Problem Definition
Predict 30 data points for the columns RUB_sol and MFA_sol.

Data Location
Data is present in the file xtsdata.csv.

library(tidyr)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
library(tseries)
library(xts)
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## 
## Attaching package: 'xts'
## The following objects are masked from 'package:dplyr':
## 
##     first, last
library(forecast)
library(quantmod)
## Loading required package: TTR
## Version 0.4-0 included new data defaults. See ?getSymbols.
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following object is masked from 'package:base':
## 
##     date
library(ggfortify)
## 
## Attaching package: 'ggfortify'
## The following object is masked from 'package:forecast':
## 
##     gglagplot
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       12.335
cat("\nClass:\n")
## 
## Class:
class(dfrdata)
## [1] "data.frame"
#nrow(dfrdata)
dfrdata$time15 <-as.POSIXlt(dfrdata$time15,format="%m/%d/%Y %H:%M")
class(dfrdata)
## [1] "data.frame"
xtsD1 <-xts(dfrdata$RUB_sol,order.by =dfrdata$time15)
names(xtsD1)[1] <-paste("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  11.682
xtsD2 <-xts(dfrdata$MFA_sol,order.by =dfrdata$time15)
names(xtsD2)[1] <-paste("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  12.397
cat("\n")
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.   :22.439
cat("\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] 0.001111111
cat("\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 12:00:00
cat("\nMonthly OHLC:\n")
## 
## Monthly OHLC:
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      20.550
cat("\nMonthly Mean:\n")
## 
## Monthly Mean:
lapply(split(xtsD1,f="months"),FUN=mean)
## [[1]]
## [1] 12.27673
## 
## [[2]]
## [1] 14.09251
## 
## [[3]]
## [1] 17.82781
## 
## [[4]]
## [1] 19.42347
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.   :19.71
cat("\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] 0.001111111
cat("\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 12:00:00
cat("\nMonthly OHLC:\n")
## 
## Monthly OHLC:
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      17.819
cat("\nMonthly Mean:\n")
## 
## Monthly Mean:
lapply(split(xtsD2,f="months"),FUN=mean)
## [[1]]
## [1] 12.69096
## 
## [[2]]
## [1] 13.41241
## 
## [[3]]
## [1] 16.45846
## 
## [[4]]
## [1] 16.94893
autoplot(xtsD1, ts.colour='blue') +
    labs(title="Times Series Plot") +
    labs(x="Month") +
    labs(y="RUB_sol")

Observation The graph depicts the fluctuations present in the data.
There are no trends visible as such in this time series plot.
This is not a stationary series.

autoplot(xtsD2, ts.colour='blue') +
    labs(title="Times Series Plot") +
    labs(x="Month") +
    labs(y="MFA_sol")

Observation The graph depicts the fluctuations present in the data.
There are no trends visible as such in this time series plot.
This is not a stationary series.

# decompose data
#autoplot(stl(xtsData, s.window = 'periodic'), ts.colour = 'blue')

Observation As the above data has no cycles hence the data cannot be decomposed.

ADF Test for RUB_sol

# Augmented Dickey-Fuller Test
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: stationary

Observation Ideally, P-value should be less than 0.05.
Here it is greater than 0.05 hence data is not stationary.

Plot ACF for RUB_sol

#tsData <-as.ts(xtsData)
acf(log(xtsD1))

# Auto Correlation Function
autoplot(acf(xtsD1, plot = FALSE))

Plot PACF

#acf(diff(log(xtsD1)))
autoplot(pacf(xtsD1, plot = FALSE))

Make ARIMA Model for RUB_sol

# get arima model (find best model)
armModel <- auto.arima(xtsD1)
armModel
## 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=-30802.37

Forecast Using ARIMA Model for RUB_sol

# forecast using
fcData <- forecast(armModel,h=30)
fcData
##         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 21.71336 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       21.86760 20.52110 23.21411 19.80831 23.92690
## 5510701       21.75732 20.37353 23.14112 19.64100 23.87365
## 5511601       21.64050 20.22193 23.05908 19.47098 23.81003
## 5512501       21.51796 20.06711 22.96882 19.29908 23.73685

Plot Forecast Using ARIMA Model for RUB_sol

autoplot(fcData)

ADF Test for MFA_sol

# Augmented Dickey-Fuller Test
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: stationary

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))

Make ARIMA Model for MFA_sol

# get arima model (find best model)
armModel <- auto.arima(xtsD2)
armModel
## Series: xtsD2 
## ARIMA(4,1,4)                    
## 
## Coefficients:
## Warning in sqrt(diag(x$var.coef)): NaNs produced
##          ar1     ar2      ar3     ar4     ma1      ma2     ma3     ma4
##       0.4856  0.7682  -0.3657  -0.008  0.1278  -0.4095  0.2634  0.1029
## s.e.     NaN     NaN      NaN     NaN     NaN   0.0508     NaN     NaN
## 
## sigma^2 estimated as 0.0009886:  log likelihood=12441.01
## AIC=-24864.02   AICc=-24863.99   BIC=-24803.58

Forecast Using ARIMA Model for MFA_sol

# forecast using
fcData <- forecast(armModel,h=30)
fcData
##         Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
## 5486401       17.89291 17.85261 17.93320 17.83128 17.95453
## 5487301       17.96065 17.88416 18.03713 17.84367 18.07762
## 5488201       18.02405 17.90482 18.14328 17.84170 18.20640
## 5489101       18.08410 17.91551 18.25269 17.82627 18.34193
## 5490001       18.13661 17.91244 18.36078 17.79377 18.47945
## 5490901       18.18452 17.90132 18.46771 17.75141 18.61763
## 5491801       18.22566 17.88072 18.57060 17.69812 18.75320
## 5492701       18.26277 17.85509 18.67045 17.63927 18.88626
## 5493601       18.29446 17.82336 18.76555 17.57398 19.01493
## 5494501       18.32293 17.78872 18.85713 17.50593 19.13992
## 5495401       18.34720 17.75028 18.94412 17.43429 19.26012
## 5496301       18.36898 17.71028 19.02767 17.36159 19.37636
## 5497201       18.38754 17.66800 19.10708 17.28710 19.48798
## 5498101       18.40418 17.62504 19.18332 17.21258 19.59577
## 5499001       18.41836 17.58079 19.25593 17.13741 19.69931
## 5499901       18.43107 17.53642 19.32573 17.06282 19.79933
## 5500801       18.44191 17.49144 19.39238 16.98829 19.89553
## 5501701       18.45162 17.44667 19.45656 16.91469 19.98854
## 5502601       18.45990 17.40175 19.51804 16.84160 20.07819
## 5503501       18.46731 17.35727 19.57736 16.76965 20.16498
## 5504401       18.47364 17.31292 19.63436 16.69847 20.24880
## 5505301       18.47930 17.26913 19.68947 16.62851 20.33009
## 5506201       18.48413 17.22567 19.74259 16.55948 20.40878
## 5507101       18.48846 17.18285 19.79407 16.49170 20.48522
## 5508001       18.49215 17.14046 19.84383 16.42492 20.55937
## 5508901       18.49545 17.09875 19.89216 16.35938 20.63153
## 5509801       18.49827 17.05754 19.93900 16.29487 20.70168
## 5510701       18.50079 17.01701 19.98458 16.23154 20.77005
## 5511601       18.50295 16.97702 20.02887 16.16925 20.83665
## 5512501       18.50487 16.93770 20.07205 16.10808 20.90167

Plot Forecast Using ARIMA Model for MFA_sol

autoplot(fcData)