 -1.235e+02 2.259e+03 -0.055 0.956578
## L(train_data.Close.diff.ardl, 1:110)99 1.420e+02 2.266e+03 0.063 0.950230
## L(train_data.Close.diff.ardl, 1:110)100 1.962e+03 2.252e+03 0.871 0.386675
## L(train_data.Close.diff.ardl, 1:110)101 2.256e+03 2.251e+03 1.002 0.319961
## L(train_data.Close.diff.ardl, 1:110)102 -6.477e+02 2.243e+03 -0.289 0.773658
## L(train_data.Close.diff.ardl, 1:110)103 -3.308e+01 2.246e+03 -0.015 0.988293
## L(train_data.Close.diff.ardl, 1:110)104 1.348e+02 2.245e+03 0.060 0.952311
## L(train_data.Close.diff.ardl, 1:110)105 -7.424e+02 2.219e+03 -0.335 0.738983
## L(train_data.Close.diff.ardl, 1:110)106 1.158e+03 2.221e+03 0.521 0.603924
## L(train_data.Close.diff.ardl, 1:110)107 -1.228e+03 2.208e+03 -0.556 0.579709
## L(train_data.Close.diff.ardl, 1:110)108 -3.935e+03 2.196e+03 -1.792 0.077601
## L(train_data.Close.diff.ardl, 1:110)109 -8.357e+02 2.259e+03 -0.370 0.712594
## L(train_data.Close.diff.ardl, 1:110)110 -9.165e+02 2.226e+03 -0.412 0.681801
##
## (Intercept) .
## L(train_data.Volume.ardl, 1:32)1 ***
## L(train_data.Volume.ardl, 1:32)2
## L(train_data.Volume.ardl, 1:32)3
## L(train_data.Volume.ardl, 1:32)4
## L(train_data.Volume.ardl, 1:32)5
## L(train_data.Volume.ardl, 1:32)6 .
## L(train_data.Volume.ardl, 1:32)7 .
## L(train_data.Volume.ardl, 1:32)8 .
## L(train_data.Volume.ardl, 1:32)9
## L(train_data.Volume.ardl, 1:32)10
## L(train_data.Volume.ardl, 1:32)11
## L(train_data.Volume.ardl, 1:32)12
## L(train_data.Volume.ardl, 1:32)13
## L(train_data.Volume.ardl, 1:32)14
## L(train_data.Volume.ardl, 1:32)15
## L(train_data.Volume.ardl, 1:32)16
## L(train_data.Volume.ardl, 1:32)17
## L(train_data.Volume.ardl, 1:32)18
## L(train_data.Volume.ardl, 1:32)19
## L(train_data.Volume.ardl, 1:32)20
## L(train_data.Volume.ardl, 1:32)21
## L(train_data.Volume.ardl, 1:32)22
## L(train_data.Volume.ardl, 1:32)23
## L(train_data.Volume.ardl, 1:32)24
## L(train_data.Volume.ardl, 1:32)25
## L(train_data.Volume.ardl, 1:32)26
## L(train_data.Volume.ardl, 1:32)27
## L(train_data.Volume.ardl, 1:32)28
## L(train_data.Volume.ardl, 1:32)29
## L(train_data.Volume.ardl, 1:32)30
## L(train_data.Volume.ardl, 1:32)31
## L(train_data.Volume.ardl, 1:32)32
## L(train_data.Volume.ardl, 91:122)91
## L(train_data.Volume.ardl, 91:122)92
## L(train_data.Volume.ardl, 91:122)93
## L(train_data.Volume.ardl, 91:122)94 *
## L(train_data.Volume.ardl, 91:122)95
## L(train_data.Volume.ardl, 91:122)96
## L(train_data.Volume.ardl, 91:122)97
## L(train_data.Volume.ardl, 91:122)98
## L(train_data.Volume.ardl, 91:122)99
## L(train_data.Volume.ardl, 91:122)100
## L(train_data.Volume.ardl, 91:122)101
## L(train_data.Volume.ardl, 91:122)102
## L(train_data.Volume.ardl, 91:122)103
## L(train_data.Volume.ardl, 91:122)104
## L(train_data.Volume.ardl, 91:122)105
## L(train_data.Volume.ardl, 91:122)106
## L(train_data.Volume.ardl, 91:122)107
## L(train_data.Volume.ardl, 91:122)108
## L(train_data.Volume.ardl, 91:122)109
## L(train_data.Volume.ardl, 91:122)110
## L(train_data.Volume.ardl, 91:122)111
## L(train_data.Volume.ardl, 91:122)112 **
## L(train_data.Volume.ardl, 91:122)113 *
## L(train_data.Volume.ardl, 91:122)114
## L(train_data.Volume.ardl, 91:122)115
## L(train_data.Volume.ardl, 91:122)116
## L(train_data.Volume.ardl, 91:122)117
## L(train_data.Volume.ardl, 91:122)118
## L(train_data.Volume.ardl, 91:122)119 *
## L(train_data.Volume.ardl, 91:122)120
## L(train_data.Volume.ardl, 91:122)121
## L(train_data.Volume.ardl, 91:122)122
## L(train_data.Close.diff.ardl, 1:110)1
## L(train_data.Close.diff.ardl, 1:110)2
## L(train_data.Close.diff.ardl, 1:110)3
## L(train_data.Close.diff.ardl, 1:110)4
## L(train_data.Close.diff.ardl, 1:110)5
## L(train_data.Close.diff.ardl, 1:110)6
## L(train_data.Close.diff.ardl, 1:110)7
## L(train_data.Close.diff.ardl, 1:110)8
## L(train_data.Close.diff.ardl, 1:110)9 .
## L(train_data.Close.diff.ardl, 1:110)10
## L(train_data.Close.diff.ardl, 1:110)11
## L(train_data.Close.diff.ardl, 1:110)12
## L(train_data.Close.diff.ardl, 1:110)13
## L(train_data.Close.diff.ardl, 1:110)14
## L(train_data.Close.diff.ardl, 1:110)15
## L(train_data.Close.diff.ardl, 1:110)16
## L(train_data.Close.diff.ardl, 1:110)17
## L(train_data.Close.diff.ardl, 1:110)18
## L(train_data.Close.diff.ardl, 1:110)19
## L(train_data.Close.diff.ardl, 1:110)20
## L(train_data.Close.diff.ardl, 1:110)21
## L(train_data.Close.diff.ardl, 1:110)22
## L(train_data.Close.diff.ardl, 1:110)23
## L(train_data.Close.diff.ardl, 1:110)24
## L(train_data.Close.diff.ardl, 1:110)25
## L(train_data.Close.diff.ardl, 1:110)26
## L(train_data.Close.diff.ardl, 1:110)27 ***
## L(train_data.Close.diff.ardl, 1:110)28
## L(train_data.Close.diff.ardl, 1:110)29
## L(train_data.Close.diff.ardl, 1:110)30
## L(train_data.Close.diff.ardl, 1:110)31
## L(train_data.Close.diff.ardl, 1:110)32
## L(train_data.Close.diff.ardl, 1:110)33
## L(train_data.Close.diff.ardl, 1:110)34
## L(train_data.Close.diff.ardl, 1:110)35
## L(train_data.Close.diff.ardl, 1:110)36
## L(train_data.Close.diff.ardl, 1:110)37
## L(train_data.Close.diff.ardl, 1:110)38
## L(train_data.Close.diff.ardl, 1:110)39
## L(train_data.Close.diff.ardl, 1:110)40
## L(train_data.Close.diff.ardl, 1:110)41
## L(train_data.Close.diff.ardl, 1:110)42
## L(train_data.Close.diff.ardl, 1:110)43
## L(train_data.Close.diff.ardl, 1:110)44
## L(train_data.Close.diff.ardl, 1:110)45
## L(train_data.Close.diff.ardl, 1:110)46
## L(train_data.Close.diff.ardl, 1:110)47
## L(train_data.Close.diff.ardl, 1:110)48
## L(train_data.Close.diff.ardl, 1:110)49
## L(train_data.Close.diff.ardl, 1:110)50
## L(train_data.Close.diff.ardl, 1:110)51
## L(train_data.Close.diff.ardl, 1:110)52
## L(train_data.Close.diff.ardl, 1:110)53
## L(train_data.Close.diff.ardl, 1:110)54
## L(train_data.Close.diff.ardl, 1:110)55
## L(train_data.Close.diff.ardl, 1:110)56
## L(train_data.Close.diff.ardl, 1:110)57
## L(train_data.Close.diff.ardl, 1:110)58
## L(train_data.Close.diff.ardl, 1:110)59
## L(train_data.Close.diff.ardl, 1:110)60
## L(train_data.Close.diff.ardl, 1:110)61
## L(train_data.Close.diff.ardl, 1:110)62
## L(train_data.Close.diff.ardl, 1:110)63
## L(train_data.Close.diff.ardl, 1:110)64
## L(train_data.Close.diff.ardl, 1:110)65
## L(train_data.Close.diff.ardl, 1:110)66
## L(train_data.Close.diff.ardl, 1:110)67
## L(train_data.Close.diff.ardl, 1:110)68
## L(train_data.Close.diff.ardl, 1:110)69
## L(train_data.Close.diff.ardl, 1:110)70
## L(train_data.Close.diff.ardl, 1:110)71
## L(train_data.Close.diff.ardl, 1:110)72
## L(train_data.Close.diff.ardl, 1:110)73 *
## L(train_data.Close.diff.ardl, 1:110)74
## L(train_data.Close.diff.ardl, 1:110)75
## L(train_data.Close.diff.ardl, 1:110)76
## L(train_data.Close.diff.ardl, 1:110)77
## L(train_data.Close.diff.ardl, 1:110)78
## L(train_data.Close.diff.ardl, 1:110)79 *
## L(train_data.Close.diff.ardl, 1:110)80
## L(train_data.Close.diff.ardl, 1:110)81
## L(train_data.Close.diff.ardl, 1:110)82
## L(train_data.Close.diff.ardl, 1:110)83 ***
## L(train_data.Close.diff.ardl, 1:110)84
## L(train_data.Close.diff.ardl, 1:110)85
## L(train_data.Close.diff.ardl, 1:110)86
## L(train_data.Close.diff.ardl, 1:110)87
## L(train_data.Close.diff.ardl, 1:110)88
## L(train_data.Close.diff.ardl, 1:110)89 .
## L(train_data.Close.diff.ardl, 1:110)90
## L(train_data.Close.diff.ardl, 1:110)91
## L(train_data.Close.diff.ardl, 1:110)92
## L(train_data.Close.diff.ardl, 1:110)93
## L(train_data.Close.diff.ardl, 1:110)94
## L(train_data.Close.diff.ardl, 1:110)95
## L(train_data.Close.diff.ardl, 1:110)96
## L(train_data.Close.diff.ardl, 1:110)97
## L(train_data.Close.diff.ardl, 1:110)98
## L(train_data.Close.diff.ardl, 1:110)99
## L(train_data.Close.diff.ardl, 1:110)100
## L(train_data.Close.diff.ardl, 1:110)101
## L(train_data.Close.diff.ardl, 1:110)102
## L(train_data.Close.diff.ardl, 1:110)103
## L(train_data.Close.diff.ardl, 1:110)104
## L(train_data.Close.diff.ardl, 1:110)105
## L(train_data.Close.diff.ardl, 1:110)106
## L(train_data.Close.diff.ardl, 1:110)107
## L(train_data.Close.diff.ardl, 1:110)108 .
## L(train_data.Close.diff.ardl, 1:110)109
## L(train_data.Close.diff.ardl, 1:110)110
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1585000 on 68 degrees of freedom
## Multiple R-squared: 0.833, Adjusted R-squared: 0.4056
## F-statistic: 1.949 on 174 and 68 DF, p-value: 0.001004Volume.Close.testing.4 <- predict(Volume.Close.training.4, n.ahead = length(test_data.Volume.ardl, test_data.Close.diff.ardl))
head(Volume.Close.testing.4)## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128)
## 3032093.7 3346910.8 2038769.9 821872.1 2431253.8 2127891.0Volume.Close.fitted_training.4 <- fitted(Volume.Close.training.4)
head(Volume.Close.fitted_training.4)## Time Series:
## Start = c(2015, 123)
## End = c(2015, 128)
## Frequency = 365
## [1] 3032093.7 3346910.8 2038769.9 821872.1 2431253.8 2127891.0Volume.Close.4.training.mse_value <- mse(train_data.Volume.ardl, Volume.Close.fitted_training.4)
Volume.Close.4.training.rmse_value <- rmse(train_data.Volume.ardl, Volume.Close.fitted_training.4)
Volume.testing.n.4 = as.numeric(Volume.Close.testing.4)
Volume.Close.4.testing.mse_value <- mse(test_data.Volume.ardl, Volume.testing.n.4)
Volume.Close.4.testing.rmse_value <- rmse(test_data.Volume.ardl, Volume.testing.n.4)
cat("Training Model MSE:", Volume.Close.4.training.mse_value, "\n Training Model RMSE:", Volume.Close.4.training.rmse_value , "\n Testing Model MSE:", Volume.Close.4.testing.mse_value, "\n Testing Model RMSE:", Volume.Close.4.testing.rmse_value , "\n")## Training Model MSE: 703209226609
## Training Model RMSE: 838575.7
## Testing Model MSE: 7.571737e+12
## Testing Model RMSE: 2751679cat(" Training Model AIC:", AIC(Volume.Close.training.4), "\n Training Model BIC:", BIC(Volume.Close.training.4), "\n")## Training Model AIC: 7670.382
## Training Model BIC: 8285.161This training model has a R-squared of 0.833, meaning a good portion of the model can be explained well by the independent variable here. The high MSE value of the testing model does not really point to a good fit though. The RMSE of the testing model is also a lot higher than that of the training model, suggesting that the accuracy of the testing model is much worse than that of the training model. The AIC and BIC of this model also result in similar values to that of the previous model.
Volume and Open
Size
train_size.Volume.ardl <- floor (2/3 * length(Volume.ts))
train_size.Open.diff.ardl <- floor (2/3 * length(Open.ts.diff))
#### Data
train_data.Volume.ardl <- Volume.ts[1:train_size.Volume.ardl]
train_data.Volume.ardl = ts(train_data.Volume.ardl,
start=c(2015,1),
end=c(2015,365),
frequency=365)
train_data.Open.diff.ardl <- Open.ts.diff[1:train_size.Open.diff.ardl]
train_data.Open.diff.ardl = ts(train_data.Open.diff.ardl,
start=c(2015,1),
end=c(2015,365),
frequency=365)
#### Test
test_data.Volume.ardl <- Volume.ts[(train_size.Volume.ardl + 1):length(Volume.ts)]
test_data.Volume.ardl = ts(test_data.Volume.ardl, start=c(2015,1), end=c(2015,365), frequency=365)
test_data.Open.diff.ardl <- Open.ts.diff[(train_size.Open.diff.ardl + 1):length(Open.ts.diff)]
test_data.Open.diff.ardl = ts(test_data.Open.diff.ardl, start=c(2015,1), end=c(2015,365), frequency=365)
length(train_data.Volume.ardl) ## [1] 365length(test_data.Open.diff.ardl)## [1] 365Testing and Training for Volume with lag (1:32) and Open lag (110)
Volume.open.training.1 <- dynlm(train_data.Volume.ardl ~ L(train_data.Volume.ardl, 1:32) + L(train_data.Open.diff.ardl, 110))
summary(Volume.open.training.1)##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Volume.ardl ~ L(train_data.Volume.ardl,
## 1:32) + L(train_data.Open.diff.ardl, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2274160 -868517 -208084 411518 16578331
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.595e+05 3.910e+05 1.431 0.1538
## L(train_data.Volume.ardl, 1:32)1 3.216e-01 6.711e-02 4.792 3.03e-06 ***
## L(train_data.Volume.ardl, 1:32)2 6.621e-02 7.059e-02 0.938 0.3493
## L(train_data.Volume.ardl, 1:32)3 -4.357e-02 7.068e-02 -0.617 0.5382
## L(train_data.Volume.ardl, 1:32)4 1.073e-01 7.054e-02 1.521 0.1298
## L(train_data.Volume.ardl, 1:32)5 -2.366e-04 7.048e-02 -0.003 0.9973
## L(train_data.Volume.ardl, 1:32)6 3.998e-02 7.085e-02 0.564 0.5732
## L(train_data.Volume.ardl, 1:32)7 9.598e-02 7.052e-02 1.361 0.1749
## L(train_data.Volume.ardl, 1:32)8 -2.614e-03 7.093e-02 -0.037 0.9706
## L(train_data.Volume.ardl, 1:32)9 -5.988e-04 7.019e-02 -0.009 0.9932
## L(train_data.Volume.ardl, 1:32)10 5.243e-02 6.969e-02 0.752 0.4527
## L(train_data.Volume.ardl, 1:32)11 -5.164e-02 6.974e-02 -0.740 0.4598
## L(train_data.Volume.ardl, 1:32)12 1.670e-02 6.978e-02 0.239 0.8111
## L(train_data.Volume.ardl, 1:32)13 -2.925e-02 6.971e-02 -0.420 0.6752
## L(train_data.Volume.ardl, 1:32)14 -2.703e-02 6.971e-02 -0.388 0.6986
## L(train_data.Volume.ardl, 1:32)15 4.979e-02 6.975e-02 0.714 0.4761
## L(train_data.Volume.ardl, 1:32)16 -4.019e-02 6.981e-02 -0.576 0.5653
## L(train_data.Volume.ardl, 1:32)17 -7.987e-03 6.982e-02 -0.114 0.9090
## L(train_data.Volume.ardl, 1:32)18 2.025e-02 6.966e-02 0.291 0.7716
## L(train_data.Volume.ardl, 1:32)19 -2.686e-02 6.966e-02 -0.386 0.7001
## L(train_data.Volume.ardl, 1:32)20 3.377e-02 6.965e-02 0.485 0.6282
## L(train_data.Volume.ardl, 1:32)21 -3.482e-02 6.973e-02 -0.499 0.6180
## L(train_data.Volume.ardl, 1:32)22 1.683e-03 7.007e-02 0.024 0.9809
## L(train_data.Volume.ardl, 1:32)23 1.823e-02 7.011e-02 0.260 0.7951
## L(train_data.Volume.ardl, 1:32)24 1.588e-01 7.005e-02 2.267 0.0243 *
## L(train_data.Volume.ardl, 1:32)25 -1.489e-02 7.074e-02 -0.211 0.8335
## L(train_data.Volume.ardl, 1:32)26 4.765e-02 7.044e-02 0.676 0.4994
## L(train_data.Volume.ardl, 1:32)27 2.449e-02 7.581e-02 0.323 0.7470
## L(train_data.Volume.ardl, 1:32)28 -1.158e-01 7.071e-02 -1.637 0.1030
## L(train_data.Volume.ardl, 1:32)29 7.143e-02 7.055e-02 1.012 0.3124
## L(train_data.Volume.ardl, 1:32)30 1.081e-02 7.076e-02 0.153 0.8787
## L(train_data.Volume.ardl, 1:32)31 2.168e-02 7.054e-02 0.307 0.7589
## L(train_data.Volume.ardl, 1:32)32 5.713e-02 6.717e-02 0.851 0.3959
## L(train_data.Open.diff.ardl, 110) 9.287e+02 1.833e+03 0.507 0.6130
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1836000 on 221 degrees of freedom
## Multiple R-squared: 0.2741, Adjusted R-squared: 0.1657
## F-statistic: 2.529 on 33 and 221 DF, p-value: 3.482e-05Volume.open.testing.1 <- predict(Volume.open.training.1, n.ahead = length(test_data.Volume.ardl, test_data.Close.diff.ardl))
head(Volume.open.testing.1)## 2015(111) 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## 2297320 2181412 2420314 2322166 2630299 2186327Volume.open.fitted_training.1 <- fitted(Volume.open.training.1)
head(Volume.open.fitted_training.1)## Time Series:
## Start = c(2015, 111)
## End = c(2015, 116)
## Frequency = 365
## [1] 2297320 2181412 2420314 2322166 2630299 2186327Volume.open.1.training.mse_value <- mse(train_data.Volume.ardl, Volume.open.fitted_training.1)
Volume.open.1.training.rmse_value <- rmse(train_data.Volume.ardl, Volume.open.fitted_training.1)
Volume.testing.n.1 = as.numeric(Volume.open.testing.1)
Volume.open.1.testing.mse_value <- mse(test_data.Volume.ardl, Volume.testing.n.1)
Volume.open.1.testing.rmse_value <- rmse(test_data.Volume.ardl, Volume.testing.n.1)
cat("Training Model MSE:", Volume.open.1.training.mse_value, "\n Training Model RMSE:", Volume.open.1.training.rmse_value , "\n Testing Model MSE:", Volume.open.1.testing.mse_value, "\n Testing Model RMSE:", Volume.open.1.testing.rmse_value , "\n")## Training Model MSE: 2.92166e+12
## Training Model RMSE: 1709286
## Testing Model MSE: 4.251657e+12
## Testing Model RMSE: 2061955cat(" Training Model AIC:", AIC(Volume.open.training.1), "\n Training Model BIC:", BIC(Volume.open.training.1), "\n")## Training Model AIC: 8112.968
## Training Model BIC: 8236.912The R-squared value of this training model is 0.2741, not the most ideal value. And the MSE of both the training and testing are very high. The RMSE results in slightly lower result but they are still not the lowest out of the ones observed here. The same apply to the AIC and BIC, which are not the lowest observed here, so we can conclude that this ARDL model is not a good fit.
Testing and Training for Volume with lag (1:32) and Open lag (1:110)
Volume.open.training.2 <- dynlm(train_data.Volume.ardl ~ L(train_data.Volume.ardl, 1:32) + L(train_data.Open.diff.ardl, 35) + L(train_data.Open.diff.ardl, 110), data = infy_stock)
summary(Volume.open.training.2)##
## Time series regression with "ts" data:
## Start = 2015(111), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Volume.ardl ~ L(train_data.Volume.ardl,
## 1:32) + L(train_data.Open.diff.ardl, 35) + L(train_data.Open.diff.ardl,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2288291 -859533 -190270 390955 16581904
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.638e+05 3.916e+05 1.440 0.151
## L(train_data.Volume.ardl, 1:32)1 3.180e-01 6.748e-02 4.712 4.34e-06 ***
## L(train_data.Volume.ardl, 1:32)2 6.883e-02 7.083e-02 0.972 0.332
## L(train_data.Volume.ardl, 1:32)3 -4.808e-02 7.117e-02 -0.676 0.500
## L(train_data.Volume.ardl, 1:32)4 1.094e-01 7.073e-02 1.547 0.123
## L(train_data.Volume.ardl, 1:32)5 3.336e-04 7.058e-02 0.005 0.996
## L(train_data.Volume.ardl, 1:32)6 4.444e-02 7.133e-02 0.623 0.534
## L(train_data.Volume.ardl, 1:32)7 9.777e-02 7.068e-02 1.383 0.168
## L(train_data.Volume.ardl, 1:32)8 -2.906e-02 8.332e-02 -0.349 0.728
## L(train_data.Volume.ardl, 1:32)9 1.030e-02 7.255e-02 0.142 0.887
## L(train_data.Volume.ardl, 1:32)10 5.605e-02 7.005e-02 0.800 0.425
## L(train_data.Volume.ardl, 1:32)11 -5.293e-02 6.987e-02 -0.758 0.450
## L(train_data.Volume.ardl, 1:32)12 1.852e-02 6.994e-02 0.265 0.791
## L(train_data.Volume.ardl, 1:32)13 -3.061e-02 6.985e-02 -0.438 0.662
## L(train_data.Volume.ardl, 1:32)14 -2.594e-02 6.984e-02 -0.371 0.711
## L(train_data.Volume.ardl, 1:32)15 5.165e-02 6.992e-02 0.739 0.461
## L(train_data.Volume.ardl, 1:32)16 -4.405e-02 7.020e-02 -0.627 0.531
## L(train_data.Volume.ardl, 1:32)17 -7.803e-03 6.992e-02 -0.112 0.911
## L(train_data.Volume.ardl, 1:32)18 2.317e-02 6.993e-02 0.331 0.741
## L(train_data.Volume.ardl, 1:32)19 -2.810e-02 6.979e-02 -0.403 0.688
## L(train_data.Volume.ardl, 1:32)20 3.653e-02 6.990e-02 0.523 0.602
## L(train_data.Volume.ardl, 1:32)21 -3.368e-02 6.986e-02 -0.482 0.630
## L(train_data.Volume.ardl, 1:32)22 -1.693e-04 7.024e-02 -0.002 0.998
## L(train_data.Volume.ardl, 1:32)23 2.079e-02 7.033e-02 0.296 0.768
## L(train_data.Volume.ardl, 1:32)24 1.584e-01 7.016e-02 2.257 0.025 *
## L(train_data.Volume.ardl, 1:32)25 -1.294e-02 7.091e-02 -0.182 0.855
## L(train_data.Volume.ardl, 1:32)26 4.676e-02 7.056e-02 0.663 0.508
## L(train_data.Volume.ardl, 1:32)27 2.217e-02 7.602e-02 0.292 0.771
## L(train_data.Volume.ardl, 1:32)28 -1.147e-01 7.083e-02 -1.620 0.107
## L(train_data.Volume.ardl, 1:32)29 7.100e-02 7.066e-02 1.005 0.316
## L(train_data.Volume.ardl, 1:32)30 8.148e-03 7.100e-02 0.115 0.909
## L(train_data.Volume.ardl, 1:32)31 2.355e-02 7.071e-02 0.333 0.739
## L(train_data.Volume.ardl, 1:32)32 5.959e-02 6.739e-02 0.884 0.378
## L(train_data.Open.diff.ardl, 35) -1.217e+03 2.005e+03 -0.607 0.544
## L(train_data.Open.diff.ardl, 110) 8.448e+02 1.841e+03 0.459 0.647
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1839000 on 220 degrees of freedom
## Multiple R-squared: 0.2753, Adjusted R-squared: 0.1633
## F-statistic: 2.458 on 34 and 220 DF, p-value: 5.07e-05Volume.open.testing.2 <- predict(Volume.open.training.2, n.ahead = length(test_data.Volume.ardl, test_data.Close.diff.ardl))
head(Volume.open.testing.2)## 2015(111) 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## 2325093 2336453 2445838 2353241 2630145 2189706Volume.open.fitted_training.2 <- fitted(Volume.open.training.2)
head(Volume.open.fitted_training.2)## Time Series:
## Start = c(2015, 111)
## End = c(2015, 116)
## Frequency = 365
## [1] 2325093 2336453 2445838 2353241 2630145 2189706Volume.open.2.training.mse_value <- mse(train_data.Volume.ardl, Volume.open.fitted_training.2)
Volume.open.2.training.rmse_value <- rmse(train_data.Volume.ardl, Volume.open.fitted_training.2)
Volume.testing.n.2 = as.numeric(Volume.open.testing.2)
Volume.open.2.testing.mse_value <- mse(test_data.Volume.ardl, Volume.testing.n.2)
Volume.open.2.testing.rmse_value <- rmse(test_data.Volume.ardl, Volume.testing.n.2)
cat("Training Model MSE:", Volume.open.2.training.mse_value, "\n Training Model RMSE:", Volume.open.2.training.rmse_value , "\n Testing Model MSE:", Volume.open.2.testing.mse_value, "\n Testing Model RMSE:", Volume.open.2.testing.rmse_value , "\n")## Training Model MSE: 2.916772e+12
## Training Model RMSE: 1707856
## Testing Model MSE: 4.263623e+12
## Testing Model RMSE: 2064854cat(" Training Model AIC:", AIC(Volume.open.training.2), "\n Training Model BIC:", BIC(Volume.open.training.2), "\n")## Training Model AIC: 8114.541
## Training Model BIC: 8242.026The same conclusion applies to this model too. Because as observed, the values of R-squared and the MSE and RMSE of both the training and the testing models are all of similar values to the previous ARDL model. The AIC and BIC are also similar, thus this ARDL model is not a good fit.
Testing and Training for Volume with lag (1:32)n(91:122) and Open lag (110)
Volume.open.training.3 <- dynlm(train_data.Volume.ardl ~ L(train_data.Volume.ardl, 1:32) + L(train_data.Volume.ardl, 91:122) + L(train_data.Open.diff.ardl, 110), data = infy_stock)
summary(Volume.open.training.3)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Volume.ardl ~ L(train_data.Volume.ardl,
## 1:32) + L(train_data.Volume.ardl, 91:122) + L(train_data.Open.diff.ardl,
## 110), data = infy_stock)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2794576 -849697 -135411 510257 16089470
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.500e+06 1.020e+06 2.452 0.0152 *
## L(train_data.Volume.ardl, 1:32)1 3.043e-01 7.493e-02 4.062 7.31e-05 ***
## L(train_data.Volume.ardl, 1:32)2 4.457e-02 7.829e-02 0.569 0.5699
## L(train_data.Volume.ardl, 1:32)3 -4.073e-02 7.906e-02 -0.515 0.6071
## L(train_data.Volume.ardl, 1:32)4 6.475e-02 7.879e-02 0.822 0.4123
## L(train_data.Volume.ardl, 1:32)5 -1.766e-02 7.882e-02 -0.224 0.8230
## L(train_data.Volume.ardl, 1:32)6 1.808e-02 7.895e-02 0.229 0.8191
## L(train_data.Volume.ardl, 1:32)7 1.117e-01 7.860e-02 1.421 0.1571
## L(train_data.Volume.ardl, 1:32)8 -3.371e-02 7.907e-02 -0.426 0.6704
## L(train_data.Volume.ardl, 1:32)9 -6.424e-03 7.882e-02 -0.081 0.9351
## L(train_data.Volume.ardl, 1:32)10 5.578e-02 7.856e-02 0.710 0.4787
## L(train_data.Volume.ardl, 1:32)11 -7.420e-02 7.799e-02 -0.951 0.3427
## L(train_data.Volume.ardl, 1:32)12 4.890e-02 7.825e-02 0.625 0.5328
## L(train_data.Volume.ardl, 1:32)13 -9.257e-02 7.842e-02 -1.181 0.2394
## L(train_data.Volume.ardl, 1:32)14 1.567e-04 7.889e-02 0.002 0.9984
## L(train_data.Volume.ardl, 1:32)15 9.153e-03 7.889e-02 0.116 0.9078
## L(train_data.Volume.ardl, 1:32)16 -3.981e-02 7.876e-02 -0.505 0.6139
## L(train_data.Volume.ardl, 1:32)17 -1.150e-02 7.866e-02 -0.146 0.8839
## L(train_data.Volume.ardl, 1:32)18 -3.204e-03 7.851e-02 -0.041 0.9675
## L(train_data.Volume.ardl, 1:32)19 -2.457e-02 7.842e-02 -0.313 0.7544
## L(train_data.Volume.ardl, 1:32)20 2.717e-02 7.834e-02 0.347 0.7291
## L(train_data.Volume.ardl, 1:32)21 -3.681e-02 7.893e-02 -0.466 0.6415
## L(train_data.Volume.ardl, 1:32)22 6.077e-03 7.960e-02 0.076 0.9392
## L(train_data.Volume.ardl, 1:32)23 2.975e-02 7.957e-02 0.374 0.7089
## L(train_data.Volume.ardl, 1:32)24 9.621e-02 7.937e-02 1.212 0.2270
## L(train_data.Volume.ardl, 1:32)25 3.506e-02 7.961e-02 0.440 0.6602
## L(train_data.Volume.ardl, 1:32)26 1.570e-02 7.940e-02 0.198 0.8435
## L(train_data.Volume.ardl, 1:32)27 6.737e-02 8.669e-02 0.777 0.4381
## L(train_data.Volume.ardl, 1:32)28 -1.205e-01 7.967e-02 -1.512 0.1323
## L(train_data.Volume.ardl, 1:32)29 3.898e-02 7.923e-02 0.492 0.6233
## L(train_data.Volume.ardl, 1:32)30 5.800e-02 7.998e-02 0.725 0.4693
## L(train_data.Volume.ardl, 1:32)31 1.043e-02 8.022e-02 0.130 0.8967
## L(train_data.Volume.ardl, 1:32)32 6.865e-02 7.555e-02 0.909 0.3648
## L(train_data.Volume.ardl, 91:122)91 -7.376e-02 7.574e-02 -0.974 0.3314
## L(train_data.Volume.ardl, 91:122)92 1.556e-02 8.020e-02 0.194 0.8464
## L(train_data.Volume.ardl, 91:122)93 -1.177e-01 7.991e-02 -1.473 0.1425
## L(train_data.Volume.ardl, 91:122)94 8.838e-02 7.923e-02 1.115 0.2662
## L(train_data.Volume.ardl, 91:122)95 -6.068e-02 7.939e-02 -0.764 0.4457
## L(train_data.Volume.ardl, 91:122)96 1.451e-02 7.937e-02 0.183 0.8551
## L(train_data.Volume.ardl, 91:122)97 -4.039e-02 7.936e-02 -0.509 0.6114
## L(train_data.Volume.ardl, 91:122)98 -2.708e-02 7.962e-02 -0.340 0.7342
## L(train_data.Volume.ardl, 91:122)99 5.681e-02 7.929e-02 0.716 0.4746
## L(train_data.Volume.ardl, 91:122)100 -5.560e-02 7.938e-02 -0.700 0.4846
## L(train_data.Volume.ardl, 91:122)101 1.215e-02 7.959e-02 0.153 0.8788
## L(train_data.Volume.ardl, 91:122)102 -1.994e-03 7.892e-02 -0.025 0.9799
## L(train_data.Volume.ardl, 91:122)103 1.052e-02 7.832e-02 0.134 0.8933
## L(train_data.Volume.ardl, 91:122)104 -5.039e-02 7.845e-02 -0.642 0.5215
## L(train_data.Volume.ardl, 91:122)105 -1.219e-02 7.861e-02 -0.155 0.8770
## L(train_data.Volume.ardl, 91:122)106 -9.619e-02 7.859e-02 -1.224 0.2226
## L(train_data.Volume.ardl, 91:122)107 6.355e-02 7.904e-02 0.804 0.4225
## L(train_data.Volume.ardl, 91:122)108 -3.665e-02 7.883e-02 -0.465 0.6426
## L(train_data.Volume.ardl, 91:122)109 -4.076e-02 7.892e-02 -0.516 0.6062
## L(train_data.Volume.ardl, 91:122)110 -4.346e-02 7.839e-02 -0.554 0.5800
## L(train_data.Volume.ardl, 91:122)111 -2.694e-02 7.829e-02 -0.344 0.7312
## L(train_data.Volume.ardl, 91:122)112 1.553e-01 7.804e-02 1.989 0.0482 *
## L(train_data.Volume.ardl, 91:122)113 -8.173e-02 7.856e-02 -1.040 0.2996
## L(train_data.Volume.ardl, 91:122)114 -5.770e-02 7.863e-02 -0.734 0.4641
## L(train_data.Volume.ardl, 91:122)115 -1.327e-02 7.968e-02 -0.166 0.8680
## L(train_data.Volume.ardl, 91:122)116 1.985e-02 7.858e-02 0.253 0.8009
## L(train_data.Volume.ardl, 91:122)117 8.518e-02 7.858e-02 1.084 0.2799
## L(train_data.Volume.ardl, 91:122)118 -3.335e-02 7.890e-02 -0.423 0.6730
## L(train_data.Volume.ardl, 91:122)119 -1.100e-01 7.901e-02 -1.393 0.1655
## L(train_data.Volume.ardl, 91:122)120 7.825e-02 7.998e-02 0.978 0.3292
## L(train_data.Volume.ardl, 91:122)121 -5.101e-02 7.822e-02 -0.652 0.5152
## L(train_data.Volume.ardl, 91:122)122 -1.084e-02 7.491e-02 -0.145 0.8851
## L(train_data.Open.diff.ardl, 110) 1.652e+03 2.025e+03 0.816 0.4157
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1930000 on 177 degrees of freedom
## Multiple R-squared: 0.3555, Adjusted R-squared: 0.1188
## F-statistic: 1.502 on 65 and 177 DF, p-value: 0.01932Volume.open.testing.3 <- predict(Volume.open.training.3, n.ahead = length(test_data.Volume.ardl, test_data.Close.diff.ardl))
head(Volume.open.testing.3)## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128)
## 3435267 4153205 3079545 2197886 3204746 2469964Volume.open.fitted_training.3 <- fitted(Volume.open.training.3)
head(Volume.open.fitted_training.3)## Time Series:
## Start = c(2015, 123)
## End = c(2015, 128)
## Frequency = 365
## [1] 3435267 4153205 3079545 2197886 3204746 2469964Volume.open.3.training.mse_value <- mse(train_data.Volume.ardl, Volume.open.fitted_training.3)
Volume.open.3.training.rmse_value <- rmse(train_data.Volume.ardl, Volume.open.fitted_training.3)
Volume.testing.n.3 = as.numeric(Volume.open.testing.3)
Volume.open.3.testing.mse_value <- mse(test_data.Volume.ardl, Volume.testing.n.3)
Volume.open.3.testing.rmse_value <- rmse(test_data.Volume.ardl, Volume.testing.n.3)
cat("Training Model MSE:", Volume.open.3.training.mse_value, "\n Training Model RMSE:", Volume.open.3.training.rmse_value , "\n Testing Model MSE:", Volume.open.3.testing.mse_value, "\n Testing Model RMSE:", Volume.open.3.testing.rmse_value , "\n")## Training Model MSE: 2.713427e+12
## Training Model RMSE: 1647248
## Testing Model MSE: 4.68818e+12
## Testing Model RMSE: 2165221cat(" Training Model AIC:", AIC(Volume.open.training.3), "\n Training Model BIC:", BIC(Volume.open.training.3), "\n")## Training Model AIC: 7780.508
## Training Model BIC: 8014.543The R-squared value is 0.3555, suggesting that only a small portion of the model can be explained by the independent variable. The AIC and BIC values are also not the lowest we have observed, so this model is not a good fit. This is supported by the high MSE and high RMSE values of both the training and the testing model.
Testing and Training for Volume with lag (1:32)n(91:122) and Open lag (35)n(110)
Volume.open.training.4 <- dynlm(train_data.Volume.ardl ~ L(train_data.Volume.ardl, 1:32) + L(train_data.Volume.ardl, 91:122) + L(train_data.Open.diff.ardl, 35) + L(train_data.Open.diff.ardl, 110))
summary(Volume.open.training.4)##
## Time series regression with "ts" data:
## Start = 2015(123), End = 2015(365)
##
## Call:
## dynlm(formula = train_data.Volume.ardl ~ L(train_data.Volume.ardl,
## 1:32) + L(train_data.Volume.ardl, 91:122) + L(train_data.Open.diff.ardl,
## 35) + L(train_data.Open.diff.ardl, 110))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2804521 -830848 -123819 520158 16106631
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.455e+06 1.026e+06 2.393 0.0178 *
## L(train_data.Volume.ardl, 1:32)1 3.029e-01 7.515e-02 4.031 8.27e-05 ***
## L(train_data.Volume.ardl, 1:32)2 4.710e-02 7.864e-02 0.599 0.5500
## L(train_data.Volume.ardl, 1:32)3 -4.467e-02 7.966e-02 -0.561 0.5757
## L(train_data.Volume.ardl, 1:32)4 6.700e-02 7.910e-02 0.847 0.3981
## L(train_data.Volume.ardl, 1:32)5 -1.626e-02 7.905e-02 -0.206 0.8373
## L(train_data.Volume.ardl, 1:32)6 2.178e-02 7.951e-02 0.274 0.7844
## L(train_data.Volume.ardl, 1:32)7 1.148e-01 7.905e-02 1.453 0.1481
## L(train_data.Volume.ardl, 1:32)8 -6.011e-02 9.674e-02 -0.621 0.5351
## L(train_data.Volume.ardl, 1:32)9 4.885e-03 8.249e-02 0.059 0.9528
## L(train_data.Volume.ardl, 1:32)10 5.843e-02 7.893e-02 0.740 0.4601
## L(train_data.Volume.ardl, 1:32)11 -7.442e-02 7.816e-02 -0.952 0.3423
## L(train_data.Volume.ardl, 1:32)12 5.061e-02 7.850e-02 0.645 0.5200
## L(train_data.Volume.ardl, 1:32)13 -9.308e-02 7.859e-02 -1.184 0.2379
## L(train_data.Volume.ardl, 1:32)14 1.043e-03 7.908e-02 0.013 0.9895
## L(train_data.Volume.ardl, 1:32)15 1.088e-02 7.914e-02 0.137 0.8908
## L(train_data.Volume.ardl, 1:32)16 -4.246e-02 7.913e-02 -0.537 0.5922
## L(train_data.Volume.ardl, 1:32)17 -1.158e-02 7.884e-02 -0.147 0.8833
## L(train_data.Volume.ardl, 1:32)18 1.135e-03 7.921e-02 0.014 0.9886
## L(train_data.Volume.ardl, 1:32)19 -2.573e-02 7.863e-02 -0.327 0.7439
## L(train_data.Volume.ardl, 1:32)20 3.064e-02 7.884e-02 0.389 0.6980
## L(train_data.Volume.ardl, 1:32)21 -3.726e-02 7.910e-02 -0.471 0.6382
## L(train_data.Volume.ardl, 1:32)22 4.854e-03 7.982e-02 0.061 0.9516
## L(train_data.Volume.ardl, 1:32)23 3.178e-02 7.985e-02 0.398 0.6911
## L(train_data.Volume.ardl, 1:32)24 9.566e-02 7.955e-02 1.202 0.2308
## L(train_data.Volume.ardl, 1:32)25 3.731e-02 7.992e-02 0.467 0.6412
## L(train_data.Volume.ardl, 1:32)26 1.356e-02 7.970e-02 0.170 0.8651
## L(train_data.Volume.ardl, 1:32)27 6.598e-02 8.692e-02 0.759 0.4488
## L(train_data.Volume.ardl, 1:32)28 -1.198e-01 7.986e-02 -1.500 0.1353
## L(train_data.Volume.ardl, 1:32)29 3.838e-02 7.941e-02 0.483 0.6295
## L(train_data.Volume.ardl, 1:32)30 5.650e-02 8.022e-02 0.704 0.4822
## L(train_data.Volume.ardl, 1:32)31 1.269e-02 8.053e-02 0.158 0.8750
## L(train_data.Volume.ardl, 1:32)32 6.939e-02 7.573e-02 0.916 0.3608
## L(train_data.Volume.ardl, 91:122)91 -7.343e-02 7.591e-02 -0.967 0.3347
## L(train_data.Volume.ardl, 91:122)92 1.546e-02 8.037e-02 0.192 0.8477
## L(train_data.Volume.ardl, 91:122)93 -1.174e-01 8.009e-02 -1.465 0.1446
## L(train_data.Volume.ardl, 91:122)94 9.082e-02 7.957e-02 1.141 0.2553
## L(train_data.Volume.ardl, 91:122)95 -6.292e-02 7.970e-02 -0.789 0.4309
## L(train_data.Volume.ardl, 91:122)96 2.041e-02 8.050e-02 0.254 0.8002
## L(train_data.Volume.ardl, 91:122)97 -4.156e-02 7.957e-02 -0.522 0.6021
## L(train_data.Volume.ardl, 91:122)98 -2.705e-02 7.979e-02 -0.339 0.7350
## L(train_data.Volume.ardl, 91:122)99 5.619e-02 7.948e-02 0.707 0.4805
## L(train_data.Volume.ardl, 91:122)100 -5.448e-02 7.959e-02 -0.684 0.4946
## L(train_data.Volume.ardl, 91:122)101 7.324e-03 8.041e-02 0.091 0.9275
## L(train_data.Volume.ardl, 91:122)102 3.481e-03 7.992e-02 0.044 0.9653
## L(train_data.Volume.ardl, 91:122)103 8.331e-03 7.863e-02 0.106 0.9157
## L(train_data.Volume.ardl, 91:122)104 -5.250e-02 7.875e-02 -0.667 0.5058
## L(train_data.Volume.ardl, 91:122)105 -1.028e-02 7.888e-02 -0.130 0.8965
## L(train_data.Volume.ardl, 91:122)106 -9.849e-02 7.891e-02 -1.248 0.2136
## L(train_data.Volume.ardl, 91:122)107 6.538e-02 7.931e-02 0.824 0.4109
## L(train_data.Volume.ardl, 91:122)108 -3.570e-02 7.903e-02 -0.452 0.6520
## L(train_data.Volume.ardl, 91:122)109 -3.946e-02 7.914e-02 -0.499 0.6187
## L(train_data.Volume.ardl, 91:122)110 -4.112e-02 7.872e-02 -0.522 0.6021
## L(train_data.Volume.ardl, 91:122)111 -2.545e-02 7.852e-02 -0.324 0.7463
## L(train_data.Volume.ardl, 91:122)112 1.538e-01 7.827e-02 1.965 0.0510 .
## L(train_data.Volume.ardl, 91:122)113 -8.162e-02 7.873e-02 -1.037 0.3013
## L(train_data.Volume.ardl, 91:122)114 -5.866e-02 7.883e-02 -0.744 0.4578
## L(train_data.Volume.ardl, 91:122)115 -1.177e-02 7.992e-02 -0.147 0.8830
## L(train_data.Volume.ardl, 91:122)116 1.963e-02 7.875e-02 0.249 0.8035
## L(train_data.Volume.ardl, 91:122)117 8.645e-02 7.880e-02 1.097 0.2741
## L(train_data.Volume.ardl, 91:122)118 -3.529e-02 7.918e-02 -0.446 0.6564
## L(train_data.Volume.ardl, 91:122)119 -1.098e-01 7.919e-02 -1.386 0.1675
## L(train_data.Volume.ardl, 91:122)120 8.284e-02 8.074e-02 1.026 0.3063
## L(train_data.Volume.ardl, 91:122)121 -5.339e-02 7.855e-02 -0.680 0.4976
## L(train_data.Volume.ardl, 91:122)122 -1.077e-02 7.507e-02 -0.143 0.8861
## L(train_data.Open.diff.ardl, 35) -1.078e+03 2.265e+03 -0.476 0.6348
## L(train_data.Open.diff.ardl, 110) 1.581e+03 2.035e+03 0.777 0.4381
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1934000 on 176 degrees of freedom
## Multiple R-squared: 0.3563, Adjusted R-squared: 0.1149
## F-statistic: 1.476 on 66 and 176 DF, p-value: 0.02348Volume.open.testing.4 <- predict(Volume.open.training.4, n.ahead = length(test_data.Volume.ardl, test_data.Close.diff.ardl))
head(Volume.open.testing.4)## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128)
## 3484569 4115900 3072290 2134982 3193647 2376375Volume.open.fitted_training.4 <- fitted(Volume.open.training.4)
head(Volume.open.fitted_training.4)## Time Series:
## Start = c(2015, 123)
## End = c(2015, 128)
## Frequency = 365
## [1] 3484569 4115900 3072290 2134982 3193647 2376375Volume.open.4.training.mse_value <- mse(train_data.Volume.ardl, Volume.open.fitted_training.4)
Volume.open.4.training.rmse_value <- rmse(train_data.Volume.ardl, Volume.open.fitted_training.4)
Volume.testing.n.4 = as.numeric(Volume.open.testing.4)
Volume.open.4.testing.mse_value <- mse(test_data.Volume.ardl, Volume.testing.n.4)
Volume.open.4.testing.rmse_value <- rmse(test_data.Volume.ardl, Volume.testing.n.4)
cat("Training Model MSE:", Volume.open.4.training.mse_value, "\n Training Model RMSE:", Volume.open.4.training.rmse_value , "\n Testing Model MSE:", Volume.open.4.testing.mse_value, "\n Testing Model RMSE:", Volume.open.4.testing.rmse_value , "\n")## Training Model MSE: 2.70994e+12
## Training Model RMSE: 1646190
## Testing Model MSE: 4.676164e+12
## Testing Model RMSE: 2162444cat(" Training Model AIC:", AIC(Volume.open.training.4), "\n Training Model BIC:", BIC(Volume.open.training.4), "\n")## Training Model AIC: 7782.195
## Training Model BIC: 8019.724This model has very similar values to that of the previous model, so we can apply the same conclusion here. The R-squared value is not high enough for a good portion to be attributed to the independent variable. The AIC and BIC are also not the lowest we have observed. And the same applies to the MSE and RMSE values. Thus, this ARDL model is not a good fit.
ARDL 10-steps Forecasting
Computation and Plot of 10 steps ahead forecast for Turnover with lag (1:4) and Close with lag (110)
Turnover.Close.forecast.1 <- predict(ardl.turnover.close.1, n.ahead = 10)
forecast_start_time <- end(Turnover.ts)[1] + 1
Turnover.Close.forecast.ts.1 <- ts(Turnover.Close.forecast.1, start = forecast_start_time, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.Close.forecast.ts.1, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Turnover")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.Close.forecast.ts.1)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117)
## 4.437920e+14 3.590315e+14 3.620933e+14 3.909650e+14 3.246154e+14 3.745337e+14
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 3.710251e+14 3.704318e+14 3.919642e+14 3.854421e+14 3.614446e+14 3.635212e+14
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## 3.752945e+14 3.811698e+14 3.351593e+14 3.100042e+14 3.347392e+14 3.170406e+14
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 3.625859e+14 3.976113e+14 3.751243e+14 3.729413e+14 3.633673e+14 3.404775e+14
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 3.251657e+14 3.199807e+14 3.314726e+14 9.479715e+14 5.525683e+14 3.824260e+14
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## 5.040927e+14 4.193220e+14 4.329106e+14 3.922072e+14 4.851816e+14 4.327322e+14
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## 4.172771e+14 4.573051e+14 3.687993e+14 4.062537e+14 3.787211e+14 3.346747e+14
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 4.113077e+14 4.608366e+14 4.525145e+14 3.812207e+14 3.458313e+14 3.692174e+14
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## 4.015904e+14 4.215053e+14 4.704729e+14 5.421397e+14 5.401602e+14 5.083112e+14
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 5.865801e+14 4.519231e+14 4.699137e+14 4.830027e+14 4.849823e+14 4.542668e+14
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## 4.160292e+14 3.856024e+14 3.771246e+14 4.400400e+14 4.240618e+14 4.481253e+14
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 4.108513e+14 3.756762e+14 4.230231e+14 4.881105e+14 3.563481e+14 4.458845e+14
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## 3.960527e+14 5.080770e+14 4.852697e+14 4.204788e+14 4.905673e+14 5.049441e+14
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## 4.258490e+14 4.532405e+14 4.792659e+14 4.504049e+14 5.118087e+14 8.700899e+14
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## 6.080644e+14 4.573935e+14 5.386391e+14 4.341377e+14 4.174722e+14 4.481885e+14
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 4.156525e+14 3.932977e+14 3.470123e+14 3.735766e+14 3.740249e+14 3.681005e+14
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## 3.455459e+14 3.298103e+14 3.400630e+14 3.219426e+14 3.026353e+14 3.120304e+14
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## 3.712733e+14 3.442781e+14 2.679878e+14 3.275805e+14 3.870523e+14 3.771940e+14
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## 4.307596e+14 4.258112e+14 3.392821e+14 3.840412e+14 3.551018e+14 4.386042e+14
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 3.670212e+14 5.804866e+14 4.163807e+14 3.665166e+14 4.250935e+14 4.142598e+14
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## 3.546830e+14 3.621149e+14 3.989168e+14 3.603930e+14 3.611433e+14 3.573641e+14
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## 3.624491e+14 3.656992e+14 3.541474e+14 3.960535e+14 3.513301e+14 3.370141e+14
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## 3.279602e+14 2.824516e+14 3.575968e+14 3.216693e+14 3.420263e+14 4.142269e+14
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 2.964342e+14 3.688935e+14 4.485723e+14 4.125687e+14 3.927391e+14 5.039927e+14
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## 1.045558e+15 5.567517e+14 4.282874e+14 6.149903e+14 4.527169e+14 4.012254e+14
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## 3.582119e+14 3.971289e+14 4.288457e+14 4.457264e+14 4.505221e+14 5.275339e+14
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## 5.338871e+14 5.650003e+14 5.071548e+14 4.584967e+14 4.046570e+14 3.804098e+14
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 4.954814e+14 4.170701e+14 3.860293e+14 4.578714e+14 3.926612e+14 3.917814e+14
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## 3.937339e+14 3.873751e+14 4.365719e+14 4.612613e+14 4.124841e+14 3.797717e+14
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## 4.107911e+14 3.957199e+14 3.889268e+14 4.216451e+14 3.373282e+14 4.004273e+14
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## 3.797836e+14 3.387465e+14 3.830787e+14 4.117118e+14 3.840553e+14 3.945863e+14
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 3.866629e+14 3.850456e+14 4.018236e+14 3.736394e+14 3.616918e+14 4.031274e+14
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## 3.904986e+14 3.600572e+14 3.976735e+14 3.895698e+14 5.460838e+14 4.769233e+14
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## 3.564974e+14 4.576607e+14 4.178561e+14 4.029019e+14 4.361262e+14 4.615378e+14
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 4.765425e+14 4.183803e+14 3.792048e+14 4.050745e+14 4.406099e+14 3.871836e+14
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 4.961077e+14 4.539445e+14 4.866502e+14 5.193706e+14 1.028338e+15 6.826244e+14
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## 4.529853e+14 5.665577e+14 5.388527e+14 5.135767e+14 4.368859e+14 4.638655e+14
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## 4.133909e+14 3.740741e+14 3.648945e+14 4.022098e+14 3.851128e+14 3.618532e+14
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## 3.602555e+14 3.765526e+14 4.404926e+14 3.703149e+14 4.366466e+14 4.114143e+14
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 3.457302e+14 3.507511e+14 4.084549e+14 4.500691e+14 5.810884e+14 3.950694e+14
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## 3.552690e+14 4.167579e+14 3.937858e+14 3.686837e+14 3.667677e+14 3.990900e+14
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## 3.787501e+14 4.593848e+14 4.437920e+14 3.590315e+14 3.620933e+14 3.909650e+14
## 2015(364) 2015(365)
## 3.246154e+14 3.745337e+14Computation and Plot of 10 steps ahead forecast for Turnover with lag (1:4) and Close with lag (1:110)
Turnover.Close.forecast.2 <- predict(ardl.turnover.close.2, n.ahead = 10)
forecast_start_time <- end(Turnover.ts)[1] + 1
Turnover.Close.forecast.ts.2 <- ts(Turnover.Close.forecast.2, start = forecast_start_time, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.Close.forecast.ts.2, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Turnover")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.Close.forecast.ts.2)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116)
## 3.401318e+14 2.338932e+14 3.218303e+14 2.833377e+14 3.651541e+14
## 2015(117) 2015(118) 2015(119) 2015(120) 2015(121)
## 2.219469e+14 -4.063762e+14 6.053470e+14 4.259575e+14 2.325385e+14
## 2015(122) 2015(123) 2015(124) 2015(125) 2015(126)
## 3.774172e+14 3.654971e+14 4.658795e+14 2.924806e+14 2.012625e+14
## 2015(127) 2015(128) 2015(129) 2015(130) 2015(131)
## 3.092900e+14 1.665426e+14 1.283406e+14 3.476191e+14 2.612407e+14
## 2015(132) 2015(133) 2015(134) 2015(135) 2015(136)
## 3.638963e+14 3.279538e+14 3.326071e+14 2.365600e+14 1.992948e+14
## 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 2.877062e+14 1.279493e+15 7.316489e+14 6.560582e+14 3.539934e+14
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146)
## 4.690115e+14 4.888085e+14 3.702461e+14 4.599903e+14 4.817456e+14
## 2015(147) 2015(148) 2015(149) 2015(150) 2015(151)
## 4.181520e+14 4.150561e+14 3.889017e+14 4.639659e+14 2.733587e+14
## 2015(152) 2015(153) 2015(154) 2015(155) 2015(156)
## 4.074308e+14 3.968737e+14 5.610284e+14 6.292885e+14 3.128268e+14
## 2015(157) 2015(158) 2015(159) 2015(160) 2015(161)
## 2.252509e+14 3.195387e+14 3.941305e+14 5.438637e+14 4.892449e+14
## 2015(162) 2015(163) 2015(164) 2015(165) 2015(166)
## 5.542212e+14 6.924154e+14 5.047103e+14 6.752668e+14 5.295086e+14
## 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 6.037651e+14 3.908516e+14 5.401445e+14 2.116612e+14 5.167922e+14
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176)
## 4.638438e+14 2.949771e+14 4.571745e+14 3.713810e+14 5.263416e+14
## 2015(177) 2015(178) 2015(179) 2015(180) 2015(181)
## 4.168483e+14 3.161120e+14 2.933597e+14 5.588356e+14 3.030180e+14
## 2015(182) 2015(183) 2015(184) 2015(185) 2015(186)
## 4.195073e+14 3.948893e+14 4.959634e+14 5.916616e+14 4.025041e+14
## 2015(187) 2015(188) 2015(189) 2015(190) 2015(191)
## 3.103091e+14 -2.897176e+14 4.941712e+14 5.636584e+14 4.793889e+14
## 2015(192) 2015(193) 2015(194) 2015(195) 2015(196)
## 4.330206e+14 6.047243e+14 1.211725e+15 8.827551e+14 6.444576e+14
## 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## 5.634722e+14 4.933624e+14 3.816110e+14 3.494870e+14 4.460652e+14
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206)
## 5.075020e+14 3.023381e+14 3.093278e+14 3.512729e+14 2.391573e+14
## 2015(207) 2015(208) 2015(209) 2015(210) 2015(211)
## 3.694466e+14 3.722383e+14 3.287333e+14 2.653437e+14 2.147208e+14
## 2015(212) 2015(213) 2015(214) 2015(215) 2015(216)
## 4.651823e+13 3.469738e+14 4.532338e+14 2.315970e+14 2.528970e+14
## 2015(217) 2015(218) 2015(219) 2015(220) 2015(221)
## 4.600565e+14 4.624728e+14 4.519861e+14 4.867926e+14 4.170756e+14
## 2015(222) 2015(223) 2015(224) 2015(225) 2015(226)
## 2.746649e+14 3.599082e+14 3.805839e+14 4.239167e+14 3.917796e+14
## 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 5.989828e+14 4.106937e+14 3.176133e+14 4.784136e+14 3.912381e+14
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236)
## 4.098479e+14 3.258567e+14 3.940063e+14 3.531199e+14 2.922597e+14
## 2015(237) 2015(238) 2015(239) 2015(240) 2015(241)
## 3.988944e+14 3.172690e+14 3.387928e+14 3.655594e+14 3.980951e+14
## 2015(242) 2015(243) 2015(244) 2015(245) 2015(246)
## 4.157989e+14 3.040309e+14 3.841061e+14 3.405772e+14 2.987049e+14
## 2015(247) 2015(248) 2015(249) 2015(250) 2015(251)
## 3.473829e+14 2.815203e+14 4.722176e+14 3.920950e+14 4.680052e+14
## 2015(252) 2015(253) 2015(254) 2015(255) 2015(256)
## 5.001279e+14 3.863022e+14 5.572186e+14 1.235517e+15 9.203286e+14
## 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## 5.466057e+14 4.855513e+14 5.655980e+14 4.518870e+14 3.854507e+14
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266)
## 4.991845e+14 5.311499e+14 5.428926e+14 5.433652e+14 6.380419e+14
## 2015(267) 2015(268) 2015(269) 2015(270) 2015(271)
## 5.569238e+14 7.007459e+14 6.262436e+14 5.176750e+14 4.564542e+14
## 2015(272) 2015(273) 2015(274) 2015(275) 2015(276)
## 3.074841e+14 6.064131e+14 5.831553e+14 -3.733846e+14 5.696591e+14
## 2015(277) 2015(278) 2015(279) 2015(280) 2015(281)
## 5.171614e+14 5.840178e+14 4.196395e+14 3.217152e+14 4.593648e+14
## 2015(282) 2015(283) 2015(284) 2015(285) 2015(286)
## 3.938961e+14 4.203784e+14 3.696770e+14 2.836953e+14 4.659271e+14
## 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## 3.993479e+14 5.175903e+14 3.700409e+14 1.826432e+14 2.600416e+14
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296)
## 4.467488e+14 3.895244e+14 4.539219e+14 5.307667e+14 3.947257e+14
## 2015(297) 2015(298) 2015(299) 2015(300) 2015(301)
## 3.438271e+14 2.923120e+14 2.997643e+14 3.284397e+14 3.229284e+14
## 2015(302) 2015(303) 2015(304) 2015(305) 2015(306)
## 2.604943e+14 4.518745e+14 3.163975e+14 4.242480e+14 2.674341e+14
## 2015(307) 2015(308) 2015(309) 2015(310) 2015(311)
## 5.855468e+14 5.121757e+14 4.665105e+14 3.268455e+14 3.003736e+14
## 2015(312) 2015(313) 2015(314) 2015(315) 2015(316)
## 4.343443e+14 3.176732e+14 4.792547e+14 5.930795e+14 4.538558e+14
## 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 2.558052e+14 5.317786e+14 4.019139e+14 5.485712e+14 3.174179e+14
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326)
## 5.048048e+14 4.982860e+14 4.739946e+14 1.240262e+15 1.086516e+15
## 2015(327) 2015(328) 2015(329) 2015(330) 2015(331)
## 5.850297e+14 2.799910e+14 6.216133e+14 5.390908e+14 -8.904842e+13
## 2015(332) 2015(333) 2015(334) 2015(335) 2015(336)
## 4.597660e+14 4.933691e+14 2.719443e+14 3.993112e+14 4.389179e+14
## 2015(337) 2015(338) 2015(339) 2015(340) 2015(341)
## 3.029156e+14 3.245496e+14 3.644563e+14 3.398786e+14 4.389719e+14
## 2015(342) 2015(343) 2015(344) 2015(345) 2015(346)
## 3.493992e+14 4.810205e+14 4.540564e+14 3.594387e+14 3.342953e+14
## 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 4.671252e+14 6.304051e+14 7.416571e+14 5.291028e+14 4.976106e+14
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356)
## 4.220819e+14 4.332032e+14 3.288699e+14 3.436884e+14 1.939856e+14
## 2015(357) 2015(358) 2015(359) 2015(360) 2015(361)
## 3.132441e+14 4.865139e+14 4.749024e+14 3.401318e+14 2.338932e+14
## 2015(362) 2015(363) 2015(364) 2015(365)
## 3.218303e+14 2.833377e+14 3.651541e+14 2.219469e+14Computation and Plot of 10 steps ahead forecast for Turnover with lag (2)n(61)n(75)n(117) and Close with lag (110)
Turnover.Close.forecast.3 <- predict(ardl.turnover.close.3, n.ahead = 10)
forecast_start_time <- end(Turnover.ts)[1] + 1
Turnover.Close.forecast.ts.3 <- ts(Turnover.Close.forecast.3, start = forecast_start_time, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.Close.forecast.ts.3, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Turnover")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.Close.forecast.ts.3)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 248)
## Frequency = 365
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 2.993358e+14 3.424255e+14 5.533546e+14 4.644747e+14 3.394110e+14 4.699272e+14
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## 9.178562e+14 4.755188e+14 4.323567e+14 4.495136e+14 4.100094e+14 3.594849e+14
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 2.750868e+14 3.621403e+14 4.464236e+14 4.201277e+14 5.263830e+14 5.118804e+14
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 5.300383e+14 5.579184e+14 9.469680e+14 5.588236e+14 6.981194e+14 4.264417e+14
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## 5.550406e+14 4.582600e+14 4.046873e+14 4.612465e+14 3.637817e+14 4.010729e+14
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## 3.589673e+14 3.949535e+14 4.420203e+14 4.125223e+14 4.410374e+14 3.547213e+14
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 3.999649e+14 3.626841e+14 4.615483e+14 4.437806e+14 2.790812e+14 3.197936e+14
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## 3.455595e+14 4.052593e+14 5.446783e+14 4.224418e+14 4.062744e+14 4.206241e+14
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 4.032920e+14 4.304905e+14 3.804402e+14 3.845161e+14 3.748008e+14 4.565436e+14
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## 4.242760e+14 3.172440e+14 3.379287e+14 3.512434e+14 5.157952e+14 4.366808e+14
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 3.513108e+14 3.920194e+14 3.597629e+14 3.937062e+14 4.206607e+14 3.831284e+14
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## 4.530551e+14 3.669344e+14 3.747754e+14 3.173511e+14 3.855212e+14 3.450803e+14
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## 5.005760e+14 4.236303e+14 4.837062e+14 4.618615e+14 9.127143e+14 5.639316e+14
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## 5.966362e+14 4.160945e+14 4.279849e+14 9.717044e+14 4.882173e+14 4.366226e+14
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 3.519394e+14 3.566232e+14 3.635864e+14 3.650158e+14 4.397052e+14 3.592529e+14
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## 3.530103e+14 3.635518e+14 3.600454e+14 3.328395e+14 3.603215e+14 3.621291e+14
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## 3.386232e+14 3.905192e+14 4.242200e+14 3.539140e+14 4.694705e+14 3.272764e+14
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## 3.626280e+14 4.104918e+14 3.543657e+14 4.783784e+14 4.519571e+14 4.313185e+14
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 5.192597e+14 3.979175e+14 5.692709e+14 3.856867e+14 4.222453e+14 3.816882e+14
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## 3.336741e+14 3.152080e+14 3.266081e+14 4.123661e+14 3.975051e+14 4.273883e+14
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## 3.451792e+14 3.278574e+14 3.807209e+14 4.354202e+14 3.077227e+14 3.469943e+14
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## 2.927580e+14 4.046257e+14 3.729873e+14 4.096422e+14 4.036148e+14 4.300341e+14
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 3.734793e+14 3.314382e+14 3.603737e+14 3.839090e+14 4.477716e+14 1.278971e+15
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## 6.557623e+14 7.659356e+14 4.127118e+14 4.094517e+14 4.495113e+14 4.390027e+14
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## 4.769693e+14 3.778427e+14 3.496903e+14 4.169691e+14 3.650255e+14 4.099932e+14
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## 3.921768e+14 4.060034e+14 4.416359e+14 4.313085e+14 3.836057e+14 2.867643e+14
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 3.018158e+14 3.687440e+14 3.103200e+14 3.583629e+14 4.637363e+14 4.950742e+14
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## 5.280309e+14 4.622608e+14 4.908684e+14 3.830377e+14 4.200616e+14 4.569787e+14
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## 4.023625e+14 5.767081e+14 3.697263e+14 3.408638e+14 3.345542e+14 3.983192e+14
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## 3.729820e+14 3.976482e+14 3.623777e+14 3.266335e+14 3.808458e+14 4.255464e+14
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 3.173479e+14 4.087073e+14 3.113900e+14 5.270556e+14 3.819742e+14 3.601227e+14
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## 3.658938e+14 3.724856e+14 3.528047e+14 3.657665e+14 3.958323e+14 5.230748e+14
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## 4.233677e+14 7.455155e+14 5.644300e+14 4.415689e+14 4.052912e+14 4.779988e+14
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 9.616208e+14 5.309058e+14 4.147107e+14 3.897701e+14 3.413010e+14 3.691361e+14
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 3.125221e+14 4.249688e+14 3.680676e+14 4.301466e+14 4.263919e+14 7.553376e+14
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## 5.087690e+14 4.847141e+14 5.251415e+14 4.363118e+14 3.133273e+14 3.249105e+14
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## 4.884309e+14 3.917118e+14 4.046629e+14 4.107162e+14 3.633998e+14 3.607975e+14
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## 3.208510e+14 4.157505e+14 3.935066e+14 6.546537e+14 3.749315e+14 3.798673e+14
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 3.527997e+14 3.699050e+14 3.269045e+14 3.932108e+14 3.508768e+14 4.760852e+14
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## 3.142466e+14 2.935245e+14 3.265106e+14 3.834052e+14 3.419004e+14 3.843322e+14
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## 3.320231e+14 4.220975e+14 3.448166e+14 2.950392e+14 3.117432e+14 3.175334e+14
## 2015(364) 2015(365)
## 3.388220e+14 3.567706e+14Computation and Plot of 10 steps ahead forecast for Turnover with lag (2)n(61)n(75)n(117) and Close with lag (1:110)
Turnover.Close.forecast.4 <- predict(ardl.turnover.close.4, n.ahead = 10)
forecast_start_time <- end(Turnover.ts)[1] + 1
Turnover.Close.forecast.ts.4 <- ts(Turnover.Close.forecast.4, start = forecast_start_time, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.Close.forecast.ts.4, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Turnover")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.Close.forecast.ts.4)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 248)
## Frequency = 365
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122)
## -9.147030e+13 4.403750e+14 6.046233e+14 2.777610e+14 2.179252e+14
## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127)
## 3.719387e+14 7.185031e+14 4.311034e+14 2.383161e+14 2.995433e+14
## 2015(128) 2015(129) 2015(130) 2015(131) 2015(132)
## 2.229374e+14 1.108457e+14 2.314214e+14 1.882900e+14 3.095181e+14
## 2015(133) 2015(134) 2015(135) 2015(136) 2015(137)
## 3.309998e+14 3.788567e+14 3.132979e+14 2.559364e+14 3.652272e+14
## 2015(138) 2015(139) 2015(140) 2015(141) 2015(142)
## 1.548984e+15 4.907873e+14 6.344545e+14 4.245207e+14 5.391988e+14
## 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## 5.811916e+14 4.032530e+14 5.367854e+14 3.898940e+14 4.489059e+14
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152)
## 4.508467e+14 3.547310e+14 6.159453e+14 3.156500e+14 3.411791e+14
## 2015(153) 2015(154) 2015(155) 2015(156) 2015(157)
## 4.140186e+14 5.381934e+14 5.522653e+14 3.350037e+14 2.096803e+14
## 2015(158) 2015(159) 2015(160) 2015(161) 2015(162)
## 2.498324e+14 3.200976e+14 4.992254e+14 4.673539e+14 5.747430e+14
## 2015(163) 2015(164) 2015(165) 2015(166) 2015(167)
## 5.749941e+14 5.139565e+14 6.509135e+14 4.330582e+14 5.867444e+14
## 2015(168) 2015(169) 2015(170) 2015(171) 2015(172)
## 3.857493e+14 4.474500e+14 1.720903e+14 4.026393e+14 4.869282e+14
## 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## 2.998815e+14 5.953239e+14 3.844186e+14 5.208964e+14 3.762367e+14
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182)
## 2.992070e+14 5.004656e+14 5.266785e+14 2.629731e+14 4.235755e+14
## 2015(183) 2015(184) 2015(185) 2015(186) 2015(187)
## 2.914328e+14 4.917572e+14 4.443714e+14 3.346386e+14 2.410550e+14
## 2015(188) 2015(189) 2015(190) 2015(191) 2015(192)
## -4.184867e+14 1.276395e+14 6.116869e+14 5.340968e+14 3.941923e+14
## 2015(193) 2015(194) 2015(195) 2015(196) 2015(197)
## 5.331480e+14 1.388134e+15 6.747306e+14 5.578641e+14 5.863145e+14
## 2015(198) 2015(199) 2015(200) 2015(201) 2015(202)
## 4.803876e+14 6.446622e+14 4.067566e+14 3.967562e+14 4.761292e+14
## 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 2.771771e+14 3.394609e+14 3.327748e+14 3.642557e+14 2.600836e+14
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212)
## 3.730842e+14 3.541572e+14 2.723214e+14 1.511876e+14 4.823182e+13
## 2015(213) 2015(214) 2015(215) 2015(216) 2015(217)
## 2.386355e+14 3.937506e+14 2.431307e+14 2.773690e+14 4.582915e+14
## 2015(218) 2015(219) 2015(220) 2015(221) 2015(222)
## 5.129609e+14 4.614766e+14 4.971942e+14 4.024065e+14 3.436348e+14
## 2015(223) 2015(224) 2015(225) 2015(226) 2015(227)
## 4.538218e+14 4.913408e+14 4.667623e+14 5.242541e+14 4.288990e+14
## 2015(228) 2015(229) 2015(230) 2015(231) 2015(232)
## 5.238341e+14 3.475917e+14 4.431891e+14 3.713087e+14 3.625285e+14
## 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## 3.143252e+14 3.257242e+14 4.006202e+14 3.330893e+14 4.424127e+14
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242)
## 3.125682e+14 2.674639e+14 3.358967e+14 4.301060e+14 3.465891e+14
## 2015(243) 2015(244) 2015(245) 2015(246) 2015(247)
## 3.071548e+14 2.864968e+14 4.416045e+14 3.513442e+14 4.154959e+14
## 2015(248) 2015(249) 2015(250) 2015(251) 2015(252)
## 3.790797e+14 4.406329e+14 4.071465e+14 4.186857e+14 3.739816e+14
## 2015(253) 2015(254) 2015(255) 2015(256) 2015(257)
## 3.698146e+14 6.000223e+14 1.625510e+15 6.380908e+14 7.372395e+14
## 2015(258) 2015(259) 2015(260) 2015(261) 2015(262)
## 6.145148e+14 4.106967e+14 4.796788e+14 6.535050e+14 6.215954e+14
## 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## 6.095984e+14 5.572123e+14 5.630313e+14 5.957813e+14 4.957548e+14
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272)
## 5.838089e+14 5.318563e+14 5.290662e+14 5.075131e+14 3.949088e+14
## 2015(273) 2015(274) 2015(275) 2015(276) 2015(277)
## 6.223171e+14 5.753717e+14 -1.048621e+14 3.590423e+14 5.102263e+14
## 2015(278) 2015(279) 2015(280) 2015(281) 2015(282)
## 6.452785e+14 5.617793e+14 4.392773e+14 4.770711e+14 4.633024e+14
## 2015(283) 2015(284) 2015(285) 2015(286) 2015(287)
## 3.482793e+14 3.778459e+14 3.299432e+14 4.364918e+14 5.076061e+14
## 2015(288) 2015(289) 2015(290) 2015(291) 2015(292)
## 5.347325e+14 3.526911e+14 1.981527e+14 2.115810e+14 3.366601e+14
## 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## 4.870974e+14 4.492811e+14 4.196700e+14 4.125640e+14 3.584261e+14
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302)
## 2.712473e+14 3.726914e+14 2.898720e+14 3.408801e+14 2.454108e+14
## 2015(303) 2015(304) 2015(305) 2015(306) 2015(307)
## 3.684715e+14 2.841402e+14 3.451856e+14 2.146926e+14 4.957966e+14
## 2015(308) 2015(309) 2015(310) 2015(311) 2015(312)
## 4.371230e+14 4.570339e+14 3.790095e+14 4.294267e+14 4.296512e+14
## 2015(313) 2015(314) 2015(315) 2015(316) 2015(317)
## 3.897813e+14 4.866330e+14 5.765523e+14 7.241087e+14 2.788757e+14
## 2015(318) 2015(319) 2015(320) 2015(321) 2015(322)
## 4.928411e+14 4.493955e+14 4.615065e+14 3.665243e+14 2.979141e+14
## 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 4.161927e+14 3.702440e+14 1.146765e+15 6.764946e+14 6.196437e+14
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332)
## 3.765359e+14 5.447062e+14 4.631560e+14 4.844542e+13 2.423842e+14
## 2015(333) 2015(334) 2015(335) 2015(336) 2015(337)
## 3.991684e+14 3.305506e+14 3.615911e+14 6.738273e+14 3.358504e+14
## 2015(338) 2015(339) 2015(340) 2015(341) 2015(342)
## 3.154553e+14 2.789261e+14 3.165390e+14 4.152743e+14 3.288897e+14
## 2015(343) 2015(344) 2015(345) 2015(346) 2015(347)
## 6.126519e+14 4.107958e+14 3.532214e+14 3.499391e+14 5.049943e+14
## 2015(348) 2015(349) 2015(350) 2015(351) 2015(352)
## 5.353002e+14 7.443162e+14 3.841729e+14 5.424194e+14 4.800150e+14
## 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## 4.143659e+14 3.310731e+14 4.059762e+14 1.651102e+14 2.419692e+14
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362)
## 4.238055e+14 4.603549e+14 2.978738e+14 2.965341e+14 3.143829e+14
## 2015(363) 2015(364) 2015(365)
## 3.014766e+14 4.011378e+14 2.204975e+14Computation and Plot of 10 steps ahead forecast for Turnover with lag (1:4) and Close with lag (110)
Turnover.open.forecast.1 <- predict(ardl.turnover.open.1, n.ahead = 10)
forecast_start_time <- end(Turnover.ts)[1] + 1
Turnover.open.forecast.ts.1 <- ts(Turnover.open.forecast.1, start = forecast_start_time, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.open.forecast.ts.1, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Turnover")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.open.forecast.ts.1)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117)
## 4.423260e+14 3.624325e+14 3.617921e+14 3.895377e+14 3.255622e+14 3.695919e+14
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 3.770848e+14 3.725887e+14 3.895356e+14 3.877218e+14 3.630154e+14 3.621858e+14
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## 3.733937e+14 3.808184e+14 3.369872e+14 3.108711e+14 3.396013e+14 3.115649e+14
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 3.620167e+14 3.988557e+14 3.738195e+14 3.732631e+14 3.626084e+14 3.389633e+14
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 3.273047e+14 3.187181e+14 3.330901e+14 9.501986e+14 5.519596e+14 3.838995e+14
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## 5.044042e+14 4.193877e+14 4.319534e+14 3.964002e+14 4.839019e+14 4.310338e+14
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## 4.159601e+14 4.613683e+14 3.661942e+14 4.048584e+14 3.809970e+14 3.333738e+14
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 4.130037e+14 4.596674e+14 4.544125e+14 3.765946e+14 3.462817e+14 3.666225e+14
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## 4.046877e+14 4.183638e+14 4.755102e+14 5.418117e+14 5.388181e+14 5.077213e+14
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 5.886867e+14 4.518798e+14 4.687702e+14 4.854254e+14 4.794297e+14 4.561899e+14
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## 4.192661e+14 3.844025e+14 3.755426e+14 4.405701e+14 4.227695e+14 4.494641e+14
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 4.100194e+14 3.774158e+14 4.240765e+14 4.879249e+14 3.540645e+14 4.475800e+14
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## 3.938254e+14 5.083526e+14 4.859973e+14 4.250275e+14 4.816392e+14 5.048204e+14
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## 4.244347e+14 4.540426e+14 4.771648e+14 4.546106e+14 5.118956e+14 8.655124e+14
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## 6.103675e+14 4.563340e+14 5.433974e+14 4.310056e+14 4.190420e+14 4.452841e+14
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 4.167466e+14 3.932237e+14 3.496722e+14 3.741149e+14 3.737521e+14 3.697302e+14
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## 3.437577e+14 3.305052e+14 3.356533e+14 3.236392e+14 3.033931e+14 3.146886e+14
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## 3.684949e+14 3.446771e+14 2.685515e+14 3.272826e+14 3.861913e+14 3.745439e+14
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## 4.351523e+14 4.246367e+14 3.098851e+14 3.849170e+14 3.564493e+14 4.378779e+14
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 3.676504e+14 5.786998e+14 4.190774e+14 3.658346e+14 4.245107e+14 4.135336e+14
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## 3.544970e+14 3.624676e+14 3.983017e+14 3.614258e+14 3.601901e+14 3.574233e+14
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## 3.624946e+14 3.662178e+14 3.533992e+14 3.953361e+14 3.502414e+14 3.369625e+14
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## 3.284399e+14 2.833569e+14 3.571266e+14 3.223331e+14 3.392851e+14 4.195412e+14
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 2.964982e+14 3.686012e+14 4.490048e+14 4.112463e+14 3.921047e+14 5.058266e+14
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## 1.044564e+15 5.570631e+14 4.290904e+14 6.136135e+14 4.551233e+14 3.998447e+14
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## 3.599875e+14 3.961550e+14 4.284444e+14 4.473074e+14 4.521825e+14 5.268226e+14
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## 5.330641e+14 5.660047e+14 5.084218e+14 4.566835e+14 4.052310e+14 3.800447e+14
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 4.957130e+14 4.161692e+14 3.856353e+14 4.610774e+14 3.897713e+14 3.918333e+14
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## 3.946467e+14 3.879329e+14 4.359462e+14 4.596314e+14 4.129456e+14 3.799983e+14
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## 4.108707e+14 3.958644e+14 3.889108e+14 4.221271e+14 3.374639e+14 3.994995e+14
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## 3.807877e+14 3.376722e+14 3.824249e+14 4.150548e+14 3.806042e+14 3.950479e+14
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 3.887074e+14 3.848354e+14 4.039927e+14 3.723457e+14 3.603010e+14 4.015287e+14
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## 3.968668e+14 3.545491e+14 3.965910e+14 3.901722e+14 5.460525e+14 4.765067e+14
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## 3.565801e+14 4.581458e+14 4.186661e+14 4.035651e+14 4.360027e+14 4.609767e+14
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 4.775493e+14 4.182829e+14 3.783851e+14 4.047568e+14 4.421792e+14 3.872525e+14
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 4.939625e+14 4.540338e+14 4.884648e+14 5.187509e+14 1.027418e+15 6.829801e+14
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## 4.534678e+14 5.665889e+14 5.371813e+14 5.147538e+14 4.369961e+14 4.645168e+14
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## 4.124217e+14 3.746613e+14 3.648395e+14 4.038099e+14 3.853149e+14 3.605378e+14
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## 3.597770e+14 3.770696e+14 4.398022e+14 3.708458e+14 4.352603e+14 4.125210e+14
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 3.445887e+14 3.521046e+14 4.083198e+14 4.506997e+14 5.823034e+14 3.924480e+14
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## 3.575202e+14 4.161328e+14 3.944164e+14 3.673918e+14 3.674740e+14 3.998689e+14
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## 3.771010e+14 4.832270e+14 4.423260e+14 3.624325e+14 3.617921e+14 3.895377e+14
## 2015(364) 2015(365)
## 3.255622e+14 3.695919e+14Computation and Plot of 10 steps ahead forecast for Turnover with lag (1:4) and Close with lag (35)n(110)
Turnover.open.forecast.2 <- predict(ardl.turnover.open.2, n.ahead = 10)
forecast_start_time <- end(Turnover.ts)[1] + 1
Turnover.open.forecast.ts.2 <- ts(Turnover.open.forecast.2, start = forecast_start_time, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.open.forecast.ts.2, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Turnover")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.open.forecast.ts.2)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117)
## 4.428011e+14 3.683766e+14 3.626447e+14 3.904003e+14 3.256125e+14 3.697454e+14
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 3.752713e+14 3.737980e+14 3.918321e+14 3.861827e+14 3.627108e+14 3.609727e+14
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## 3.752209e+14 3.804938e+14 3.381004e+14 3.094434e+14 3.388987e+14 3.092743e+14
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 3.617614e+14 3.990582e+14 3.735752e+14 3.746318e+14 3.631745e+14 3.403870e+14
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 3.260730e+14 3.175593e+14 3.325085e+14 9.516748e+14 5.504302e+14 3.846733e+14
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## 5.041592e+14 4.200472e+14 4.324661e+14 3.943957e+14 4.852940e+14 4.758273e+14
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## 4.152998e+14 4.605092e+14 3.663474e+14 4.047450e+14 3.811031e+14 3.325980e+14
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 4.134680e+14 4.602906e+14 4.543924e+14 3.770623e+14 3.461819e+14 3.666355e+14
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## 4.042658e+14 4.188421e+14 4.756730e+14 5.417125e+14 5.389215e+14 5.085435e+14
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 5.889727e+14 4.518604e+14 4.682618e+14 4.844631e+14 4.786477e+14 4.558933e+14
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## 4.188211e+14 3.828334e+14 3.724839e+14 4.406012e+14 4.230613e+14 4.499054e+14
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 4.106976e+14 3.772281e+14 4.233333e+14 4.883671e+14 3.539605e+14 4.477790e+14
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## 3.942115e+14 5.071757e+14 4.862655e+14 4.243601e+14 4.814118e+14 5.039874e+14
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## 4.228992e+14 4.532919e+14 4.776340e+14 4.545812e+14 5.109536e+14 8.658599e+14
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## 6.104606e+14 4.579758e+14 5.433777e+14 4.312290e+14 4.191161e+14 4.446112e+14
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 4.152493e+14 3.952025e+14 3.492999e+14 3.736518e+14 3.740085e+14 3.706044e+14
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## 3.447555e+14 3.294853e+14 3.357704e+14 3.234122e+14 3.031601e+14 3.147773e+14
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## 3.681835e+14 3.445221e+14 2.691875e+14 3.267592e+14 3.864944e+14 3.743306e+14
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## 4.340797e+14 4.262033e+14 3.082298e+14 3.833546e+14 3.562878e+14 4.373319e+14
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 3.688693e+14 5.797805e+14 4.186071e+14 3.634571e+14 4.282125e+14 4.142850e+14
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## 3.540418e+14 3.626483e+14 3.981022e+14 3.609711e+14 3.597207e+14 3.566921e+14
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## 3.620085e+14 3.664086e+14 3.536750e+14 3.950092e+14 3.505484e+14 3.377433e+14
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## 3.282852e+14 2.827194e+14 3.575677e+14 3.231718e+14 3.396293e+14 4.192124e+14
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 2.968921e+14 3.696175e+14 4.495614e+14 4.114320e+14 3.938242e+14 5.063112e+14
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## 1.043639e+15 5.560024e+14 4.297634e+14 6.132252e+14 4.541981e+14 3.993007e+14
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## 3.591661e+14 3.965495e+14 4.292068e+14 4.478568e+14 4.518555e+14 5.272400e+14
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## 5.329408e+14 5.662267e+14 5.073944e+14 4.568283e+14 4.040150e+14 3.795929e+14
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 4.949545e+14 4.158412e+14 3.869476e+14 4.600858e+14 3.897649e+14 3.916053e+14
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## 3.950995e+14 3.874708e+14 4.359359e+14 4.600479e+14 3.744355e+14 3.798779e+14
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## 4.091805e+14 3.971131e+14 3.896066e+14 4.212170e+14 3.376526e+14 3.947440e+14
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## 3.799376e+14 3.382205e+14 3.808204e+14 4.145051e+14 3.818001e+14 3.956896e+14
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 3.875875e+14 3.829777e+14 4.028723e+14 3.714108e+14 3.634473e+14 4.017602e+14
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## 3.961215e+14 3.554459e+14 3.968234e+14 3.899885e+14 5.456499e+14 4.738345e+14
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## 3.569394e+14 4.562060e+14 4.168321e+14 4.035476e+14 4.352053e+14 4.617954e+14
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 4.770180e+14 4.180522e+14 3.768664e+14 4.059707e+14 4.430527e+14 3.867685e+14
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 4.932372e+14 4.552050e+14 4.885886e+14 5.172567e+14 1.028013e+15 6.814411e+14
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## 4.554023e+14 5.662889e+14 5.396218e+14 5.147340e+14 4.376055e+14 4.624728e+14
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## 4.128761e+14 3.722505e+14 3.653279e+14 4.047324e+14 3.849746e+14 3.600905e+14
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## 3.605657e+14 3.776312e+14 4.404526e+14 3.727003e+14 4.335782e+14 4.106021e+14
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 3.467090e+14 3.529687e+14 4.085332e+14 4.503227e+14 5.810565e+14 3.922018e+14
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## 3.565640e+14 4.159535e+14 3.950669e+14 3.692215e+14 3.677280e+14 4.010882e+14
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## 3.769461e+14 4.836075e+14 4.428011e+14 3.683766e+14 3.626447e+14 3.904003e+14
## 2015(364) 2015(365)
## 3.256125e+14 3.697454e+14Computation and Plot of 10 steps ahead forecast for Turnover with lag (2)n(61)n(75)n(117) and Close with lag (110)
Turnover.open.forecast.3 <- predict(ardl.turnover.open.3, n.ahead = 10)
forecast_start_time <- end(Turnover.ts)[1] + 1
Turnover.open.forecast.ts.3 <- ts(Turnover.open.forecast.3, start = forecast_start_time, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.open.forecast.ts.3, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Turnover")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.open.forecast.ts.3)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 248)
## Frequency = 365
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 3.083939e+14 3.475449e+14 5.471139e+14 4.684545e+14 3.429746e+14 4.684314e+14
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## 9.160187e+14 4.735396e+14 4.347671e+14 4.504672e+14 4.217490e+14 3.492652e+14
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 2.741138e+14 3.646252e+14 4.444103e+14 4.216012e+14 5.241131e+14 5.075960e+14
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 5.327146e+14 5.553482e+14 9.474126e+14 5.623414e+14 6.955905e+14 4.303001e+14
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## 5.547322e+14 4.571885e+14 4.016375e+14 4.705903e+14 3.621531e+14 3.976283e+14
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## 3.550502e+14 4.043182e+14 4.371504e+14 4.091608e+14 4.457240e+14 3.523134e+14
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 4.037839e+14 3.616575e+14 4.672434e+14 4.351924e+14 2.802653e+14 3.137111e+14
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## 3.509756e+14 3.975593e+14 5.543224e+14 4.223796e+14 4.037774e+14 4.184064e+14
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 4.075957e+14 4.308704e+14 3.780648e+14 3.911060e+14 3.624947e+14 4.587968e+14
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## 4.303193e+14 3.164820e+14 3.349105e+14 3.529127e+14 5.128276e+14 4.389284e+14
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 3.488269e+14 3.950708e+14 3.624760e+14 3.941270e+14 4.173253e+14 3.884134e+14
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## 4.485515e+14 3.679068e+14 3.764638e+14 3.308625e+14 3.695638e+14 3.457320e+14
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## 4.982666e+14 4.258072e+14 4.780045e+14 4.710508e+14 9.168485e+14 5.555129e+14
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## 6.003463e+14 4.130915e+14 4.376372e+14 9.638915e+14 4.915918e+14 4.302655e+14
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 3.527688e+14 3.552082e+14 3.671066e+14 3.659607e+14 4.389502e+14 3.633705e+14
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## 3.499238e+14 3.661697e+14 3.504311e+14 3.356298e+14 3.611475e+14 3.690727e+14
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## 3.330709e+14 3.907332e+14 4.259269e+14 3.541493e+14 4.691827e+14 3.214205e+14
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## 3.717533e+14 4.089722e+14 3.382342e+14 4.790594e+14 4.540025e+14 4.295730e+14
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 5.201246e+14 3.938404e+14 5.747718e+14 3.847419e+14 4.203725e+14 3.796680e+14
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## 3.335735e+14 3.162065e+14 3.248470e+14 4.145853e+14 3.957011e+14 4.276572e+14
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## 3.453821e+14 3.297432e+14 3.801631e+14 4.339080e+14 3.052114e+14 3.457735e+14
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## 2.930322e+14 4.055880e+14 3.715575e+14 4.109000e+14 3.944611e+14 4.397778e+14
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 3.737662e+14 3.311458e+14 3.614332e+14 3.814156e+14 4.453209e+14 1.283807e+15
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## 6.534567e+14 7.661852e+14 4.150609e+14 4.040246e+14 4.536640e+14 4.360176e+14
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## 4.807811e+14 3.752662e+14 3.478192e+14 4.196957e+14 3.683328e+14 4.089956e+14
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## 3.896921e+14 4.075523e+14 4.454718e+14 4.276561e+14 3.869366e+14 2.862528e+14
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 3.026959e+14 3.663657e+14 3.090643e+14 3.648590e+14 4.588824e+14 4.953188e+14
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## 5.298868e+14 4.645288e+14 4.909099e+14 3.801481e+14 4.200997e+14 4.576230e+14
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## 4.022920e+14 5.760733e+14 3.698655e+14 3.415171e+14 3.345929e+14 3.967386e+14
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## 3.747755e+14 3.958526e+14 3.602335e+14 3.340958e+14 3.741406e+14 4.253666e+14
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 3.204343e+14 4.083311e+14 3.162859e+14 5.261592e+14 3.798546e+14 3.561148e+14
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## 3.796252e+14 3.640881e+14 3.509658e+14 3.671744e+14 3.962333e+14 5.216580e+14
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## 4.237794e+14 7.472870e+14 5.656820e+14 4.428686e+14 4.051716e+14 4.765233e+14
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 9.619183e+14 5.308652e+14 4.131753e+14 3.882021e+14 3.440975e+14 3.697392e+14
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 3.081242e+14 4.250510e+14 3.723335e+14 4.281314e+14 4.245817e+14 7.556479e+14
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## 5.100271e+14 4.839759e+14 5.205958e+14 4.379170e+14 3.131504e+14 3.262665e+14
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## 4.856832e+14 3.921666e+14 4.037541e+14 4.139813e+14 3.644819e+14 3.586025e+14
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## 3.201529e+14 4.170880e+14 3.921725e+14 6.570054e+14 3.717262e+14 3.815159e+14
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 3.500779e+14 3.720097e+14 3.258364e+14 3.938364e+14 3.543075e+14 4.703184e+14
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## 3.190981e+14 2.910725e+14 3.278027e+14 3.806619e+14 3.432078e+14 3.864848e+14
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## 3.282010e+14 4.322171e+14 3.403185e+14 3.016090e+14 3.127493e+14 3.141802e+14
## 2015(364) 2015(365)
## 3.400957e+14 3.441979e+14Computation and Plot of 10 steps ahead forecast for Turnover with lag (2)n(61)n(75)n(117) and Open with lag (35)n(110)
Turnover.open.forecast.4 <- predict(ardl.turnover.open.4, n.ahead = 10)
forecast_start_time <- end(Turnover.ts)[1] + 1
Turnover.open.forecast.ts.4 <- ts(Turnover.open.forecast.4, start = forecast_start_time, frequency = frequency(Turnover.ts))
ts.plot(Turnover.ts, Turnover.open.forecast.ts.4, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Turnover")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Turnover.open.forecast.ts.4)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 248)
## Frequency = 365
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 3.052734e+14 3.497444e+14 5.511955e+14 4.657055e+14 3.426099e+14 4.666037e+14
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## 9.213501e+14 4.733431e+14 4.368447e+14 4.480973e+14 4.207413e+14 3.453013e+14
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 2.735640e+14 3.652154e+14 4.439557e+14 4.242640e+14 5.246819e+14 5.103209e+14
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 5.309552e+14 5.536280e+14 9.456003e+14 5.645535e+14 6.931615e+14 4.298194e+14
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## 5.554125e+14 4.584705e+14 4.028343e+14 4.671394e+14 3.644429e+14 4.769369e+14
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## 3.534381e+14 4.029285e+14 4.373564e+14 4.089037e+14 4.442410e+14 3.501854e+14
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 4.045129e+14 3.628787e+14 4.667888e+14 4.357720e+14 2.799544e+14 3.139846e+14
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## 3.503396e+14 3.983241e+14 5.543400e+14 4.223341e+14 4.040741e+14 4.199972e+14
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 4.082842e+14 4.311935e+14 3.769178e+14 3.898963e+14 3.608529e+14 4.584394e+14
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## 4.296104e+14 3.140838e+14 3.296599e+14 3.529330e+14 5.133983e+14 4.399205e+14
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 3.502771e+14 3.949395e+14 3.613705e+14 3.951731e+14 4.174301e+14 3.888182e+14
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## 4.500176e+14 3.655352e+14 3.772314e+14 3.296054e+14 3.697348e+14 3.445628e+14
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## 4.961974e+14 4.245917e+14 4.795222e+14 4.713537e+14 9.172015e+14 5.568857e+14
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## 6.011673e+14 4.154528e+14 4.388352e+14 9.639674e+14 4.919191e+14 4.296116e+14
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 3.504167e+14 3.588634e+14 3.664771e+14 3.652370e+14 4.394679e+14 3.648656e+14
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## 3.517526e+14 3.644776e+14 3.512193e+14 3.354741e+14 3.611777e+14 3.674684e+14
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## 3.320956e+14 3.901920e+14 4.270689e+14 3.535436e+14 4.705755e+14 3.210081e+14
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## 3.693560e+14 4.116309e+14 3.348713e+14 4.760203e+14 4.537517e+14 4.285068e+14
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 5.222780e+14 3.957440e+14 5.743916e+14 3.795727e+14 4.270644e+14 3.810152e+14
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## 3.329433e+14 3.166171e+14 3.246740e+14 4.136198e+14 3.945672e+14 4.259316e+14
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## 3.440959e+14 3.298707e+14 3.801068e+14 4.331685e+14 3.056070e+14 3.466446e+14
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## 2.926032e+14 4.040117e+14 3.722590e+14 4.126443e+14 3.948982e+14 4.390305e+14
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 3.743043e+14 3.323854e+14 3.625114e+14 3.814719e+14 4.479584e+14 1.285354e+15
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## 6.521200e+14 7.644452e+14 4.148535e+14 4.042931e+14 4.521954e+14 4.349132e+14
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## 4.795432e+14 3.758557e+14 3.495076e+14 4.206574e+14 3.675575e+14 4.096230e+14
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## 3.892930e+14 4.063221e+14 4.434782e+14 4.280923e+14 3.853277e+14 2.856726e+14
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 3.013383e+14 3.657682e+14 3.113338e+14 3.636206e+14 4.594826e+14 4.953669e+14
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## 5.312685e+14 4.640074e+14 4.916397e+14 3.812267e+14 3.526209e+14 4.576874e+14
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## 4.000692e+14 5.784302e+14 3.711987e+14 3.400576e+14 3.353746e+14 3.885919e+14
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## 3.737789e+14 3.969086e+14 3.574063e+14 3.331272e+14 3.764495e+14 4.269040e+14
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 3.187172e+14 4.051561e+14 3.145085e+14 5.242861e+14 3.857546e+14 3.568858e+14
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## 3.788459e+14 3.660245e+14 3.516764e+14 3.673374e+14 3.957155e+14 5.173793e+14
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## 4.246700e+14 7.456383e+14 5.632958e+14 4.429000e+14 4.041239e+14 4.778004e+14
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 9.601308e+14 5.306174e+14 4.107836e+14 3.907760e+14 3.456698e+14 3.691010e+14
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 3.068867e+14 4.273035e+14 3.724578e+14 4.255649e+14 4.250615e+14 7.529925e+14
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## 5.117695e+14 4.837529e+14 5.230849e+14 4.376166e+14 3.138030e+14 3.224314e+14
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## 4.865171e+14 3.879552e+14 4.051668e+14 4.157264e+14 3.639128e+14 3.574972e+14
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## 3.213908e+14 4.179358e+14 3.928967e+14 6.603604e+14 3.683399e+14 3.783634e+14
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 3.537506e+14 3.739240e+14 3.259215e+14 3.931507e+14 3.521170e+14 4.697975e+14
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## 3.171117e+14 2.913342e+14 3.290748e+14 3.838682e+14 3.434351e+14 3.885816e+14
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## 3.278987e+14 4.330557e+14 3.410997e+14 3.118720e+14 3.142782e+14 3.156899e+14
## 2015(364) 2015(365)
## 3.404182e+14 3.445406e+14Computation and Plot of 10 steps ahead forecast for Volume with lag (1:32) and Close lag (110)
Volume.Close.forecast.1 <- predict(ardl.volume.close.1, n.ahead = 10)
forecast_start_time <- end(Volume.ts)[1] + 1
Volume.Close.forecast.ts.1 <- ts(Volume.Close.forecast.1, start = forecast_start_time, frequency = frequency(Volume.ts))
ts.plot(Volume.ts, Volume.Close.forecast.ts.1, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Volume")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.Close.forecast.ts.1)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117) 2015(118) 2015(119)
## 1994992 2457637 2298166 2573195 2149188 2609977 2652780 2875449
## 2015(120) 2015(121) 2015(122) 2015(123) 2015(124) 2015(125) 2015(126) 2015(127)
## 2928882 2741523 2493924 2605516 2970943 3156726 2716471 2017789
## 2015(128) 2015(129) 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 2364431 2024631 2961938 3051374 2772822 2566865 2668419 2242096
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141) 2015(142) 2015(143)
## 2477745 2605670 2552585 8063245 4695041 2373198 3896998 3194042
## 2015(144) 2015(145) 2015(146) 2015(147) 2015(148) 2015(149) 2015(150) 2015(151)
## 4081485 5461897 4255647 3618670 4209851 2977700 3021281 2669715
## 2015(152) 2015(153) 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 2663439 3893860 3085251 3732704 4085081 2593574 2541105 1917414
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165) 2015(166) 2015(167)
## 3577992 3354666 5272785 5462280 4793086 4333853 3298395 5673696
## 2015(168) 2015(169) 2015(170) 2015(171) 2015(172) 2015(173) 2015(174) 2015(175)
## 4195765 5734370 5443032 4563309 4287539 3001770 3551993 3807175
## 2015(176) 2015(177) 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 3371657 4337684 3245622 3328977 3732761 3808110 2847535 3792346
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189) 2015(190) 2015(191)
## 3552277 4379356 4735457 4091315 4158507 4806219 3687993 4452498
## 2015(192) 2015(193) 2015(194) 2015(195) 2015(196) 2015(197) 2015(198) 2015(199)
## 4812646 3901122 5819742 7617383 5547978 3905064 4893640 4121615
## 2015(200) 2015(201) 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 4883630 5248194 4038551 3424150 3331796 2518833 3347746 2620881
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213) 2015(214) 2015(215)
## 2592350 3784841 2189646 2861794 2577967 2704544 3119001 2635347
## 2015(216) 2015(217) 2015(218) 2015(219) 2015(220) 2015(221) 2015(222) 2015(223)
## 2303283 2902475 3914475 4052924 4421223 3713099 2430633 4399493
## 2015(224) 2015(225) 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 3443604 4325496 4202173 5028381 3634232 2902791 3260849 3633501
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237) 2015(238) 2015(239)
## 2921815 3273011 3179645 2518553 3002345 2342002 2645152 2555586
## 2015(240) 2015(241) 2015(242) 2015(243) 2015(244) 2015(245) 2015(246) 2015(247)
## 2202543 3030884 2633400 2555925 2656138 1983187 2717873 2059380
## 2015(248) 2015(249) 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 2864547 3156567 2572807 2345633 2914705 2762866 1816571 4147167
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261) 2015(262) 2015(263)
## 5040642 3639674 2586489 3299111 2721730 2766800 3348094 2508307
## 2015(264) 2015(265) 2015(266) 2015(267) 2015(268) 2015(269) 2015(270) 2015(271)
## 2359728 2903129 1929201 2600214 2047834 2735397 3261108 2210836
## 2015(272) 2015(273) 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 2480150 2373644 2829942 2286551 1775212 2748923 1770066 2647553
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285) 2015(286) 2015(287)
## 2578688 2240218 2175857 1864270 3019386 1718476 2272523 2273135
## 2015(288) 2015(289) 2015(290) 2015(291) 2015(292) 2015(293) 2015(294) 2015(295)
## 2284738 2188287 1748631 2170225 2053274 1818487 1871547 2135176
## 2015(296) 2015(297) 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 1771392 2219482 2007993 1929956 2196424 1694388 1907722 1907820
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309) 2015(310) 2015(311)
## 1776118 1938542 1962444 1821306 2570834 2263684 1609642 2146330
## 2015(312) 2015(313) 2015(314) 2015(315) 2015(316) 2015(317) 2015(318) 2015(319)
## 2132628 1963827 2486799 2203961 2077798 2271774 1569471 1972678
## 2015(320) 2015(321) 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 2227294 1818028 2577998 2219534 2086387 2659434 4892082 3566430
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333) 2015(334) 2015(335)
## 2325334 2956092 2899666 3504095 3526304 2820279 2222501 2044136
## 2015(336) 2015(337) 2015(338) 2015(339) 2015(340) 2015(341) 2015(342) 2015(343)
## 1896649 2278607 1862108 2006582 2297716 1679841 1917760 2189515
## 2015(344) 2015(345) 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 2235688 2332459 1591579 2079181 2394806 2918016 3827048 2469599
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357) 2015(358) 2015(359)
## 1924078 1647966 3187724 2457207 2792567 2335366 2129153 2183032
## 2015(360) 2015(361) 2015(362) 2015(363) 2015(364) 2015(365)
## 1994992 2457637 2298166 2573195 2149188 2609977Computation and Plot of 10 steps ahead forecast for Volume with lag (1:32) and Close lag (1:110)
Volume.Close.forecast.2 <- predict(ardl.volume.close.2, n.ahead = 10)
forecast_start_time <- end(Volume.ts)[1] + 1
Volume.Close.forecast.ts.2 <- ts(Volume.Close.forecast.2, start = forecast_start_time, frequency = frequency(Volume.ts))
ts.plot(Volume.ts, Volume.Close.forecast.ts.2, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Volume")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.Close.forecast.ts.2)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117)
## 1912063.773 2499281.714 3252154.662 2122389.630 3551780.953 2587263.604
## 2015(118) 2015(119) 2015(120) 2015(121) 2015(122) 2015(123)
## 420676.995 4724265.492 4234223.257 3554583.128 2994853.499 3421436.168
## 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129)
## 4736130.609 3609176.453 2352799.675 2793897.441 2432217.114 2098509.696
## 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 3935279.406 2960330.195 2509168.007 3217567.820 2627478.195 2951698.101
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141)
## 2817103.474 2913778.356 13111129.244 6411075.199 5082967.443 2194986.326
## 2015(142) 2015(143) 2015(144) 2015(145) 2015(146) 2015(147)
## 3760810.127 4103327.222 4282832.754 5716494.549 4239413.755 4616209.108
## 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153)
## 4208190.945 2901286.822 4518277.522 2740789.895 2688483.965 3794274.463
## 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 4727678.037 5593126.322 2782211.382 1691292.182 3403312.136 2877441.356
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165)
## 4214343.390 3690962.065 5889715.225 6956572.017 3776316.732 6421678.847
## 2015(166) 2015(167) 2015(168) 2015(169) 2015(170) 2015(171)
## 3681235.434 5656781.768 4435752.129 5211715.138 3860181.931 5013363.599
## 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177)
## 3931995.880 2600530.710 4278597.664 3228594.638 4504763.205 3943163.445
## 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 2583486.540 2866211.732 5146892.036 2942180.602 4490894.166 3338243.394
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189)
## 4465140.928 5301191.504 4144999.431 3008636.952 530867.115 3457203.624
## 2015(190) 2015(191) 2015(192) 2015(193) 2015(194) 2015(195)
## 4294628.962 3934065.341 3851795.316 5250077.075 12191000.897 8266224.512
## 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201)
## 5391288.855 4665504.737 3788654.537 3383442.633 4345395.154 3759525.810
## 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 3338059.455 1930970.612 2736742.323 2209239.967 2624166.516 2517821.557
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213)
## 2874614.138 2506456.639 1464516.306 2056608.439 1698244.574 2891764.213
## 2015(214) 2015(215) 2015(216) 2015(217) 2015(218) 2015(219)
## 3603935.098 1352176.710 1577014.077 3466792.708 4605386.828 4809847.222
## 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225)
## 4750722.025 3582786.124 2245114.655 4068057.064 4126882.148 4473005.735
## 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 5477211.476 4965480.865 3502421.022 2397349.880 3806042.191 2603830.179
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237)
## 3786437.722 3316424.261 3014721.580 2455954.242 2721845.758 2874989.257
## 2015(238) 2015(239) 2015(240) 2015(241) 2015(242) 2015(243)
## 2724097.765 2394260.238 1925493.884 2739076.013 2822737.037 2433343.187
## 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249)
## 3231792.239 2160248.252 3446459.499 1829585.276 1844830.668 2908929.907
## 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 1900705.795 2447286.806 2243146.340 2146604.599 3110501.319 6825422.651
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261)
## 4039776.049 2865049.522 2792956.663 2639311.947 2170571.839 2656682.902
## 2015(262) 2015(263) 2015(264) 2015(265) 2015(266) 2015(267)
## 4060874.976 3135304.842 2607104.355 3203130.103 2350526.822 2246831.334
## 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273)
## 2454789.904 1902768.568 2818170.114 2147906.375 2378575.906 3594492.211
## 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 3560676.524 -3891471.602 2657093.057 2550936.727 2026863.963 2060075.441
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285)
## 699173.724 2184373.757 2200132.405 1214206.310 1790037.969 1195359.402
## 2015(286) 2015(287) 2015(288) 2015(289) 2015(290) 2015(291)
## 1892186.019 2673745.460 2530556.321 1766990.958 805628.489 608801.087
## 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297)
## 2748110.609 2293192.014 1931068.835 3566826.219 1594285.189 1987075.969
## 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 6385.402 973762.660 2093339.570 250505.780 451689.793 1416469.512
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309)
## 1928141.151 2675496.470 1129739.997 3532194.303 3064926.113 2582263.794
## 2015(310) 2015(311) 2015(312) 2015(313) 2015(314) 2015(315)
## 1330815.088 1005928.342 1716445.790 965060.310 2521355.662 2614221.136
## 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321)
## 2022283.102 875460.388 2846514.054 2095023.808 3428460.666 767046.662
## 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 2249372.038 2695777.607 1447475.929 5159899.039 4848886.681 2776225.240
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333)
## 1149403.967 2829604.687 2474545.306 -350805.779 2795732.943 2554959.966
## 2015(334) 2015(335) 2015(336) 2015(337) 2015(338) 2015(339)
## 976138.003 2004998.140 1783085.526 2244437.721 1818920.702 1311660.640
## 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345)
## 1699177.559 2203778.907 1140181.445 2343533.386 1767527.693 1870533.796
## 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 2023219.856 2060507.377 3636949.097 4596058.028 2859504.558 3100633.677
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357)
## 1985959.567 1774211.155 1607160.166 1999972.933 694989.881 1305698.924
## 2015(358) 2015(359) 2015(360) 2015(361) 2015(362) 2015(363)
## 2563110.297 2047685.302 1912063.773 2499281.714 3252154.662 2122389.630
## 2015(364) 2015(365)
## 3551780.953 2587263.604Computation and Plot of 10 steps ahead forecast for Volume with lag (1:32)n(91:122) and Close lag (110)
Volume.Close.forecast.3 <- predict(ardl.volume.close.3, n.ahead = 10)
forecast_start_time <- end(Volume.ts)[1] + 1
Volume.Close.forecast.ts.3 <- ts(Volume.Close.forecast.3, start = forecast_start_time, frequency = frequency(Volume.ts))
ts.plot(Volume.ts, Volume.Close.forecast.ts.3, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Volume")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.Close.forecast.ts.3)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 243)
## Frequency = 365
## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129) 2015(130)
## 3968635.8 5703498.3 2376786.5 2403605.3 2948639.6 2425389.5 1594387.1 2783332.9
## 2015(131) 2015(132) 2015(133) 2015(134) 2015(135) 2015(136) 2015(137) 2015(138)
## 3398401.4 3342289.0 3006934.2 2949834.9 3024290.6 2870849.0 3207191.2 3309724.8
## 2015(139) 2015(140) 2015(141) 2015(142) 2015(143) 2015(144) 2015(145) 2015(146)
## 8263316.5 5207646.7 2546113.1 3724938.9 3614248.3 4403769.5 5620606.3 4409449.4
## 2015(147) 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153) 2015(154)
## 4267306.4 4546899.2 2824306.1 3974193.3 2601531.0 3083577.6 3940657.6 3367020.0
## 2015(155) 2015(156) 2015(157) 2015(158) 2015(159) 2015(160) 2015(161) 2015(162)
## 3832846.7 3914452.3 3066298.8 2724452.3 2527933.6 3803190.6 3700081.8 5118041.1
## 2015(163) 2015(164) 2015(165) 2015(166) 2015(167) 2015(168) 2015(169) 2015(170)
## 5854603.9 5243285.7 4965316.4 3560692.3 5045018.9 4340095.6 5420260.4 5514500.1
## 2015(171) 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177) 2015(178)
## 4499105.5 4217909.9 2349313.3 2927421.5 3356569.8 4433651.1 3910921.3 3038501.3
## 2015(179) 2015(180) 2015(181) 2015(182) 2015(183) 2015(184) 2015(185) 2015(186)
## 3259693.4 3894872.2 3947783.9 3141738.5 3827965.4 3917164.1 4170361.2 4130435.3
## 2015(187) 2015(188) 2015(189) 2015(190) 2015(191) 2015(192) 2015(193) 2015(194)
## 4290231.7 3172963.1 4713945.8 4671175.2 3648221.7 4009798.0 4277929.7 8331800.2
## 2015(195) 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201) 2015(202)
## 7339045.2 4781257.9 3850135.2 4445860.4 3796687.7 5012442.2 5189263.3 4085518.7
## 2015(203) 2015(204) 2015(205) 2015(206) 2015(207) 2015(208) 2015(209) 2015(210)
## 3435890.9 3301789.0 2552101.4 3792481.5 2232479.0 2501918.0 3610165.6 2429881.9
## 2015(211) 2015(212) 2015(213) 2015(214) 2015(215) 2015(216) 2015(217) 2015(218)
## 2444083.6 2749958.4 2959083.0 3381294.0 2524742.6 2490166.5 3555562.0 4815587.8
## 2015(219) 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225) 2015(226)
## 3788428.2 4360925.5 4459971.3 2688641.7 4003313.1 4077292.7 4132405.4 4532059.0
## 2015(227) 2015(228) 2015(229) 2015(230) 2015(231) 2015(232) 2015(233) 2015(234)
## 4946906.4 3765351.5 1989643.3 3529425.3 3636751.3 3057076.1 2429246.8 2774018.2
## 2015(235) 2015(236) 2015(237) 2015(238) 2015(239) 2015(240) 2015(241) 2015(242)
## 1664150.9 1766777.0 3549598.8 1431947.2 2732397.1 2330232.9 2337720.1 2427339.8
## 2015(243) 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249) 2015(250)
## 2352995.2 1864877.3 2163505.6 2362227.4 2126257.1 3019145.0 1375112.3 2304665.1
## 2015(251) 2015(252) 2015(253) 2015(254) 2015(255) 2015(256) 2015(257) 2015(258)
## 3107666.6 1455567.4 698323.3 2257232.8 8152802.6 3586870.7 2054670.9 2310496.9
## 2015(259) 2015(260) 2015(261) 2015(262) 2015(263) 2015(264) 2015(265) 2015(266)
## 1831866.2 1708884.4 2062083.3 3133495.4 2100513.9 2495945.5 2426848.2 1422381.2
## 2015(267) 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273) 2015(274)
## 2831407.7 1731855.1 1821672.6 3168255.7 1915604.2 2281377.4 945564.4 2113708.7
## 2015(275) 2015(276) 2015(277) 2015(278) 2015(279) 2015(280) 2015(281) 2015(282)
## 2028824.1 972048.9 1973433.6 2262911.3 2420796.7 2062289.8 2431572.6 2150673.6
## 2015(283) 2015(284) 2015(285) 2015(286) 2015(287) 2015(288) 2015(289) 2015(290)
## 1062764.5 1863530.4 1168776.8 1978508.7 2193375.6 1470244.5 1419251.1 706434.0
## 2015(291) 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297) 2015(298)
## 1054769.5 1526999.1 2398976.5 1108491.8 1683645.9 1967625.9 2539258.9 1447221.2
## 2015(299) 2015(300) 2015(301) 2015(302) 2015(303) 2015(304) 2015(305) 2015(306)
## 1978014.9 1944390.4 2834862.8 1079820.8 1220435.3 2224380.0 1033915.1 1514388.6
## 2015(307) 2015(308) 2015(309) 2015(310) 2015(311) 2015(312) 2015(313) 2015(314)
## 2955765.4 1940923.8 1351759.3 2310369.6 4846883.9 1951520.9 1369598.5 2699907.8
## 2015(315) 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321) 2015(322)
## 1579743.0 1561267.4 2036847.5 2299664.1 1735467.9 2306827.2 1840890.9 2698756.5
## 2015(323) 2015(324) 2015(325) 2015(326) 2015(327) 2015(328) 2015(329) 2015(330)
## 2561978.7 1565112.0 3245359.6 5055206.6 3909953.7 1376718.9 2981801.7 3388906.9
## 2015(331) 2015(332) 2015(333) 2015(334) 2015(335) 2015(336) 2015(337) 2015(338)
## 3612036.4 2618933.3 3069584.7 2710839.0 1867995.2 2192483.0 2415720.2 1359316.6
## 2015(339) 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345) 2015(346)
## 2463860.6 2042361.6 1706502.6 2175694.2 3452935.2 2009400.7 1972418.8 1763115.1
## 2015(347) 2015(348) 2015(349) 2015(350) 2015(351) 2015(352) 2015(353) 2015(354)
## 3004041.0 1638858.4 3172892.2 3970008.7 2460697.1 1939097.0 1598985.9 3574430.0
## 2015(355) 2015(356) 2015(357) 2015(358) 2015(359) 2015(360) 2015(361) 2015(362)
## 3141217.1 2984408.2 3253807.0 2758387.3 2309903.7 2520866.5 2286902.0 2783683.2
## 2015(363) 2015(364) 2015(365)
## 2234192.1 2299501.6 3464905.4Computation and Plot of 10 steps ahead forecast for Volume with lag (1:32)n(91:122) and Close lag (1:110)
Volume.Close.forecast.4 <- predict(ardl.volume.close.4, n.ahead = 10)
forecast_start_time <- end(Volume.ts)[1] + 1
Volume.Close.forecast.ts.4 <- ts(Volume.Close.forecast.4, start = forecast_start_time, frequency = frequency(Volume.ts))
ts.plot(Volume.ts, Volume.Close.forecast.ts.4, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Volume")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.Close.forecast.ts.4)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 243)
## Frequency = 365
## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128)
## 2952175.90 5027214.29 2569285.67 2061319.89 2695701.70 2603725.16
## 2015(129) 2015(130) 2015(131) 2015(132) 2015(133) 2015(134)
## 2431804.86 4178376.88 3228708.26 2969411.84 3788839.08 2624603.13
## 2015(135) 2015(136) 2015(137) 2015(138) 2015(139) 2015(140)
## 2948661.41 2813787.05 2354234.34 14589626.81 6105660.97 5228664.83
## 2015(141) 2015(142) 2015(143) 2015(144) 2015(145) 2015(146)
## 2050217.16 3988561.07 3626334.58 4595217.70 5376960.71 4371675.68
## 2015(147) 2015(148) 2015(149) 2015(150) 2015(151) 2015(152)
## 3948517.03 4007658.26 2489464.24 4677373.23 2054610.15 2459456.53
## 2015(153) 2015(154) 2015(155) 2015(156) 2015(157) 2015(158)
## 3306065.59 4665665.90 5142800.66 3120934.06 1542705.29 3928324.45
## 2015(159) 2015(160) 2015(161) 2015(162) 2015(163) 2015(164)
## 3303915.44 4354288.49 4584279.85 6045573.77 7095385.45 4606785.68
## 2015(165) 2015(166) 2015(167) 2015(168) 2015(169) 2015(170)
## 6510335.11 3800374.93 5167434.94 4887667.00 5241427.49 4360989.08
## 2015(171) 2015(172) 2015(173) 2015(174) 2015(175) 2015(176)
## 4489845.94 3266803.00 2515216.11 4912979.25 3111422.45 3611155.05
## 2015(177) 2015(178) 2015(179) 2015(180) 2015(181) 2015(182)
## 3260726.30 2240435.38 2729717.01 5474738.46 3240382.34 4887942.36
## 2015(183) 2015(184) 2015(185) 2015(186) 2015(187) 2015(188)
## 2980944.86 5243967.21 5190890.81 4573590.72 3842582.48 1197536.32
## 2015(189) 2015(190) 2015(191) 2015(192) 2015(193) 2015(194)
## 4360674.17 4198434.11 3852129.18 4220547.52 5306336.81 13547944.85
## 2015(195) 2015(196) 2015(197) 2015(198) 2015(199) 2015(200)
## 7378986.23 4922759.87 4570184.78 3518176.74 3559540.62 4591618.17
## 2015(201) 2015(202) 2015(203) 2015(204) 2015(205) 2015(206)
## 4298164.25 3806583.79 2424807.41 2508134.78 2286012.44 3244193.02
## 2015(207) 2015(208) 2015(209) 2015(210) 2015(211) 2015(212)
## 2533765.64 2505837.19 2618659.49 1624760.89 1644869.17 724273.22
## 2015(213) 2015(214) 2015(215) 2015(216) 2015(217) 2015(218)
## 3352762.34 3068183.41 1281802.84 1037812.49 3099432.48 4739076.67
## 2015(219) 2015(220) 2015(221) 2015(222) 2015(223) 2015(224)
## 4267552.02 5219743.57 3687771.04 2596618.54 2381476.87 4380789.00
## 2015(225) 2015(226) 2015(227) 2015(228) 2015(229) 2015(230)
## 3706044.66 6066507.33 5399426.22 4511006.46 3781994.02 3785157.61
## 2015(231) 2015(232) 2015(233) 2015(234) 2015(235) 2015(236)
## 3501482.92 2265145.97 3399725.40 2623439.05 1464991.73 1585517.35
## 2015(237) 2015(238) 2015(239) 2015(240) 2015(241) 2015(242)
## 3295186.65 677438.82 1525135.14 3001798.66 1224132.19 2629571.19
## 2015(243) 2015(244) 2015(245) 2015(246) 2015(247) 2015(248)
## 2830341.36 2268743.45 2601634.88 2177138.32 1315573.96 3279533.72
## 2015(249) 2015(250) 2015(251) 2015(252) 2015(253) 2015(254)
## 2110890.19 1714689.83 2699749.64 1423293.16 977644.99 3699820.76
## 2015(255) 2015(256) 2015(257) 2015(258) 2015(259) 2015(260)
## 10353001.18 2778303.20 2123405.33 1653518.70 2395375.82 2058398.20
## 2015(261) 2015(262) 2015(263) 2015(264) 2015(265) 2015(266)
## 3106232.76 3052961.32 2975548.82 3073668.47 3290282.46 2552427.27
## 2015(267) 2015(268) 2015(269) 2015(270) 2015(271) 2015(272)
## 2588230.84 3108192.31 1930232.77 3683498.07 1920763.04 2224023.96
## 2015(273) 2015(274) 2015(275) 2015(276) 2015(277) 2015(278)
## 3662616.59 2443658.64 -2585799.41 2191649.73 2430592.36 1761700.95
## 2015(279) 2015(280) 2015(281) 2015(282) 2015(283) 2015(284)
## 2448750.32 -88357.02 2759285.56 1760537.02 2067807.03 1095727.16
## 2015(285) 2015(286) 2015(287) 2015(288) 2015(289) 2015(290)
## 1183501.94 1855882.56 2697305.63 2192041.45 1374414.74 812113.83
## 2015(291) 2015(292) 2015(293) 2015(294) 2015(295) 2015(296)
## 254764.67 1924469.11 2135967.90 1804789.46 3907447.86 1895436.81
## 2015(297) 2015(298) 2015(299) 2015(300) 2015(301) 2015(302)
## 1943692.43 676224.94 998681.98 2067202.59 722134.03 763572.12
## 2015(303) 2015(304) 2015(305) 2015(306) 2015(307) 2015(308)
## 1769461.59 1719396.91 2887507.08 1268746.02 4365848.68 3028222.68
## 2015(309) 2015(310) 2015(311) 2015(312) 2015(313) 2015(314)
## 2353509.94 1232780.97 1517642.10 1069730.38 -137573.35 2398786.91
## 2015(315) 2015(316) 2015(317) 2015(318) 2015(319) 2015(320)
## 1873566.81 1670416.40 496757.29 3017259.04 2647425.58 2636620.54
## 2015(321) 2015(322) 2015(323) 2015(324) 2015(325) 2015(326)
## 1738624.87 2103173.92 3177654.80 2122573.70 5773901.45 5833228.97
## 2015(327) 2015(328) 2015(329) 2015(330) 2015(331) 2015(332)
## 2763886.66 1458356.03 2877059.53 2697121.65 816539.08 2177419.41
## 2015(333) 2015(334) 2015(335) 2015(336) 2015(337) 2015(338)
## 1869609.19 1066284.41 1906189.24 2280993.88 2555063.28 2424332.54
## 2015(339) 2015(340) 2015(341) 2015(342) 2015(343) 2015(344)
## 1512514.87 2694846.07 1962670.05 1154809.08 2873412.95 1891846.87
## 2015(345) 2015(346) 2015(347) 2015(348) 2015(349) 2015(350)
## 1377648.05 2014985.23 2460452.64 3081201.17 4092980.42 2994542.47
## 2015(351) 2015(352) 2015(353) 2015(354) 2015(355) 2015(356)
## 1814382.35 2202806.93 1171283.21 1155312.25 2472069.34 -55872.57
## 2015(357) 2015(358) 2015(359) 2015(360) 2015(361) 2015(362)
## 2344243.16 2878704.04 2342698.39 2699071.31 2196467.92 3278785.47
## 2015(363) 2015(364) 2015(365)
## 1268452.16 2529815.59 3425681.04Computation and Plot of 10 steps ahead forecast for Volume with lag (1:32) and Open lag (110)
Volume.open.forecast.1 <- predict(ardl.volume.open.1, n.ahead = 10)
forecast_start_time <- end(Volume.ts)[1] + 1
Volume.open.forecast.ts.1 <- ts(Volume.open.forecast.1, start = forecast_start_time, frequency = frequency(Volume.ts))
ts.plot(Volume.ts, Volume.open.forecast.ts.1, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Volume")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.open.forecast.ts.1)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117) 2015(118) 2015(119)
## 2002594 2442619 2303508 2583932 2139049 2634302 2617877 2871069
## 2015(120) 2015(121) 2015(122) 2015(123) 2015(124) 2015(125) 2015(126) 2015(127)
## 2939799 2727932 2488495 2616460 2982951 3160216 2708017 2011351
## 2015(128) 2015(129) 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 2341959 2048535 2975390 3050091 2783392 2563201 2676453 2246945
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141) 2015(142) 2015(143)
## 2464957 2613733 2542231 8054520 4699881 2363079 3897000 3185036
## 2015(144) 2015(145) 2015(146) 2015(147) 2015(148) 2015(149) 2015(150) 2015(151)
## 4078311 5462295 4251230 3614160 4231110 2974342 3035704 2673866
## 2015(152) 2015(153) 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 2650870 3897023 3080569 3736671 4098250 2610834 2533740 1922910
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165) 2015(166) 2015(167)
## 3570920 3366923 5258286 5459704 4801182 4338238 3234790 5678651
## 2015(168) 2015(169) 2015(170) 2015(171) 2015(172) 2015(173) 2015(174) 2015(175)
## 4197454 5734038 5460465 4547650 4279560 3002886 3563427 3808821
## 2015(176) 2015(177) 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 3374641 4333655 3244543 3319685 3730163 3809734 2851197 3785597
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189) 2015(190) 2015(191)
## 3564669 4382693 4738594 4075988 4197783 4803738 3681332 4444026
## 2015(192) 2015(193) 2015(194) 2015(195) 2015(196) 2015(197) 2015(198) 2015(199)
## 4817766 3863551 5829207 7640031 5529012 3896781 4876632 4123971
## 2015(200) 2015(201) 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 4880576 5273322 4025181 3413319 3327995 2523242 3359020 2608413
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213) 2015(214) 2015(215)
## 2595223 3782792 2200496 2852702 2569416 2686383 3127287 2628839
## 2015(216) 2015(217) 2015(218) 2015(219) 2015(220) 2015(221) 2015(222) 2015(223)
## 2298149 2902058 3920374 4055918 4394406 3709388 2606718 4391714
## 2015(224) 2015(225) 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 3438368 4323875 4196407 5034046 3616482 2904101 3267597 3642540
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237) 2015(238) 2015(239)
## 2920495 3274863 3178384 2513868 3017084 2350581 2646443 2555774
## 2015(240) 2015(241) 2015(242) 2015(243) 2015(244) 2015(245) 2015(246) 2015(247)
## 2213942 3029894 2641773 2558372 2661185 1968641 2719209 2048354
## 2015(248) 2015(249) 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 2877693 3123205 2577262 2345037 2908081 2769516 1796632 4147501
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261) 2015(262) 2015(263)
## 5042372 3639162 2579585 3309816 2699240 2773764 3350408 2506544
## 2015(264) 2015(265) 2015(266) 2015(267) 2015(268) 2015(269) 2015(270) 2015(271)
## 2358209 2905924 1929618 2603576 2046309 2734348 3255183 2218109
## 2015(272) 2015(273) 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 2482639 2380973 2832125 2290703 1774320 2747980 1785611 2652630
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285) 2015(286) 2015(287)
## 2572427 2238890 2175729 1845225 3023774 1718639 2275010 2270974
## 2015(288) 2015(289) 2015(290) 2015(291) 2015(292) 2015(293) 2015(294) 2015(295)
## 2288243 2190074 1748142 2176777 2049646 1823416 1871713 2118248
## 2015(296) 2015(297) 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 1783865 2217237 1997391 1932562 2190253 1699813 1916830 1917132
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309) 2015(310) 2015(311)
## 1745506 1973564 1972574 1819536 2573824 2266794 1607148 2144578
## 2015(312) 2015(313) 2015(314) 2015(315) 2015(316) 2015(317) 2015(318) 2015(319)
## 2132145 1959933 2494320 2208092 2071995 2282048 1577671 1976506
## 2015(320) 2015(321) 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 2223531 1822026 2589499 2222459 2078888 2670575 4903087 3565908
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333) 2015(334) 2015(335)
## 2324180 2964511 2903359 3501509 3540924 2817664 2225886 2044143
## 2015(336) 2015(337) 2015(338) 2015(339) 2015(340) 2015(341) 2015(342) 2015(343)
## 1907921 2278758 1860425 2018337 2298800 1677516 1917432 2197950
## 2015(344) 2015(345) 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 2241344 2328506 1595258 2077501 2396288 2914107 3823031 2480243
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357) 2015(358) 2015(359)
## 1910477 1623164 3187808 2465935 2793767 2323819 2133924 2007182
## 2015(360) 2015(361) 2015(362) 2015(363) 2015(364) 2015(365)
## 2002594 2442619 2303508 2583932 2139049 2634302Computation and Plot of 10 steps ahead forecast for Volume with lag (1:32) and Open lag (1:110)
Volume.open.forecast.2 <- predict(ardl.volume.open.2, n.ahead = 10)
forecast_start_time <- end(Volume.ts)[1] + 1
Volume.open.forecast.ts.2 <- ts(Volume.open.forecast.2, start = forecast_start_time, frequency = frequency(Volume.ts))
ts.plot(Volume.ts, Volume.open.forecast.ts.2, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Volume")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.open.forecast.ts.2)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 254)
## Frequency = 365
## 2015(112) 2015(113) 2015(114) 2015(115) 2015(116) 2015(117) 2015(118) 2015(119)
## 2054172 2639728 2331332 2620081 2145456 2650603 2539472 2906786
## 2015(120) 2015(121) 2015(122) 2015(123) 2015(124) 2015(125) 2015(126) 2015(127)
## 3004928 2660789 2472216 2523678 3071728 3115897 2724541 1941983
## 2015(128) 2015(129) 2015(130) 2015(131) 2015(132) 2015(133) 2015(134) 2015(135)
## 2283887 1970416 3026035 3031287 2755735 2569290 2715919 2323144
## 2015(136) 2015(137) 2015(138) 2015(139) 2015(140) 2015(141) 2015(142) 2015(143)
## 2400364 2602392 2488901 8034690 4655085 2357789 3818517 3226654
## 2015(144) 2015(145) 2015(146) 2015(147) 2015(148) 2015(149) 2015(150) 2015(151)
## 4092804 5476447 4371882 4553258 4319301 3062915 3012895 2668694
## 2015(152) 2015(153) 2015(154) 2015(155) 2015(156) 2015(157) 2015(158) 2015(159)
## 2564902 3933353 3089609 3701208 4113694 2617697 2582724 1931378
## 2015(160) 2015(161) 2015(162) 2015(163) 2015(164) 2015(165) 2015(166) 2015(167)
## 3555581 3374740 5240770 5354475 4813048 4350896 3193187 5910609
## 2015(168) 2015(169) 2015(170) 2015(171) 2015(172) 2015(173) 2015(174) 2015(175)
## 4125155 5669757 5395427 4455340 4223249 2917153 3403609 3863920
## 2015(176) 2015(177) 2015(178) 2015(179) 2015(180) 2015(181) 2015(182) 2015(183)
## 3355777 4338824 3209652 3325239 3730214 3862409 2873456 3770446
## 2015(184) 2015(185) 2015(186) 2015(187) 2015(188) 2015(189) 2015(190) 2015(191)
## 3590573 4284449 4735232 4070928 4145515 4699616 3713243 4403007
## 2015(192) 2015(193) 2015(194) 2015(195) 2015(196) 2015(197) 2015(198) 2015(199)
## 4894414 3760446 5824349 7672561 5501348 3879292 4893099 4103796
## 2015(200) 2015(201) 2015(202) 2015(203) 2015(204) 2015(205) 2015(206) 2015(207)
## 4891573 5272142 3939461 3156705 3347553 2598890 3351890 2630958
## 2015(208) 2015(209) 2015(210) 2015(211) 2015(212) 2015(213) 2015(214) 2015(215)
## 2621105 3779915 2247104 2861192 2600143 2773045 3134687 2632440
## 2015(216) 2015(217) 2015(218) 2015(219) 2015(220) 2015(221) 2015(222) 2015(223)
## 2348427 2879608 3933628 4062509 4429383 3776015 2561404 4490218
## 2015(224) 2015(225) 2015(226) 2015(227) 2015(228) 2015(229) 2015(230) 2015(231)
## 3531087 4293663 4222861 5049506 3537460 2823845 3388023 3662848
## 2015(232) 2015(233) 2015(234) 2015(235) 2015(236) 2015(237) 2015(238) 2015(239)
## 2928857 3222412 3222801 2320066 3057424 2358525 2613794 2526741
## 2015(240) 2015(241) 2015(242) 2015(243) 2015(244) 2015(245) 2015(246) 2015(247)
## 2246556 3000205 2658475 2584109 2622102 1981872 2745870 2066640
## 2015(248) 2015(249) 2015(250) 2015(251) 2015(252) 2015(253) 2015(254) 2015(255)
## 2935677 3048840 2634476 2375392 2943893 2866578 1788113 4285189
## 2015(256) 2015(257) 2015(258) 2015(259) 2015(260) 2015(261) 2015(262) 2015(263)
## 4997858 3545223 2682350 3309928 2623572 2786011 3376365 2520375
## 2015(264) 2015(265) 2015(266) 2015(267) 2015(268) 2015(269) 2015(270) 2015(271)
## 2111629 3001346 2013460 2587747 2042604 2766962 3268674 2276295
## 2015(272) 2015(273) 2015(274) 2015(275) 2015(276) 2015(277) 2015(278) 2015(279)
## 2415473 2352447 2879229 2238438 1813144 2695517 1727281 2666162
## 2015(280) 2015(281) 2015(282) 2015(283) 2015(284) 2015(285) 2015(286) 2015(287)
## 2606996 2279584 2120904 1873925 1907359 1691618 2229144 2340425
## 2015(288) 2015(289) 2015(290) 2015(291) 2015(292) 2015(293) 2015(294) 2015(295)
## 2332834 2176103 1724515 1993987 2051239 1868747 1825160 2125389
## 2015(296) 2015(297) 2015(298) 2015(299) 2015(300) 2015(301) 2015(302) 2015(303)
## 1840213 2257988 2002737 1865365 2162937 1691604 2052486 1915626
## 2015(304) 2015(305) 2015(306) 2015(307) 2015(308) 2015(309) 2015(310) 2015(311)
## 1723184 2019984 1994975 1820426 2549945 2198398 1638351 2072717
## 2015(312) 2015(313) 2015(314) 2015(315) 2015(316) 2015(317) 2015(318) 2015(319)
## 2082865 1972102 2482072 2254989 1979484 2285323 1566325 1999074
## 2015(320) 2015(321) 2015(322) 2015(323) 2015(324) 2015(325) 2015(326) 2015(327)
## 2260599 1807177 2560741 2277392 2056812 2633190 4950252 3527479
## 2015(328) 2015(329) 2015(330) 2015(331) 2015(332) 2015(333) 2015(334) 2015(335)
## 2365900 2957510 2929111 3531319 3568420 2758117 1978174 1965051
## 2015(336) 2015(337) 2015(338) 2015(339) 2015(340) 2015(341) 2015(342) 2015(343)
## 2033595 2311253 1804953 1984941 2371190 1738685 1946294 2297010
## 2015(344) 2015(345) 2015(346) 2015(347) 2015(348) 2015(349) 2015(350) 2015(351)
## 2241321 2264858 1667142 2110193 2393451 2907809 3756500 2526619
## 2015(352) 2015(353) 2015(354) 2015(355) 2015(356) 2015(357) 2015(358) 2015(359)
## 1848881 1583648 3366250 2572108 2792501 2353583 2067529 2028551
## 2015(360) 2015(361) 2015(362) 2015(363) 2015(364) 2015(365)
## 2054172 2639728 2331332 2620081 2145456 2650603Computation and Plot of 10 steps ahead forecast for Volume with lag (1:32)n(91:122) and Open lag (110)
Volume.open.forecast.3 <- predict(ardl.volume.open.3, n.ahead = 10)
forecast_start_time <- end(Volume.ts)[1] + 1
Volume.open.forecast.ts.3 <- ts(Volume.open.forecast.3, start = forecast_start_time, frequency = frequency(Volume.ts))
ts.plot(Volume.ts, Volume.open.forecast.ts.3, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Volume")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.open.forecast.ts.3)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 243)
## Frequency = 365
## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129) 2015(130)
## 3992428.9 5709725.5 2381194.8 2404348.3 2948087.7 2389716.1 1624118.8 2795122.9
## 2015(131) 2015(132) 2015(133) 2015(134) 2015(135) 2015(136) 2015(137) 2015(138)
## 3390025.4 3352731.0 2995435.8 2960545.1 3030967.7 2859752.6 3215877.5 3303243.8
## 2015(139) 2015(140) 2015(141) 2015(142) 2015(143) 2015(144) 2015(145) 2015(146)
## 8258305.5 5204895.3 2535872.7 3727712.2 3606139.3 4403099.2 5613502.2 4405288.4
## 2015(147) 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153) 2015(154)
## 4268760.9 4562085.4 2821223.7 3987203.0 2606177.5 3074654.0 3941715.9 3362426.1
## 2015(155) 2015(156) 2015(157) 2015(158) 2015(159) 2015(160) 2015(161) 2015(162)
## 3831271.9 3924717.5 3079564.8 2718239.3 2530218.4 3804251.0 3709632.6 5102301.7
## 2015(163) 2015(164) 2015(165) 2015(166) 2015(167) 2015(168) 2015(169) 2015(170)
## 5855541.5 5245239.9 4978011.9 3504766.4 5053289.5 4339535.8 5414718.8 5536392.0
## 2015(171) 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177) 2015(178)
## 4486090.4 4210330.0 2348035.0 2936441.3 3354931.3 4435461.5 3900524.6 3044591.8
## 2015(179) 2015(180) 2015(181) 2015(182) 2015(183) 2015(184) 2015(185) 2015(186)
## 3250296.9 3886480.2 3957493.0 3147662.8 3816677.9 3937981.1 4169263.9 4132039.5
## 2015(187) 2015(188) 2015(189) 2015(190) 2015(191) 2015(192) 2015(193) 2015(194)
## 4260138.8 3212968.0 4715743.9 4660122.3 3643704.2 4016135.7 4246598.9 8334112.6
## 2015(195) 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201) 2015(202)
## 7363997.8 4769238.8 3851033.8 4426100.1 3801380.5 5008351.7 5215444.3 4081988.4
## 2015(203) 2015(204) 2015(205) 2015(206) 2015(207) 2015(208) 2015(209) 2015(210)
## 3424248.2 3301310.2 2559779.7 3803272.0 2216888.0 2511325.8 3604135.0 2442235.6
## 2015(211) 2015(212) 2015(213) 2015(214) 2015(215) 2015(216) 2015(217) 2015(218)
## 2434455.3 2745072.9 2937455.3 3389402.4 2521744.2 2484211.1 3557803.7 4823023.7
## 2015(219) 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225) 2015(226)
## 3799277.2 4332146.5 4465041.6 2807191.6 4002679.9 4069616.9 4137996.0 4522641.8
## 2015(227) 2015(228) 2015(229) 2015(230) 2015(231) 2015(232) 2015(233) 2015(234)
## 4956782.1 3743161.8 1990841.9 3526752.6 3643564.5 3052644.2 2438404.2 2775227.2
## 2015(235) 2015(236) 2015(237) 2015(238) 2015(239) 2015(240) 2015(241) 2015(242)
## 1650991.4 1780997.5 3547719.9 1424557.4 2737763.3 2330710.8 2332451.2 2454272.9
## 2015(243) 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249) 2015(250)
## 2352536.8 1869992.4 2161183.6 2358141.4 2114614.2 3033929.6 1341636.9 2307743.3
## 2015(251) 2015(252) 2015(253) 2015(254) 2015(255) 2015(256) 2015(257) 2015(258)
## 3100648.4 1454429.9 691058.9 2261040.1 8139586.5 3579203.9 2064138.0 2312034.5
## 2015(259) 2015(260) 2015(261) 2015(262) 2015(263) 2015(264) 2015(265) 2015(266)
## 1845057.1 1683310.7 2066146.4 3132251.2 2097144.7 2499537.0 2425377.1 1427030.2
## 2015(267) 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273) 2015(274)
## 2836459.7 1730405.8 1830583.6 3159539.5 1920546.2 2276225.1 949940.1 2112385.0
## 2015(275) 2015(276) 2015(277) 2015(278) 2015(279) 2015(280) 2015(281) 2015(282)
## 2031379.3 964066.4 1969481.0 2273145.9 2428098.0 2054364.4 2433123.7 2150716.8
## 2015(283) 2015(284) 2015(285) 2015(286) 2015(287) 2015(288) 2015(289) 2015(290)
## 1052876.9 1871544.0 1169038.6 1977013.5 2188671.2 1475520.3 1428697.1 699805.9
## 2015(291) 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297) 2015(298)
## 1064331.8 1517071.1 2397258.5 1104993.3 1670446.1 1981821.3 2530805.4 1451964.3
## 2015(299) 2015(300) 2015(301) 2015(302) 2015(303) 2015(304) 2015(305) 2015(306)
## 1978898.0 1937446.5 2846778.9 1081794.1 1232448.5 2185448.6 1059341.7 1523568.2
## 2015(307) 2015(308) 2015(309) 2015(310) 2015(311) 2015(312) 2015(313) 2015(314)
## 2949249.5 1945780.7 1348648.8 2318635.8 4839369.4 1945801.4 1375145.7 2716820.9
## 2015(315) 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321) 2015(322)
## 1580457.5 1552906.8 2046976.6 2302352.1 1737069.8 2304350.5 1846731.5 2709449.8
## 2015(323) 2015(324) 2015(325) 2015(326) 2015(327) 2015(328) 2015(329) 2015(330)
## 2562256.6 1554987.5 3256769.0 5063799.5 3903159.7 1368994.0 2987132.3 3399022.9
## 2015(331) 2015(332) 2015(333) 2015(334) 2015(335) 2015(336) 2015(337) 2015(338)
## 3603389.2 2625901.5 3075546.3 2707428.5 1866850.1 2202662.7 2411736.8 1353872.8
## 2015(339) 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345) 2015(346)
## 2475402.6 2042375.4 1700339.2 2181310.6 3456455.7 2015793.5 1967556.4 1776572.9
## 2015(347) 2015(348) 2015(349) 2015(350) 2015(351) 2015(352) 2015(353) 2015(354)
## 2993770.6 1638744.2 3178375.9 3965304.8 2466385.9 1932879.7 1574995.9 3576042.1
## 2015(355) 2015(356) 2015(357) 2015(358) 2015(359) 2015(360) 2015(361) 2015(362)
## 3143488.9 2991736.1 3237882.8 2763479.6 2202661.8 2528740.3 2268930.7 2792843.0
## 2015(363) 2015(364) 2015(365)
## 2237084.7 2290776.4 3486417.5Computation and Plot of 10 steps ahead forecast for Volume with lag (1:32)n(91:122) and Open lag (35)n(110)
Volume.open.forecast.4 <- predict(ardl.volume.open.4, n.ahead = 10)
forecast_start_time <- end(Volume.ts)[1] + 1
Volume.open.forecast.ts.4 <- ts(Volume.open.forecast.4, start = forecast_start_time, frequency = frequency(Volume.ts))
ts.plot(Volume.ts, Volume.open.forecast.ts.4, col = c("black", "red"), lty = c(1, 2),
xlab = "Time", ylab = "Volume")
legend("topleft", legend = c("Actual", "Forecast"), col = c("black", "red"), lty = c(1, 2))
print(Volume.open.forecast.ts.4)## Time Series:
## Start = c(2016, 1)
## End = c(2016, 243)
## Frequency = 365
## 2015(123) 2015(124) 2015(125) 2015(126) 2015(127) 2015(128) 2015(129) 2015(130)
## 3992753.8 5709610.8 2381343.9 2404180.1 2948450.8 2389893.2 1624257.0 2795027.8
## 2015(131) 2015(132) 2015(133) 2015(134) 2015(135) 2015(136) 2015(137) 2015(138)
## 3390147.7 3352948.7 2995505.2 2960537.9 3030853.4 2860001.4 3215938.2 3303511.5
## 2015(139) 2015(140) 2015(141) 2015(142) 2015(143) 2015(144) 2015(145) 2015(146)
## 8258296.1 5205134.0 2535965.6 3727886.6 3606129.0 4403070.5 5613521.1 4404955.2
## 2015(147) 2015(148) 2015(149) 2015(150) 2015(151) 2015(152) 2015(153) 2015(154)
## 4266312.2 4561884.7 2821020.9 3987315.2 2606127.5 3075015.2 3941612.1 3362553.3
## 2015(155) 2015(156) 2015(157) 2015(158) 2015(159) 2015(160) 2015(161) 2015(162)
## 3831414.7 3924628.3 3079564.6 2718166.5 2530251.6 3804409.9 3709666.1 5102324.6
## 2015(163) 2015(164) 2015(165) 2015(166) 2015(167) 2015(168) 2015(169) 2015(170)
## 5855871.6 5245229.3 4978112.3 3504920.7 5052678.2 4339738.4 5414950.8 5536563.5
## 2015(171) 2015(172) 2015(173) 2015(174) 2015(175) 2015(176) 2015(177) 2015(178)
## 4486433.6 4210503.3 2348261.5 2936731.7 3354687.0 4435566.0 3900478.8 3044709.0
## 2015(179) 2015(180) 2015(181) 2015(182) 2015(183) 2015(184) 2015(185) 2015(186)
## 3250276.0 3886571.4 3957241.6 3147599.3 3816778.0 3937992.6 4169516.4 4131953.7
## 2015(187) 2015(188) 2015(189) 2015(190) 2015(191) 2015(192) 2015(193) 2015(194)
## 4260123.7 3213058.2 4716136.7 4660097.3 3643922.1 4015804.9 4246859.6 8334182.7
## 2015(195) 2015(196) 2015(197) 2015(198) 2015(199) 2015(200) 2015(201) 2015(202)
## 7363808.9 4769114.8 3851032.2 4425847.2 3801296.9 5008281.3 5215353.3 4082258.7
## 2015(203) 2015(204) 2015(205) 2015(206) 2015(207) 2015(208) 2015(209) 2015(210)
## 3425004.5 3301257.6 2559532.0 3803334.8 2216753.1 2511262.9 3604109.4 2442158.2
## 2015(211) 2015(212) 2015(213) 2015(214) 2015(215) 2015(216) 2015(217) 2015(218)
## 2434443.6 2745010.2 2937263.9 3389395.8 2521749.9 2484078.1 3557926.5 4822992.4
## 2015(219) 2015(220) 2015(221) 2015(222) 2015(223) 2015(224) 2015(225) 2015(226)
## 3799290.2 4332005.9 4464944.2 2807347.7 4002522.4 4069465.3 4138161.6 4522590.9
## 2015(227) 2015(228) 2015(229) 2015(230) 2015(231) 2015(232) 2015(233) 2015(234)
## 4956678.0 3743456.0 1990929.8 3526585.1 3643675.1 3052637.3 2438481.7 2775117.0
## 2015(235) 2015(236) 2015(237) 2015(238) 2015(239) 2015(240) 2015(241) 2015(242)
## 1651128.6 1780894.9 3547750.2 1424479.3 2737908.1 2330505.1 2332553.7 2454112.0
## 2015(243) 2015(244) 2015(245) 2015(246) 2015(247) 2015(248) 2015(249) 2015(250)
## 2352420.9 1870192.4 2161222.9 2357978.4 2114569.8 3033691.2 1341729.6 2307669.1
## 2015(251) 2015(252) 2015(253) 2015(254) 2015(255) 2015(256) 2015(257) 2015(258)
## 3100647.7 1454307.4 690736.5 2260949.3 8139301.7 3579326.8 2064084.0 2311723.3
## 2015(259) 2015(260) 2015(261) 2015(262) 2015(263) 2015(264) 2015(265) 2015(266)
## 1844756.9 1683235.1 2065987.4 3132035.1 2097100.4 2500153.0 2424996.9 1426740.1
## 2015(267) 2015(268) 2015(269) 2015(270) 2015(271) 2015(272) 2015(273) 2015(274)
## 2836424.4 1730467.5 1830411.6 3159428.1 1920332.7 2276416.7 949876.1 2112241.8
## 2015(275) 2015(276) 2015(277) 2015(278) 2015(279) 2015(280) 2015(281) 2015(282)
## 2031546.0 963922.4 1969586.5 2273353.4 2427907.4 2054239.1 2432863.5 2150790.2
## 2015(283) 2015(284) 2015(285) 2015(286) 2015(287) 2015(288) 2015(289) 2015(290)
## 1052719.4 1874411.3 1168971.4 1977063.3 2188451.5 1475266.8 1428670.2 699717.1
## 2015(291) 2015(292) 2015(293) 2015(294) 2015(295) 2015(296) 2015(297) 2015(298)
## 1064528.0 1517014.0 2397152.6 1105097.3 1670439.7 1981626.5 2530776.7 1451892.3
## 2015(299) 2015(300) 2015(301) 2015(302) 2015(303) 2015(304) 2015(305) 2015(306)
## 1979056.1 1937683.6 2846828.4 1081367.9 1232337.4 2185453.5 1059170.4 1523590.2
## 2015(307) 2015(308) 2015(309) 2015(310) 2015(311) 2015(312) 2015(313) 2015(314)
## 2949347.1 1945900.5 1348787.0 2318384.1 4839630.9 1946033.9 1374858.3 2716840.8
## 2015(315) 2015(316) 2015(317) 2015(318) 2015(319) 2015(320) 2015(321) 2015(322)
## 1580150.2 1552918.4 2046848.2 2302463.7 1737050.6 2304326.2 1846690.3 2709609.3
## 2015(323) 2015(324) 2015(325) 2015(326) 2015(327) 2015(328) 2015(329) 2015(330)
## 2561993.0 1555125.1 3257002.9 5063655.5 3903364.4 1368859.9 2987208.2 3399017.4
## 2015(331) 2015(332) 2015(333) 2015(334) 2015(335) 2015(336) 2015(337) 2015(338)
## 3603461.9 2625876.7 3075836.1 2708222.7 1867064.0 2202300.0 2411667.3 1354018.1
## 2015(339) 2015(340) 2015(341) 2015(342) 2015(343) 2015(344) 2015(345) 2015(346)
## 2475549.3 2042191.5 1700253.3 2181163.5 3456188.6 2015852.9 1967508.2 1776445.8
## 2015(347) 2015(348) 2015(349) 2015(350) 2015(351) 2015(352) 2015(353) 2015(354)
## 2993759.6 1638739.7 3178359.2 3965500.4 2466286.2 1932914.6 1575201.6 3575657.1
## 2015(355) 2015(356) 2015(357) 2015(358) 2015(359) 2015(360) 2015(361) 2015(362)
## 3143224.2 2991802.7 3237849.3 2763870.9 2202668.2 2528729.7 2268475.0 2792873.7
## 2015(363) 2015(364) 2015(365)
## 2236961.0 2290754.4 3486490.6VAR Model
library(vars)
library(tseries)
library(ggplot2)
library(gridExtra)##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combinelibrary(forecast)
Turnover.and.Close = cbind(Turnover.ts,Close.ts.diff)
Turnover.and.Close_tot = data.frame(Turnover.and.Close)
Turnover.and.Close_tot <- na.omit(Turnover.and.Close_tot)
Turnover.and.Close_tot <- scale(Turnover.and.Close_tot)
VARselect(Turnover.and.Close_tot,lag.max=10)## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 1 1 1 1
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) -0.1969958 -0.18075835 -0.161994050 -0.15150978 -0.13226251 -0.18036993
## HQ(n) -0.1709031 -0.13727050 -0.101111067 -0.07323166 -0.03658926 -0.06730153
## SC(n) -0.1314145 -0.07145618 -0.008971008 0.04523413 0.10820227 0.10381572
## FPE(n) 0.8211947 0.83464016 0.850455035 0.85942832 0.87614604 0.83501646
## 7 8 9 10
## AIC(n) -0.16611271 -0.150455587 -0.13882774 -0.11732548
## HQ(n) -0.03564918 -0.002596916 0.02642607 0.06532347
## SC(n) 0.16179381 0.221171800 0.27652052 0.34174364
## FPE(n) 0.84703678 0.860443162 0.87055771 0.88954379Turnover.and.Close.VAR = VAR(Turnover.and.Close_tot, p=1)
summary(Turnover.and.Close.VAR)##
## VAR Estimation Results:
## =========================
## Endogenous variables: Turnover.ts, Close.ts.diff
## Deterministic variables: const
## Sample size: 363
## Log Likelihood: -1007.532
## Roots of the characteristic polynomial:
## 0.3394 0.02485
## Call:
## VAR(y = Turnover.and.Close_tot, p = 1)
##
##
## Estimation results for equation Turnover.ts:
## ============================================
## Turnover.ts = Turnover.ts.l1 + Close.ts.diff.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Turnover.ts.l1 0.3393548 0.0495697 6.846 3.29e-11 ***
## Close.ts.diff.l1 0.0254277 0.0495593 0.513 0.608
## const 0.0004657 0.0495509 0.009 0.993
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.9441 on 360 degrees of freedom
## Multiple R-Squared: 0.1158, Adjusted R-squared: 0.1109
## F-statistic: 23.58 on 2 and 360 DF, p-value: 2.385e-10
##
##
## Estimation results for equation Close.ts.diff:
## ==============================================
## Close.ts.diff = Turnover.ts.l1 + Close.ts.diff.l1 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Turnover.ts.l1 0.0006793 0.0526931 0.013 0.990
## Close.ts.diff.l1 0.0249030 0.0526819 0.473 0.637
## const -0.0012379 0.0526731 -0.024 0.981
##
##
## Residual standard error: 1.004 on 360 degrees of freedom
## Multiple R-Squared: 0.0006209, Adjusted R-squared: -0.004931
## F-statistic: 0.1118 on 2 and 360 DF, p-value: 0.8942
##
##
##
## Covariance matrix of residuals:
## Turnover.ts Close.ts.diff
## Turnover.ts 0.891270 0.002571
## Close.ts.diff 0.002571 1.007124
##
## Correlation matrix of residuals:
## Turnover.ts Close.ts.diff
## Turnover.ts 1.000000 0.002714
## Close.ts.diff 0.002714 1.000000Granger-Causality Test
Testing if Turnover.ts Granger-causes
Close.ts.diff## Time Series:
## Start = c(2015, 2)
## End = c(2015, 365)
## Frequency = 365
## [1] 38.80 -17.30 -41.70 9.35 9.90 101.00 41.50 -27.05 39.75
## [10] 5.60 -15.95 -15.80 21.70 45.70 26.55 18.60 -78.55 8.05
## [19] 0.95 -3.60 -5.05 -15.95 21.95 50.95 36.70 18.40 29.40
## [28] 6.55 26.35 -15.10 -17.35 17.75 28.20 -41.60 -17.50 7.20
## [37] 44.80 -59.50 7.65 30.70 -4.75 6.15 -23.20 -27.05 -57.55
## [46] 7.95 -15.80 36.10 2.10 46.25 -26.15 -11.00 0.95 27.00
## [55] -24.00 -22.00 7.65 -72.75 55.80 25.85 -9.65 -44.40 4.25
## [64] -18.70 41.05 14.45 18.95 4.85 -25.10 -19.05 -15.40 -47.10
## [73] 10.45 -4.90 -15.70 -126.80 -10.55 -23.75 0.25 -18.90 50.85
## [82] -30.35 -40.70 21.95 13.95 35.70 -46.55 9.60 -21.90 26.95
## [91] 31.30 29.30 24.95 1.15 -2.00 -29.65 -9.50 -38.80 48.10
## [100] 6.55 24.65 -39.15 12.25 7.15 -16.40 -11.60 -7.95 34.40
## [109] -28.85 -22.60 -984.60 8.90 -3.65 6.25 -6.60 28.50 -23.45
## [118] -5.30 -4.65 14.80 -15.10 -5.80 13.05 -9.40 2.30 -7.00
## [127] -2.80 -23.00 -19.50 -0.50 12.65 21.10 12.75 5.05 12.80
## [136] -0.60 111.40 -9.50 -5.15 -10.40 -22.30 -2.45 22.55 -15.40
## [145] 7.05 1.90 -21.70 29.10 0.60 8.65 -9.60 23.15 35.25
## [154] 13.60 -8.75 -7.10 22.20 11.20 -41.00 15.35 -57.85 -6.40
## [163] -21.05 18.20 28.25 -16.65 -5.40 10.45 -0.10 -25.40 -15.20
## [172] 0.05 29.90 -8.25 10.30 9.00 -0.55 2.45 2.80 0.20
## [181] 2.80 8.80 24.30 -35.00 16.30 40.10 11.10 8.70 -27.15
## [190] -21.40 -1.05 35.25 -44.50 -23.50 -1.80 -0.25 -2.45 17.05
## [199] 14.00 12.45 11.50 2.25 -2.75 3.80 -8.15 -9.60 -4.25
## [208] 14.30 -8.70 -13.90 15.40 -3.70 -30.75 3.75 -6.80 -20.60
## [217] -18.70 -41.50 27.80 4.60 1.30 -12.55 11.25 13.95 21.55
## [226] -8.90 -18.30 -2.95 -8.70 -2.80 -1.85 -16.20 19.15 5.45
## [235] 16.70 8.05 18.30 11.25 -23.95 20.30 -19.70 17.10 -4.50
## [244] 8.40 -0.05 -18.40 19.10 869.00 38.80 -17.30 -41.70 9.35
## [253] 9.90 101.00 41.50 -27.05 39.75 5.60 -15.95 -15.80 21.70
## [262] 45.70 26.55 18.60 -78.55 8.05 0.95 -3.60 -5.05 -15.95
## [271] 21.95 50.95 36.70 18.40 29.40 6.55 26.35 -15.10 -17.35
## [280] 17.75 28.20 -41.60 -17.50 7.20 44.80 -59.50 7.65 30.70
## [289] -4.75 6.15 -23.20 -27.05 -57.55 7.95 -15.80 36.10 2.10
## [298] 46.25 -26.15 -11.00 0.95 27.00 -24.00 -22.00 7.65 -72.75
## [307] 55.80 25.85 -9.65 -44.40 4.25 -18.70 41.05 14.45 18.95
## [316] 4.85 -25.10 -19.05 -15.40 -47.10 10.45 -4.90 -15.70 -126.80
## [325] -10.55 -23.75 0.25 -18.90 50.85 -30.35 -40.70 21.95 13.95
## [334] 35.70 -46.55 9.60 -21.90 26.95 31.30 29.30 24.95 1.15
## [343] -2.00 -29.65 -9.50 -38.80 48.10 6.55 24.65 -39.15 12.25
## [352] 7.15 -16.40 -11.60 -7.95 34.40 -28.85 -22.60 -984.60 8.90
## [361] -3.65 6.25 -6.60 28.50causality_test1 <- causality(Turnover.and.Close.VAR, cause = "Turnover.ts")
print(causality_test1)## $Granger
##
## Granger causality H0: Turnover.ts do not Granger-cause Close.ts.diff
##
## data: VAR object Turnover.and.Close.VAR
## F-Test = 0.00016621, df1 = 1, df2 = 720, p-value = 0.9897
##
##
## $Instant
##
## H0: No instantaneous causality between: Turnover.ts and Close.ts.diff
##
## data: VAR object Turnover.and.Close.VAR
## Chi-squared = 0.002674, df = 1, p-value = 0.9588According to the Granger-Causality test for testing if Turnover is Granger-causing Close price, we can see from the test result that the p-value for the test is 0.9588. Since the p-value is too large, we fail to reject the null that Turnover does not Granger-cause the close price and conclude that we can not establish Granger causality.
Testing if Close.ts.diff Granger-causes Turnover.ts
causality_test2 <- causality(Turnover.and.Close.VAR, cause = "Close.ts.diff")
print(causality_test2)## $Granger
##
## Granger causality H0: Close.ts.diff do not Granger-cause Turnover.ts
##
## data: VAR object Turnover.and.Close.VAR
## F-Test = 0.26325, df1 = 1, df2 = 720, p-value = 0.6081
##
##
## $Instant
##
## H0: No instantaneous causality between: Close.ts.diff and Turnover.ts
##
## data: VAR object Turnover.and.Close.VAR
## Chi-squared = 0.002674, df = 1, p-value = 0.9588According to the Granger-Causality test for testing if the difference in Close price is Granger-causing Turnover, we can see from the test result that the p-value for the test is 0.9588. Since the p-value is too large, we fail to reject the null that the Close price does not Granger-cause turnover and conclude that we can not establish Granger causality.
Plots
library(vars)
library(tseries)
library(ggplot2)
library(gridExtra)1. Cross-Correlation Function (CCF) plot
ccf(Turnover.and.Close_tot[,1], Turnover.and.Close_tot[,2], main="Cross-Correlation Function (CCF)")
There is a significant positive peak around lag +10: This suggests that the yt1, which is Turnover here, leads the second yt2, which is Close here, by about 10 time lags. The correlation of this lag is around 0.2, which is relatively weak but still noteworthy. Additionally, there is a significant negative spike around lag -10: This means that the second series yts, Close.diff, may lead the firs yt1, Turnover by about 10 time units but in an inverse relationship. The correlation is slightly below -0.1, indicating a weak negative effect. The majority of bars are within the blue threshold, meaning their correlation are not statistically significant. However, it’s worth noting that the correlation is very small, therefore is likely not statistically significant.
Impulse Response Functions (IRFs)
irf_result <- irf(Turnover.and.Close.VAR, impulse="Turnover.ts", response="Close.ts.diff", boot=TRUE)
plot(irf_result)
Initially, the response of Close.ts.diff is very close to zero, indicating that a shock in Turnover.ts has little to no immediate impact on Close.ts.diff. In the short term, the response begins to diverge, with an upper bound peaking slightly above 0.05 and a lower bound dropping to around -0.15. This suggests that Close.ts.diff could react in either direction, implying some uncertainty in the short-term response. Over time, The response gradually returns to zero, indicating that the effect of the Turnover.ts shock is temporary. The confidence bands (red dashed lines) shrink, meaning the uncertainty in the impact also decreases over time. However, it’s worth noting that the correlation is very small, therefore is likely not statistically significant.
irf_result.1 <- irf(Turnover.and.Close.VAR, impulse="Close.ts.diff", response="Turnover.ts", boot=TRUE)
plot(irf_result.1)
Initially, the response of Turnover is very close to zero, indicating that a shock in difference in close price.ts has little immediate impact on Turnover the short term, the response begins to diverge, with an upper bound peaking approximately around 0.05 and a lower bound dropping to below -0.05. This suggests that Close.ts.diff could react in either direction, implying uncertainty in the short-term response. Over time, The response gradually returns to zero at around lag 6, indicating that the effect of the Close.diff shock is temporary and doesn’t last long. The confidence bands (red dashed lines) also shrink, meaning the uncertainty in the impact also decreases over time.
Data, Fitted Values, ACF, and PACF in one figure
library(vars)
library(ggplot2)
library(gridExtra)
library(forecast)
fitted_values <- fitted(Turnover.and.Close.VAR)
n_obs <- nrow(Turnover.and.Close_tot)
optimal_lag <- 1 # Based on your VAR selection
plot_data <- data.frame(
Time = 1:n_obs,
Actual_Turnover = Turnover.and.Close_tot[, 1],
Fitted_Turnover = c(rep(NA, optimal_lag), fitted_values[, 1]),
Actual_Close = Turnover.and.Close_tot[, 2],
Fitted_Close = c(rep(NA, optimal_lag), fitted_values[, 2])
)Time Series Plot
Turnover_plot <- ggplot(plot_data, aes(x=Time)) +
geom_line(aes(y=Actual_Turnover, color="Actual Turnover")) +
geom_line(aes(y=Fitted_Turnover, color="Fitted Turnover"), linetype="dashed") +
labs(title="Actual vs. Fitted Turnover") + theme_minimal()
Close_plot <- ggplot(plot_data, aes(x=Time)) +
geom_line(aes(y=Actual_Close, color="Actual Close")) +
geom_line(aes(y=Fitted_Close, color="Fitted Close"), linetype="dashed") +
labs(title="Actual vs. Fitted Close") + theme_minimal()
# ACF and PACF for Residuals of VAR Model
VAR_residuals <- residuals(Turnover.and.Close.VAR)
acf_residuals_plot <- function(series, title) {
par(mfrow=c(2,1)) # Arrange in 2-row figure (ACF, PACF)
acf(series, main=paste("ACF of Residuals -", title))
pacf(series, main=paste("PACF of Residuals -", title))
}
# Save ACF/PACF residuals plot
png("acf_pacf_residuals.png", width=800, height=600)
par(mfrow=c(2,2)) # Arrange plots in a 2x2 grid
acf(VAR_residuals[,1], main="ACF of Residuals (Turnover.ts)")
pacf(VAR_residuals[,1], main="PACF of Residuals (Turnover.ts)")
acf(VAR_residuals[,2], main="ACF of Residuals (Close.ts.diff)")
pacf(VAR_residuals[,2], main="PACF of Residuals (Close.ts.diff)")
dev.off()## quartz_off_screen
## 2library(png)
acf_pacf_image <- ggplot() +
annotation_raster(readPNG("acf_pacf_residuals.png"), xmin=-Inf, xmax=Inf, ymin=-Inf, ymax=Inf) +
theme_void()
# Arrange All Plots in One Figure
library(grid)
grid.newpage()
grid.arrange(
Turnover_plot,
Close_plot,
acf_pacf_image,
ncol=1,
heights=c(1, 1, 2))
For the Actual vs. Fitted value plot, we can see that the fitted value of the VAR model captures the dynamic of the actual value for Turnover, including the small turbulences and the peaks. The fitted value shows less variances across time. For the Close.diff variable (difference in close price), the fitted value doesn’t capture the outlier peaks as well as that of Turnover. The fitted value of Close.diff also has smaller variance compared to the actual values.
For the Residuals ACF and PACF, we can see that in the ACFs there are no values over the statistically significant boundaries other than lag 0, which indicates that the residuals don’t have a specific pattern and it can be deemed as white noise. In the PACF, there’s on value at around lag 18 that is reaching the statistical significance line, but the rest exhibits no patterns and no significance, we can also conclude from them that the model does not exhibit serial correlation.
Training and Testing of the VAR Model
library(vars)
library(forecast)
train_size <- floor(2/3 * nrow(Turnover.and.Close_tot))
train_data.Turnover.and.Close_tot <- Turnover.and.Close_tot[1:train_size, ]
test_data.Turnover.and.Close_tot <- Turnover.and.Close_tot[(train_size + 1):nrow(Turnover.and.Close_tot), ]
lag_selection <- VARselect(train_data.Turnover.and.Close_tot, lag.max = 10)
optimal_lag <- lag_selection$selection["AIC(n)"]
Turnover.and.Close.training.VAR <- VAR(train_data.Turnover.and.Close_tot, p = optimal_lag)
fitted_values <- fitted(Turnover.and.Close.training.VAR)
adjusted_train_data <- train_data.Turnover.and.Close_tot[(optimal_lag + 1):nrow(train_data.Turnover.and.Close_tot), ]
VAR.training_mse <- colMeans((adjusted_train_data - fitted_values)^2)
VAR.training_rmse <- sqrt(VAR.training_mse)
test_length <- nrow(test_data.Turnover.and.Close_tot)
Turnover.and.Close.testing.VAR <- predict(Turnover.and.Close.training.VAR, n.ahead = test_length)
forecasted_values <- sapply(Turnover.and.Close.testing.VAR$fcst, function(x) x[, "fcst"])
VAR.testing_mse <- colMeans((test_data.Turnover.and.Close_tot - forecasted_values)^2)
VAR.testing_rmse <- sqrt(VAR.testing_mse)
VAR.AIC <- AIC(Turnover.and.Close.training.VAR)
VAR.BIC <- BIC(Turnover.and.Close.training.VAR)
cat("Training MSE:", VAR.training_mse, "\n")## Training MSE: 0.8594865 0.5723925cat("Training RMSE:", VAR.training_rmse, "\n")## Training RMSE: 0.9270849 0.7565662cat("Testing MSE:", VAR.testing_mse, "\n")## Testing MSE: 1.053269 1.843219cat("Testing RMSE:", VAR.testing_rmse, "\n")## Testing RMSE: 1.026289 1.357652cat("Model AIC:", VAR.AIC, "\n")## Model AIC: 1208.189cat("Model BIC:", VAR.BIC, "\n")## Model BIC: 1229.098The MSE for the training model for Turnover (y1t) and Closing Price (y2t) are respectively 0.8594865 and 0.5723925. The MSE for y2t has a lower value, thus we can assume the model predicts y2t more accurately than y1t. For the RMSE of the training model, again, y2t has a lower value than that of y1t. However, the MSE for the testing model shows that y1t has a lower value than y2t and here, it suggests that the model could be better for testing for Turnover than it is for Closing Price. Then, we have AIC at 1208.189 and BIC at 1229.098. These are high AIC and BIC values but compared to the previous models we have run, these are the lowest observed and might suggest that the VAR is a better fit.
VAR Forecast
forecast_horizon <- 10
VAR_forecast <- predict(Turnover.and.Close.VAR, n.ahead = forecast_horizon)
Turnover_forecast <- VAR_forecast$fcst[[1]][, "fcst"]
Close_forecast <- VAR_forecast$fcst[[2]][, "fcst"]
forecast_time <- (nrow(Turnover.and.Close_tot) + 1):(nrow(Turnover.and.Close_tot) + forecast_horizon)
plot_forecast_data <- data.frame(
Time = 1:(nrow(Turnover.and.Close_tot) + forecast_horizon),
Actual_Turnover = c(Turnover.and.Close_tot[, 1], rep(NA, forecast_horizon)),
Forecasted_Turnover = c(rep(NA, nrow(Turnover.and.Close_tot)), Turnover_forecast),
Actual_Close = c(Turnover.and.Close_tot[, 2], rep(NA, forecast_horizon)),
Forecasted_Close = c(rep(NA, nrow(Turnover.and.Close_tot)), Close_forecast)
)
Turnover_plot <- ggplot(plot_forecast_data, aes(x = Time)) +
geom_line(aes(y = Actual_Turnover, color = "Actual Turnover")) +
geom_line(aes(y = Forecasted_Turnover, color = "Forecasted Turnover"), linetype = "dashed") +
labs(title = "Actual and 10-Step-Ahead Forecast for Turnover", y = "Turnover") +
theme_minimal()
Close_plot <- ggplot(plot_forecast_data, aes(x = Time)) +
geom_line(aes(y = Actual_Close, color = "Actual Close")) +
geom_line(aes(y = Forecasted_Close, color = "Forecasted Close"), linetype = "dashed") +
labs(title = "Actual and 10-Step-Ahead Forecast for Close", y = "Close") +
theme_minimal()
grid.arrange(Turnover_plot, Close_plot, ncol = 1)
FEVD
fevd_result <- fevd(Turnover.and.Close.VAR, n.ahead = forecast_horizon)
plot(fevd_result)
The FEVD results indicate that both Turnover.ts and Close.ts.diff are primarily driven by their own past values, with minimal influence from each other. The top plot shows that Turnover.ts explains nearly 100% of its own forecast error variance, suggesting that trading volume is largely self-driven and not significantly affected by stock price changes. Similarly, the bottom plot reveals that Close.ts.diff also explains nearly all of its own variance, meaning that price movements are not strongly influenced by trading volume. This suggests that, within the chosen VAR framework, the interaction between these two variables is weak, and their fluctuations are likely determined by external factors not included in this model.
CUSUM
residuals_VAR <- residuals(Turnover.and.Close.VAR)
cusum_test_turnover <- efp(residuals_VAR[, 1] ~ 1, type = "Rec-CUSUM")
cusum_test_close <- efp(residuals_VAR[, 2] ~ 1, type = "Rec-CUSUM")
plot(cusum_test_turnover, main = "CUSUM Test for Turnover Residuals")
plot(cusum_test_close, main = "CUSUM Test for Close Residuals")
The CUSUM test results confirm that the model exhibits structural stability over time, as the black CUSUM line remains within the red confidence bands throughout the observation period. This indicates that there are no significant structural breaks or parameter instabilities in the residuals of the VAR model. Since the relationship between the variables remains stable, the model’s predictions and interpretations are consistent over time, making it a reliable tool for analyzing the dynamics between Turnover.ts and Close.ts.diff.
Conclusion
Looking back on our findings and the test run on our models, AR and ARDL models exhibit extremely high MSE and RMSE values for the training and the testing models, suggesting that the models might not be a good fit for our variables.
Comparing the three different models conducted, the VAR model is observed to be the best suited model for both of the response variables. Among all three models, the VAR model results in much lower values for MSE and RMSE for both the training and the testing models. The lower values of MSE and RMSE suggest that the VAR model provides more accurate estimates. The AIC and BIC values of the VAR model are also lowest of all observed, suggesting a better model fit.
Initially, by setting the two response variables Turnover and Close (closing price), we wanted to see if turnover will increase as there’s positive indifference to close price - if the trend can increase “popularity” of a stock. However, upon doing these analysis, we have realized that none of the variables (Open, close, volume, and turnover) ae good for AR and ARDL model, this suggests that although there is dynamics in the variables themselves, we can not argue that they are statistically correlated with their own lags or lags of another variable. Although VAR is a better fit among them, we can’t establish Granger causality between the two response variables. Meaning that our intuition that a positive difference in close can drive up turnover, vice-versa. It stands true to what can be happening in real life - the market.