ts<-ts(crudeoil$crudeOilImport,start=c(2009,1),frequency=12)
autoplot(ts)
train=ts(crudeoil$crudeOilImport,start=c(2009,1),end=c(2020,7),frequency=12)
train
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct
## 2009 317275 262339 303897 285934 281147 284093 287569 279111 289561 272678
## 2010 274568 253150 299033 302836 310396 310153 318991 309053 284192 272415
## 2011 296158 235122 292010 265822 289106 285572 295338 287633 273698 284594
## 2012 257536 242560 271697 258417 272766 270684 266782 263945 250160 250303
## 2013 245715 203162 231414 231621 238809 231912 245724 251079 237699 230822
## 2014 234969 201572 225487 226639 222177 212025 236534 231649 224851 221600
## 2015 222315 198807 235360 216229 224604 219618 228160 239212 216838 220171
## 2016 236065 229492 248383 228344 245749 226802 250986 248482 241213 234666
## 2017 262811 220558 253114 246132 264554 242677 245369 245611 219708 238109
## 2018 248552 209942 236216 247608 242857 254283 246671 247656 227795 227975
## 2019 234307 178257 210276 209958 221259 214563 215083 215273 194485 193493
## 2020 198663 189060 195181 165586 188693 191919 183087
## Nov Dec
## 2009 273248 265615
## 2010 271185 279096
## 2011 268189 279359
## 2012 244987 235120
## 2013 222248 240519
## 2014 218845 223978
## 2015 221130 244965
## 2016 240691 242213
## 2017 230230 241245
## 2018 226251 219240
## 2019 174531 211837
## 2020
test=ts(crudeoil$crudeOilImport,start=c(2020,8),end=c(2021,1),frequency=12)
test
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2020 317275 262339 303897 285934 281147
## 2021 284093
#ARIMA Model
arima_tr<- auto.arima(train)
summary(arima_tr)
## Series: train
## ARIMA(1,1,0)(2,0,0)[12]
##
## Coefficients:
## ar1 sar1 sar2
## -0.5196 0.3609 0.3754
## s.e. 0.0756 0.0876 0.0988
##
## sigma^2 estimated as 141690927: log likelihood=-1493.79
## AIC=2995.57 AICc=2995.87 BIC=3007.28
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -670.0541 11730.88 8721.999 -0.4638492 3.685447 0.5007121
## ACF1
## Training set -0.04130865
forecast<- forecast(arima_tr, h = 6)
forecast
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Aug 2020 186727.2 171472.4 201982.1 163397.0 210057.5
## Sep 2020 170106.1 153182.4 187029.9 144223.4 195988.9
## Oct 2020 170680.2 150248.7 191111.7 139432.8 201927.6
## Nov 2020 162740.9 140289.4 185192.3 128404.4 197077.4
## Dec 2020 173805.4 149054.2 198556.6 135951.8 211659.1
## Jan 2021 174585.8 147949.9 201221.6 133849.8 215321.8
autoplot(forecast)
ARIMA_accuracy<- accuracy(forecast, test)
print(ARIMA_accuracy)
## ME RMSE MAE MPE MAPE MASE
## Training set -670.0541 11730.88 8721.999 -0.4638492 3.685447 0.5007121
## Test set 116006.5527 116895.19 116006.553 39.9918683 39.991868 6.6596988
## ACF1 Theil's U
## Training set -0.04130865 NA
## Test set -0.51306379 3.682059
#ETS model
ets_tr<-ets(train)
forecast2<- forecast(ets_tr,h=6)
forecast2
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Aug 2020 188501.6 177718.1 199285.1 172009.6 204993.5
## Sep 2020 178324.3 166878.0 189770.7 160818.6 195830.0
## Oct 2020 178434.6 165857.6 191011.7 159199.8 197669.5
## Nov 2020 175174.3 161814.3 188534.3 154742.0 195606.6
## Dec 2020 182969.6 168031.5 197907.8 160123.8 205815.5
## Jan 2021 186252.6 170106.7 202398.5 161559.6 210945.6
autoplot(forecast2)
ets_accuracy<- accuracy(forecast2, test)
print(ets_accuracy)
## ME RMSE MAE MPE MAPE MASE
## Training set -1486.742 10072.44 7954.49 -0.7895483 3.345313 0.456651
## Test set 107504.660 108674.68 107504.66 36.9988398 36.998840 6.171623
## ACF1 Theil's U
## Training set -0.05644102 NA
## Test set -0.52924984 3.372708