Problem Definition
In the xts data there are 5 columns.
The aim is to use the columns(RUB_sol & MFA_sol)
and predict 30 data data points each for two columns

Setup

Load Lobs

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

Read

dfrdata <- read.csv("C:/firstproject/xtsdata (3).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)

xtsData

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

Xts Info

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

Plot xts

autoplot(xtsD1, ts.colour='blue') +
    labs(title="Times Series Plot") +
    labs(x="Month") +
    labs(y="RUB_sol")
## Warning: Ignoring unknown parameters: ts.colour

autoplot(xtsD2, ts.colour='blue') +
    labs(title="Times Series Plot") +
    labs(x="Month") +
    labs(y="MFA_sol")
## Warning: Ignoring unknown parameters: ts.colour

ADF Test

# 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 P Value is more than 0.05, this shows that data is not stationary

ADF TEST

# 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

The P value is greater then the printed P value

Observation P Value is more than 0.05, this shows that data is not stationary

Plot ACF

#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

# 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

# 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

Observation Forecast using ARIMA model succesful created

Plot Forecast Using ARIMA Model

autoplot(fcData)

Observation The forecast values are refecleted in the graph.

ADF Test for XTSD2

# 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 XTSD2

#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 XTSD2

# 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 XTSD2

# 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

Observation Forecast using ARIMA model succesful created

Plot Forecast Using ARIMA Model for XTSD2

autoplot(fcData)

Observation The forecast values are refecleted in the graph.