Time Series Assignment
Sonia Mathew
August 3, 2017
Load Lobs
library(tidyr)## Warning: package 'tidyr' was built under R version 3.3.3library(dplyr)## Warning: package 'dplyr' was built under R version 3.3.3##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(ggplot2)## Warning: package 'ggplot2' was built under R version 3.3.3library(lubridate)## Warning: package 'lubridate' was built under R version 3.3.3##
## Attaching package: 'lubridate'## The following object is masked from 'package:base':
##
## datelibrary(tseries)## Warning: package 'tseries' was built under R version 3.3.3library(xts)## Warning: package 'xts' was built under R version 3.3.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.3.3##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
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## as.Date, as.Date.numeric##
## Attaching package: 'xts'## The following objects are masked from 'package:dplyr':
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## first, lastlibrary(forecast)## Warning: package 'forecast' was built under R version 3.3.3library(quantmod)## Warning: package 'quantmod' was built under R version 3.3.3## Loading required package: TTR## Warning: package 'TTR' was built under R version 3.3.3## Version 0.4-0 included new data defaults. See ?getSymbols.library(ggfortify)##
## Attaching package: 'ggfortify'## The following object is masked from 'package:forecast':
##
## gglagplotRead Data From a csv file
setwd("D:/PGDM/Trim 4/MachineLearning")
dfrData <- read.csv("./Data/xtsdata.csv", header=T, stringsAsFactors=F)
head(dfrData)## time15 RUB_sol MFA_sol NFA_sol NFY_sol SFY_baro_air NFA_baro_air
## 1 4/30/2012 0:15 11.929 12.689 11.26 8.19 9.43 13.134
## 2 4/30/2012 0:30 11.879 12.627 11.28 8.18 9.25 12.925
## 3 4/30/2012 0:45 11.828 12.570 11.26 8.21 9.03 12.736
## 4 4/30/2012 1:00 11.779 12.511 11.23 8.22 8.82 12.605
## 5 4/30/2012 1:15 11.730 12.459 11.17 8.23 8.60 12.455
## 6 4/30/2012 1:30 11.682 12.397 11.15 8.24 8.42 12.335class(dfrData)## [1] "data.frame"Create Extensible Time Series From a csv
dfrData$time15 <- as.POSIXlt(dfrData$time15,format="%m/%d/%Y %H:%M")
cat("\n Class of variable:\n")##
## Class of variable:class(dfrData)## [1] "data.frame"xtsD1 <- xts(dfrData$RUB_sol, order.by=dfrData$time15,frequency = 24)
names(xtsD1)[1]<-paste("RUB_sol")
cat("\n Class of RUB_sol:\n")##
## Class of RUB_sol:class(xtsD1)## [1] "xts" "zoo"head(xtsD1)## RUB_sol
## 2012-04-30 00:15:00 11.929
## 2012-04-30 00:30:00 11.879
## 2012-04-30 00:45:00 11.828
## 2012-04-30 01:00:00 11.779
## 2012-04-30 01:15:00 11.730
## 2012-04-30 01:30:00 11.682xtsD2 <- xts(dfrData$MFA_sol, order.by=dfrData$time15, frequency = 24)
names(xtsD2)[1]<-paste("MFA_sol")
cat("\n Class of MFA_sol:\n")##
## Class of MFA_sol:class(xtsD2)## [1] "xts" "zoo"head(xtsD2)## MFA_sol
## 2012-04-30 00:15:00 12.689
## 2012-04-30 00:30:00 12.627
## 2012-04-30 00:45:00 12.570
## 2012-04-30 01:00:00 12.511
## 2012-04-30 01:15:00 12.459
## 2012-04-30 01:30:00 12.397Xts Info for RUB_sol
cat("\nSummary:\n")##
## Summary:summary(xtsD1)## Index RUB_sol
## Min. :2012-04-30 00:15:00 Min. : 9.489
## 1st Qu.:2012-05-15 21:11:15 1st Qu.:13.906
## Median :2012-05-31 18:07:30 Median :16.043
## Mean :2012-05-31 18:07:30 Mean :15.956
## 3rd Qu.:2012-06-16 15:03:45 3rd Qu.:17.971
## Max. :2012-07-02 12:00:00 Max. :22.439cat("\nStart:\n")##
## Start:start(xtsD1)## [1] "2012-04-30 00:15:00 IST"cat("\nEnds:\n")##
## Ends:end(xtsD1)## [1] "2012-07-02 12:00:00 IST"cat("\nFreq:\n")##
## Freq:frequency(xtsD1)## [1] 0.001111111cat("\nIndex:\n")##
## Index:head(index(xtsD1))## [1] "2012-04-30 00:15:00 IST" "2012-04-30 00:30:00 IST"
## [3] "2012-04-30 00:45:00 IST" "2012-04-30 01:00:00 IST"
## [5] "2012-04-30 01:15:00 IST" "2012-04-30 01:30:00 IST"cat("\nPeriodicity:\n")##
## Periodicity:periodicity(xtsD1)## 15 minute periodicity from 2012-04-30 00:15:00 to 2012-07-02 12:00:00cat("\nMonthly OHLC:\n")##
## Monthly OHLC:head(to.monthly(xtsD1))## xtsD1.Open xtsD1.High xtsD1.Low xtsD1.Close
## Apr 2012 11.929 13.665 10.914 12.589
## May 2012 12.546 18.891 9.489 17.254
## Jun 2012 17.207 22.439 12.995 18.997
## Jul 2012 18.960 21.896 17.883 20.550cat("\nMonthly Mean:\n")##
## Monthly Mean:head(lapply(split(xtsD1,f="months"),FUN=mean))## [[1]]
## [1] 12.27673
##
## [[2]]
## [1] 14.09251
##
## [[3]]
## [1] 17.82781
##
## [[4]]
## [1] 19.42347#cat("\nYearly OHLC:\n")
#to.yearly(xtsD1)
#cat("\nYearly Mean:\n")
#lapply(split(xtsD1,f="years"),FUN=mean)
cat("\nQuarterly OHLC:\n")##
## Quarterly OHLC:head(to.quarterly(xtsD1))## xtsD1.Open xtsD1.High xtsD1.Low xtsD1.Close
## 2012 Q2 11.929 22.439 9.489 18.997
## 2012 Q3 18.960 21.896 17.883 20.550Xts Info for MFA_sol
cat("\nSummary:\n")##
## Summary:summary(xtsD2)## Index MFA_sol
## Min. :2012-04-30 00:15:00 Min. :10.54
## 1st Qu.:2012-05-15 21:11:15 1st Qu.:13.30
## Median :2012-05-31 18:07:30 Median :15.09
## Mean :2012-05-31 18:07:30 Mean :14.92
## 3rd Qu.:2012-06-16 15:03:45 3rd Qu.:16.45
## Max. :2012-07-02 12:00:00 Max. :19.71cat("\nStart:\n")##
## Start:start(xtsD2)## [1] "2012-04-30 00:15:00 IST"cat("\nEnds:\n")##
## Ends:end(xtsD2)## [1] "2012-07-02 12:00:00 IST"cat("\nFreq:\n")##
## Freq:frequency(xtsD2)## [1] 0.001111111cat("\nIndex:\n")##
## Index:head(index(xtsD2))## [1] "2012-04-30 00:15:00 IST" "2012-04-30 00:30:00 IST"
## [3] "2012-04-30 00:45:00 IST" "2012-04-30 01:00:00 IST"
## [5] "2012-04-30 01:15:00 IST" "2012-04-30 01:30:00 IST"cat("\nPeriodicity:\n")##
## Periodicity:periodicity(xtsD2)## 15 minute periodicity from 2012-04-30 00:15:00 to 2012-07-02 12:00:00cat("\nMonthly OHLC:\n")##
## Monthly OHLC:head(to.monthly(xtsD2))## xtsD2.Open xtsD2.High xtsD2.Low xtsD2.Close
## Apr 2012 12.689 13.855 11.579 12.769
## May 2012 12.701 17.203 10.541 15.834
## Jun 2012 15.796 19.709 13.883 16.295
## Jul 2012 16.252 18.691 15.603 17.819cat("\nMonthly Mean:\n")##
## Monthly Mean:head(lapply(split(xtsD2,f="months"),FUN=mean))## [[1]]
## [1] 12.69096
##
## [[2]]
## [1] 13.41241
##
## [[3]]
## [1] 16.45846
##
## [[4]]
## [1] 16.94893#cat("\nYearly OHLC:\n")
#to.yearly(xtsD1)
#cat("\nYearly Mean:\n")
#lapply(split(xtsD1,f="years"),FUN=mean)
cat("\nQuarterly OHLC:\n")##
## Quarterly OHLC:head(to.quarterly(xtsD2))## xtsD2.Open xtsD2.High xtsD2.Low xtsD2.Close
## 2012 Q2 12.689 19.709 10.541 16.295
## 2012 Q3 16.252 18.691 15.603 17.819Plot xts for RUB_sol
# plot xts using base
plot(xtsD1)
# plot xts using ggplot
autoplot(xtsD1$RUB_sol, ts.colour='blue') +
#ggplot(xtsD1, aes(x = Index, y = xtsD1$RUB_sol)) + geom_point()+
labs(title="Times Series Plot") +
labs(x="Month-Time") +
labs(y="RUB_sol")
observation
The graph displays the fluctuations in the data.
The data doesnt look stationary and no clear trend in the data is visible.
Plot xts for MFA_sol
# plot xts using base
plot(xtsD2)
# plot xts using ggplot
autoplot(xtsD2$MFA_sol, ts.colour='blue') +
labs(title="Times Series Plot") +
labs(x="Month-Time") +
labs(y="MFA_sol")
observation
The graph displays the fluctuations in the data.
The data doesnt look stationary and no clear trend in the data is visible.
Decompose xts for RUB_sol
# decompose data
#decompose(xtsD1) # OK decompose(xtsD1)
#To make the time series more stationary remove the seasonality values from the timeseries. Observation
On execution “Error in decompose(xtsD1) : time series has no or less than 2 periods” is received.
This confirms that the data is not seasonal and the distance between the data points is small.
Decompose xts for MFA_sol
# decompose data
#decompose(as.ts(xtsD2))
#To make the time series more stationary remove the seasonality values from the timeseries. Observation
On execution “Error in decompose(xtsD1) : time series has no or less than 2 periods” is received.
This confirms that the data is not seasonal and the distance between the data points is small.
ADF Test for RUB_sol
# Augmented Dickey-Fuller Test to check stationarity
adf.test(xtsD1, alternative="stationary", k=0)##
## Augmented Dickey-Fuller Test
##
## data: xtsD1
## Dickey-Fuller = -1.9731, Lag order = 0, p-value = 0.5898
## alternative hypothesis: stationaryObservation
p-value here is greater than 0.05. Thus the data points are not stationary.
ADF Test for MFA_sol
# Augmented Dickey-Fuller Test to check stationarity
adf.test(xtsD2, alternative="stationary", k=0)##
## Augmented Dickey-Fuller Test
##
## data: xtsD2
## Dickey-Fuller = -2.0628, Lag order = 0, p-value = 0.5517
## alternative hypothesis: stationaryObservation
p-value here is greater than 0.05. Thus the data points are not stationary.
Plot ACF for RUB_sol
#Plots should be greater than zero
# Auto Correlation Function
autoplot(acf(xtsD1, plot = FALSE))## Warning: package 'bindrcpp' was built under R version 3.3.3
#plot in base
acf(log(xtsD1))
Observation
This displays the ACF graph as mentioned by ARIMA with values above the zero line.
Plot PACF for RUB_sol
#PACF plot should go below zero
# Partial Auto Correlation Function
autoplot(pacf(xtsD1, plot = FALSE))
observation This displays the ACF graph as mentioned by ARIMA with values below the zero line.
Plot ACF for MFA_sol
#Plots should be greater than zero
# Auto Correlation Function
autoplot(acf(xtsD2, plot = FALSE))
#plot in base
#tsData <- as.ts(xtsData)
acf(log(xtsD2))
observation This displays the ACF graph as mentioned by ARIMA with values above the zero line.
Plot PACF for MFA_sol
#PACF plot should go below zero
#plot in base
#tsData <- as.ts(xtsD1)
#acf(diff(log(tsData)))
# Partial Auto Correlation Function
autoplot(pacf(xtsD1, plot = FALSE)) observation This displays the ACF graph as mentioned by ARIMA with values below the zero line. Thus we make use of ARIMA model to forecast values.
Make ARIMA Model for RUB_Sol
# get arima model (find best model)
armModel1 <- auto.arima(xtsD1)
armModel1## Series: xtsD1
## ARIMA(5,1,1)
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 ma1
## 1.9571 -1.0185 0.1645 -0.1499 0.0409 -0.9766
## s.e. 0.0131 0.0282 0.0309 0.0282 0.0130 0.0029
##
## sigma^2 estimated as 0.0003703: log likelihood=15431.69
## AIC=-30849.37 AICc=-30849.36 BIC=-30802.37Make ARIMA Model for MFA_Sol
# get arima model (find best model)
armModel2 <- auto.arima(xtsD2)
armModel2## Series: xtsD2
## ARIMA(4,1,4)
##
## Coefficients:## Warning in sqrt(diag(x$var.coef)): NaNs produced## ar1 ar2 ar3 ar4 ma1 ma2 ma3 ma4
## 0.4867 0.7978 -0.3897 -0.0122 0.1243 -0.4434 0.2734 0.1057
## s.e. NaN NaN NaN NaN NaN 0.0442 NaN NaN
##
## sigma^2 estimated as 0.0009886: log likelihood=12441.15
## AIC=-24864.31 AICc=-24864.28 BIC=-24803.87Forecast RUB_sol Using ARIMA Model
# forecast using
fcData1 <- forecast(armModel1,h=30)
fcData1## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 5486401 20.75225 20.72759 20.77691 20.71453 20.78996
## 5487301 20.94708 20.89236 21.00179 20.86340 21.03075
## 5488201 21.13238 21.04270 21.22205 20.99523 21.26953
## 5489101 21.30777 21.17789 21.43764 21.10914 21.50640
## 5490001 21.47257 21.29815 21.64698 21.20582 21.73931
## 5490901 21.62601 21.40354 21.84849 21.28577 21.96626
## 5491801 21.76750 21.49399 22.04101 21.34920 22.18580
## 5492701 21.89651 21.56949 22.22354 21.39637 22.39666
## 5493601 22.01261 21.63006 22.39516 21.42755 22.59767
## 5494501 22.11543 21.67577 22.55508 21.44303 22.78782
## 5495401 22.20469 21.70674 22.70263 21.44315 22.96623
## 5496301 22.28020 21.72316 22.83724 21.42828 23.13212
## 5497201 22.34186 21.72526 22.95846 21.39886 23.28486
## 5498101 22.38964 21.71337 23.06591 21.35537 23.42390
## 5499001 22.42358 21.68783 23.15933 21.29835 23.54882
## 5499901 22.44382 21.64908 23.23857 21.22837 23.65928
## 5500801 22.45057 21.59760 23.30354 21.14607 23.75508
## 5501701 22.44410 21.53393 23.35427 21.05211 23.83609
## 5502601 22.42475 21.45864 23.39087 20.94721 23.90230
## 5503501 22.39294 21.37236 23.41352 20.83210 23.95378
## 5504401 22.34914 21.27577 23.42251 20.70756 23.99072
## 5505301 22.29388 21.16957 23.41818 20.57440 24.01336
## 5506201 22.22773 21.05449 23.40097 20.43342 24.02205
## 5507101 22.15134 20.93131 23.37137 20.28547 24.01721
## 5508001 22.06537 20.80082 23.32993 20.13140 23.99935
## 5508901 21.97055 20.66381 23.27729 19.97206 23.96903
## 5509801 21.86761 20.52110 23.21411 19.80831 23.92690
## 5510701 21.75732 20.37353 23.14112 19.64100 23.87365
## 5511601 21.64051 20.22193 23.05908 19.47098 23.81003
## 5512501 21.51796 20.06711 22.96882 19.29908 23.73685Plot RUB_sol Forecast Using ARIMA Model
autoplot(fcData1)
Forecast MFA_sol Using ARIMA Model
# forecast using
fcData2 <- forecast(armModel2,h=30)
fcData2## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 5486401 17.89277 17.85248 17.93307 17.83115 17.95440
## 5487301 17.95961 17.88321 18.03601 17.84276 18.07645
## 5488201 18.02245 17.90350 18.14141 17.84053 18.20438
## 5489101 18.08158 17.91339 18.24977 17.82435 18.33881
## 5490001 18.13355 17.90982 18.35729 17.79138 18.47572
## 5490901 18.18072 17.89786 18.46358 17.74812 18.61331
## 5491801 18.22133 17.87652 18.56615 17.69398 18.74868
## 5492701 18.25775 17.84990 18.66561 17.63399 18.88151
## 5493601 18.28887 17.81725 18.76050 17.56758 19.01016
## 5494501 18.31667 17.78157 18.85178 17.49830 19.13505
## 5495401 18.34034 17.74214 18.93855 17.42547 19.25522
## 5496301 18.36147 17.70115 19.02180 17.35160 19.37135
## 5497201 18.37943 17.65793 19.10093 17.27600 19.48287
## 5498101 18.39547 17.61408 19.17686 17.20044 19.59050
## 5499001 18.40908 17.56900 19.24915 17.12430 19.69386
## 5499901 18.42124 17.52388 19.31860 17.04884 19.79364
## 5500801 18.43155 17.47819 19.38490 16.97351 19.88958
## 5501701 18.44077 17.43281 19.44873 16.89923 19.98231
## 5502601 18.44858 17.38732 19.50984 16.82552 20.07163
## 5503501 18.45557 17.34235 19.56879 16.75305 20.15809
## 5504401 18.46148 17.29755 19.62542 16.68140 20.24157
## 5505301 18.46679 17.25339 19.68018 16.61106 20.32251
## 5506201 18.47126 17.20959 19.73294 16.54170 20.40082
## 5507101 18.47528 17.16650 19.78407 16.47367 20.47690
## 5508001 18.47868 17.12387 19.83348 16.40668 20.55067
## 5508901 18.48172 17.08197 19.88148 16.34098 20.62246
## 5509801 18.48429 17.04059 19.92799 16.27635 20.69224
## 5510701 18.48660 16.99995 19.97326 16.21296 20.76025
## 5511601 18.48855 16.95985 20.01724 16.15061 20.82648
## 5512501 18.49030 16.92047 20.06013 16.08945 20.89115Plot MFA_sol Forecast Using ARIMA Model
autoplot(fcData2)