AUTO REGRESSIVE INTEGRATED MOVING AVERAGE MODELS
#install.packages("rmarkdown",repos = "http://cran.us.r-project.org")
# install.packages("forecast",repos = "http://cran.us.r-project.org")
# install.packages("fpp",repos = "http://cran.us.r-project.org")
# install.packages("smooth",repos = "http://cran.us.r-project.org")
# install.packages("readxl",repos = "http://cran.us.r-project.org")
# install.packages("tseries",repos = "http://cran.us.r-project.org")
# install.packages("lubridate",repos = "http://cran.us.r-project.org")
# install.packages("dlypr",repos = "http://cran.us.r-project.org")
library(forecast)
## Warning: package 'forecast' was built under R version 3.5.1
library(fpp)
## Warning: package 'fpp' was built under R version 3.5.1
## Loading required package: fma
## Warning: package 'fma' was built under R version 3.5.1
## Loading required package: expsmooth
## Warning: package 'expsmooth' was built under R version 3.5.1
## Loading required package: lmtest
## Warning: package 'lmtest' was built under R version 3.5.1
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 3.5.1
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: tseries
## Warning: package 'tseries' was built under R version 3.5.1
library(smooth)
## Warning: package 'smooth' was built under R version 3.5.1
## Loading required package: greybox
## Warning: package 'greybox' was built under R version 3.5.1
## Package "greybox", v0.3.3 loaded.
## This is package "smooth", v2.4.7
library(readxl)
## Warning: package 'readxl' was built under R version 3.5.1
library(tseries)
library(lubridate)
## Warning: package 'lubridate' was built under R version 3.5.1
##
## Attaching package: 'lubridate'
## The following object is masked from 'package:smooth':
##
## hm
## The following object is masked from 'package:base':
##
## date
library(dplyr)
## Warning: package 'dplyr' was built under R version 3.5.1
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:lubridate':
##
## intersect, setdiff, union
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
# Using Arima Model -
Stock<-read_excel(file.choose()) # read the Stock data
class(Stock)
## [1] "tbl_df" "tbl" "data.frame"
stockMon <- as.yearmon(Stock$Date)
stockMon <- as.data.frame(stockMon)
class(stockMon)
## [1] "data.frame"
stockdat <- cbind(stockMon,Stock$Price)
agg <- aggregate(stockdat, by = list(stockdat$stockMon), FUN = median)
stockFin <- agg$`Stock$Price`
# ACF, PACF and Dickey-Fuller Test
acf(stockFin, lag.max = 20)
pacf(stockFin, lag.max = 20)
difflnstock=diff(stockFin,1)
difflnstock
## [1] -59.250 -5.575 28.425 12.200 -4.000 11.050 56.125
## [8] 244.175 7.950 205.350 59.400 -0.750 212.100 122.000
## [15] 460.425 -51.725 -288.450 -173.925 -67.150 -189.025 -127.675
## [22] 37.375 505.150 174.150 -37.575 -30.275 432.800 20.900
## [29] 199.675 286.600 -202.475 -215.325 -45.550 -93.725 259.300
## [36] 477.425 -79.150 -185.525 -9.275 -115.425 338.975 66.475
## [43] 571.200 -420.350 -876.125 98.375 1073.700 258.400 586.400
## [50] -127.975 0.850 -66.400 -337.375 -533.900 -44.300 523.600
## [57] 42.000 219.975 -267.100 -35.825 615.075 2862.425 -47.500
## [64] -927.000 -1663.000 -562.500 22.150 89.350 -288.000 -623.050
## [71] 172.050 -172.000 -925.500 -500.025 35.525 -86.000 -157.000
## [78] -35.050 580.050 195.000 993.950 6.050 895.100 919.900
## [85] 481.175 287.825 56.000 260.000 -475.850 550.250 697.800
## [92] 222.950 155.350 290.150 -246.850 1469.500 265.200 -424.450
## [99] -1495.350 -677.650 -719.150 480.900 209.225 341.325 -175.800
## [106] 668.250 -602.800 55.500 -296.050 141.325 256.900 221.825
## [113] 2203.700 441.250 1101.050 -412.800 -160.700 -236.200 517.300
## [120] -455.650 27.250 -96.100 2183.100 996.500 -661.200 -683.200
## [127] 275.400 2669.200 -611.400 -1467.200 177.000 -29.000 2198.500
## [134] 1461.900 2666.300 -62.700 -223.200 1916.800 1347.300
adf.test(stockFin)
## Warning in adf.test(stockFin): p-value greater than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: stockFin
## Dickey-Fuller = 0.45594, Lag order = 5, p-value = 0.99
## alternative hypothesis: stationary
adf.test(difflnstock)
## Warning in adf.test(difflnstock): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: difflnstock
## Dickey-Fuller = -4.4661, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
stock2 <- cbind(agg$stockMon,agg$`Stock$Price`)
plot(stock2)
class(stockFin)
## [1] "numeric"
Stock <- as.ts(stockFin)
View(Stock)
class(Stock)
## [1] "ts"
Stock1 <- ts(Stock,start=c(2002,9),end=c(2014,4),frequency=12)
start(Stock1)
## [1] 2002 9
end(Stock1)
## [1] 2014 4
class(Stock1)
## [1] "ts"
sum(is.na(Stock1))
## [1] 0
summary(Stock1)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 843.8 2394.3 3999.2 5712.9 7293.5 22290.7
View(Stock1)
# decomdata<- decompose(Stock1, "additive")
decomdata<- decompose(Stock1, "multiplicative")
plot(decomdata)
plot(decomdata$seasonal)
plot(decomdata$trend)
plot(decomdata$random)
# EDA on the Original Data
plot(Stock1)
abline(reg=lm(Stock1~time(Stock1)))
cycle(Stock1)
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2002 9 10 11 12
## 2003 1 2 3 4 5 6 7 8 9 10 11 12
## 2004 1 2 3 4 5 6 7 8 9 10 11 12
## 2005 1 2 3 4 5 6 7 8 9 10 11 12
## 2006 1 2 3 4 5 6 7 8 9 10 11 12
## 2007 1 2 3 4 5 6 7 8 9 10 11 12
## 2008 1 2 3 4 5 6 7 8 9 10 11 12
## 2009 1 2 3 4 5 6 7 8 9 10 11 12
## 2010 1 2 3 4 5 6 7 8 9 10 11 12
## 2011 1 2 3 4 5 6 7 8 9 10 11 12
## 2012 1 2 3 4 5 6 7 8 9 10 11 12
## 2013 1 2 3 4 5 6 7 8 9 10 11 12
## 2014 1 2 3 4
# Boxplot by Cycle
boxplot(Stock1~cycle(Stock1,xlab = "Date", ylab = "Stock Price(100's)",
main = "Monthly Boxplot of Stock Price from Sep 2002 to Apr 2014"))
# Use Auto Arima for the Best Model
Newmodel <- auto.arima(Stock1)
Newmodel
## Series: Stock1
## ARIMA(3,2,1)
##
## Coefficients:
## ar1 ar2 ar3 ma1
## 0.1809 -0.1041 -0.2424 -0.9117
## s.e. 0.0959 0.0871 0.0928 0.0665
##
## sigma^2 estimated as 467815: log likelihood=-1095.76
## AIC=2201.52 AICc=2201.97 BIC=2216.16
# Use the trace function to understand the determine the best p,d,q values that were selected.
auto.arima(Stock1, ic = "aic", trace = TRUE)
##
## ARIMA(2,2,2)(1,0,1)[12] : Inf
## ARIMA(0,2,0) : 2263.143
## ARIMA(1,2,0)(1,0,0)[12] : 2252.928
## ARIMA(0,2,1)(0,0,1)[12] : 2213.665
## ARIMA(0,2,1)(1,0,1)[12] : Inf
## ARIMA(0,2,1) : 2211.67
## ARIMA(1,2,1) : 2206.86
## ARIMA(1,2,0) : 2250.931
## ARIMA(1,2,2) : 2208.074
## ARIMA(2,2,2) : 2206.299
## ARIMA(2,2,2)(1,0,0)[12] : Inf
## ARIMA(2,2,2)(0,0,1)[12] : 2208.266
## ARIMA(3,2,2) : 2202.714
## ARIMA(3,2,1) : 2201.52
## ARIMA(2,2,0) : 2247.611
## ARIMA(4,2,2) : 2203.449
## ARIMA(3,2,1)(1,0,0)[12] : 2203.488
## ARIMA(3,2,1)(0,0,1)[12] : 2203.475
## ARIMA(3,2,1)(1,0,1)[12] : 2204.344
## ARIMA(2,2,1) : 2206.43
## ARIMA(4,2,1) : 2201.826
## ARIMA(3,2,0) : 2222.544
##
## Best model: ARIMA(3,2,1)
## Series: Stock1
## ARIMA(3,2,1)
##
## Coefficients:
## ar1 ar2 ar3 ma1
## 0.1809 -0.1041 -0.2424 -0.9117
## s.e. 0.0959 0.0871 0.0928 0.0665
##
## sigma^2 estimated as 467815: log likelihood=-1095.76
## AIC=2201.52 AICc=2201.97 BIC=2216.16
# tseries evaluation
plot.ts(Newmodel$residuals)
acf(ts(Newmodel$residuals),main = 'ACF Residual')
pacf(ts(Newmodel$residuals),main = 'PACF Residual')
# Forecast for next 10 year
Pass_Forecast <- forecast(Newmodel,Level=c(95),h=10*12)
## Warning in forecast.Arima(Newmodel, Level = c(95), h = 10 * 12): The non-
## existent Level arguments will be ignored.
Pass_Forecast
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## May 2014 23152.79 22276.25 24029.33 21812.24 24493.35
## Jun 2014 23467.71 22051.35 24884.07 21301.58 25633.85
## Jul 2014 23872.18 22053.17 25691.19 21090.25 26654.12
## Aug 2014 24467.43 22397.92 26536.94 21302.38 27632.48
## Sep 2014 25220.49 22932.29 27508.70 21720.99 28720.00
## Oct 2014 25960.54 23438.42 28482.66 22103.30 29817.79
## Nov 2014 26635.56 23845.95 29425.17 22369.22 30901.90
## Dec 2014 27261.92 24189.77 30334.08 22563.47 31960.37
## Jan 2015 27889.40 24534.78 31244.02 22758.96 33019.85
## Feb 2015 28537.92 24905.19 32170.64 22982.15 34093.69
## Mar 2015 29201.91 25290.30 33113.52 23219.62 35184.20
## Apr 2015 29866.24 25670.18 34062.31 23448.92 36283.57
## May 2015 30523.93 26036.30 35011.56 23660.70 37387.16
## Jun 2015 31176.63 26391.51 35961.75 23858.42 38494.84
## Jul 2015 31829.03 26741.85 36916.21 24048.86 39609.19
## Aug 2015 32483.51 27090.15 37876.86 24235.09 40731.93
## Sep 2015 33139.60 27435.63 38843.58 24416.13 41863.08
## Oct 2015 33795.85 27776.39 39815.30 24589.89 43001.81
## Nov 2015 34451.45 28111.53 40791.36 24755.38 44147.51
## Dec 2015 35106.52 28441.28 41771.76 24912.92 45300.12
## Jan 2016 35761.53 28766.26 42756.80 25063.19 46459.87
## Feb 2016 36416.74 29086.82 43746.66 25206.60 47626.88
## Mar 2016 37072.12 29402.94 44741.30 25343.13 48801.12
## Apr 2016 37727.53 29714.48 45740.57 25472.63 49982.42
## May 2016 38382.87 30021.38 46744.36 25595.07 51170.67
## Jun 2016 39038.16 30323.69 47752.63 25710.52 52365.80
## Jul 2016 39693.44 30621.51 48765.37 25819.11 53567.77
## Aug 2016 40348.74 30914.91 49782.57 25920.94 54776.54
## Sep 2016 41004.05 31203.94 50804.17 26016.07 55992.04
## Oct 2016 41659.37 31488.61 51830.13 26104.54 57214.21
## Nov 2016 42314.69 31768.97 52860.41 26186.40 58442.97
## Dec 2016 42970.00 32045.04 53894.95 26261.72 59678.27
## Jan 2017 43625.30 32316.88 54933.72 26330.57 60920.04
## Feb 2017 44280.61 32584.53 55976.69 26393.00 62168.22
## Mar 2017 44935.92 32848.03 57023.82 26449.08 63422.76
## Apr 2017 45591.23 33107.41 58075.06 26498.87 64683.60
## May 2017 46246.54 33362.70 59130.38 26542.41 65950.68
## Jun 2017 46901.85 33613.96 60189.75 26579.77 67223.94
## Jul 2017 47557.16 33861.20 61253.12 26611.00 68503.32
## Aug 2017 48212.47 34104.48 62320.47 26636.16 69788.79
## Sep 2017 48867.78 34343.81 63391.75 26655.29 71080.27
## Oct 2017 49523.09 34579.25 64466.94 26668.45 72377.73
## Nov 2017 50178.40 34810.81 65546.00 26675.70 73681.11
## Dec 2017 50833.71 35038.53 66628.89 26677.07 74990.35
## Jan 2018 51489.02 35262.45 67715.59 26672.62 76305.42
## Feb 2018 52144.33 35482.59 68806.07 26662.40 77626.27
## Mar 2018 52799.64 35698.99 69900.30 26646.45 78952.84
## Apr 2018 53454.95 35911.67 70998.24 26624.81 80285.09
## May 2018 54110.26 36120.66 72099.86 26597.54 81622.98
## Jun 2018 54765.57 36326.00 73205.15 26564.68 82966.47
## Jul 2018 55420.88 36527.70 74314.06 26526.26 84315.50
## Aug 2018 56076.19 36725.81 75426.58 26482.33 85670.05
## Sep 2018 56731.50 36920.34 76542.67 26432.94 87030.06
## Oct 2018 57386.81 37111.32 77662.31 26378.12 88395.51
## Nov 2018 58042.12 37298.77 78785.47 26317.91 89766.34
## Dec 2018 58697.43 37482.73 79912.13 26252.34 91142.52
## Jan 2019 59352.74 37663.21 81042.27 26181.47 92524.01
## Feb 2019 60008.05 37840.25 82175.85 26105.32 93910.78
## Mar 2019 60663.36 38013.86 83312.87 26023.93 95302.79
## Apr 2019 61318.67 38184.07 84453.28 25937.34 96700.00
## May 2019 61973.98 38350.89 85597.07 25845.59 98102.38
## Jun 2019 62629.29 38514.37 86744.22 25748.70 99509.89
## Jul 2019 63284.60 38674.50 87894.70 25646.71 100922.50
## Aug 2019 63939.91 38831.33 89048.49 25539.65 102340.17
## Sep 2019 64595.22 38984.86 90205.58 25427.56 103762.88
## Oct 2019 65250.53 39135.13 91365.94 25310.46 105190.60
## Nov 2019 65905.84 39282.14 92529.54 25188.40 106623.28
## Dec 2019 66561.15 39425.92 93696.38 25061.40 108060.90
## Jan 2020 67216.46 39566.49 94866.43 24929.48 109503.44
## Feb 2020 67871.77 39703.88 96039.67 24792.69 110950.85
## Mar 2020 68527.08 39838.09 97216.08 24651.05 112403.11
## Apr 2020 69182.39 39969.14 98395.64 24504.58 113860.20
## May 2020 69837.70 40097.07 99578.33 24353.33 115322.07
## Jun 2020 70493.01 40221.87 100764.15 24197.30 116788.72
## Jul 2020 71148.32 40343.58 101953.06 24036.54 118260.10
## Aug 2020 71803.63 40462.21 103145.05 23871.07 119736.20
## Sep 2020 72458.94 40577.78 104340.11 23700.91 121216.97
## Oct 2020 73114.25 40690.29 105538.21 23526.09 122702.41
## Nov 2020 73769.56 40799.78 106739.34 23346.64 124192.48
## Dec 2020 74424.87 40906.26 107943.48 23162.58 125687.16
## Jan 2021 75080.18 41009.74 109150.62 22973.93 127186.43
## Feb 2021 75735.49 41110.23 110360.75 22780.73 128690.25
## Mar 2021 76390.80 41207.76 111573.84 22582.99 130198.61
## Apr 2021 77046.11 41302.35 112789.87 22380.74 131711.48
## May 2021 77701.42 41393.99 114008.85 22174.00 133228.84
## Jun 2021 78356.73 41482.72 115230.74 21962.80 134750.66
## Jul 2021 79012.04 41568.54 116455.54 21747.15 136276.93
## Aug 2021 79667.35 41651.48 117683.22 21527.09 137807.61
## Sep 2021 80322.66 41731.53 118913.79 21302.62 139342.70
## Oct 2021 80977.97 41808.73 120147.21 21073.78 140882.16
## Nov 2021 81633.28 41883.07 121383.49 20840.58 142425.98
## Dec 2021 82288.59 41954.58 122622.59 20603.05 143974.13
## Jan 2022 82943.90 42023.28 123864.52 20361.21 145526.59
## Feb 2022 83599.21 42089.16 125109.26 20115.07 147083.35
## Mar 2022 84254.52 42152.25 126356.79 19864.66 148644.38
## Apr 2022 84909.83 42212.56 127607.10 19609.99 150209.67
## May 2022 85565.14 42270.10 128860.18 19351.09 151779.19
## Jun 2022 86220.45 42324.89 130116.01 19087.98 153352.92
## Jul 2022 86875.76 42376.93 131374.59 18820.67 154930.85
## Aug 2022 87531.07 42426.24 132635.90 18549.19 156512.95
## Sep 2022 88186.38 42472.83 133899.93 18273.54 158099.22
## Oct 2022 88841.69 42516.72 135166.66 17993.76 159689.62
## Nov 2022 89497.00 42557.91 136436.09 17709.86 161284.14
## Dec 2022 90152.31 42596.42 137708.20 17421.85 162882.77
## Jan 2023 90807.62 42632.25 138982.98 17129.76 164485.48
## Feb 2023 91462.93 42665.43 140260.43 16833.59 166092.26
## Mar 2023 92118.24 42695.96 141540.52 16533.38 167703.10
## Apr 2023 92773.55 42723.85 142823.25 16229.13 169317.96
## May 2023 93428.86 42749.11 144108.61 15920.87 170936.85
## Jun 2023 94084.17 42771.76 145396.58 15608.60 172559.73
## Jul 2023 94739.48 42791.80 146687.16 15292.35 174186.60
## Aug 2023 95394.79 42809.24 147980.33 14972.14 175817.44
## Sep 2023 96050.10 42824.10 149276.09 14647.96 177452.23
## Oct 2023 96705.41 42836.39 150574.43 14319.86 179090.96
## Nov 2023 97360.72 42846.12 151875.32 13987.83 180733.61
## Dec 2023 98016.03 42853.29 153178.77 13651.89 182380.16
## Jan 2024 98671.34 42857.91 154484.76 13312.07 184030.61
## Feb 2024 99326.65 42860.00 155793.29 12968.37 185684.93
## Mar 2024 99981.96 42859.57 157104.34 12620.81 187343.11
## Apr 2024 100637.27 42856.63 158417.91 12269.40 189005.13
plot(Pass_Forecast)
# Test your final model
Box.test(Newmodel$resid, lag = 2, type = "Ljung-Box")
##
## Box-Ljung test
##
## data: Newmodel$resid
## X-squared = 0.058414, df = 2, p-value = 0.9712
Box.test(Newmodel$resid, lag = 15, type = "Ljung-Box")
##
## Box-Ljung test
##
## data: Newmodel$resid
## X-squared = 13.924, df = 15, p-value = 0.5313
Box.test(Newmodel$resid, lag = 40, type = "Ljung-Box")
##
## Box-Ljung test
##
## data: Newmodel$resid
## X-squared = 41.12, df = 40, p-value = 0.4213