Model Regresi Dengan Peubah Lag
Abdussalam Ahmad
9/14/2022
Tujuan
Tujuan dari regresi yakni membuat dan menentukan sebuah model regresi yang cocok digunakan sebagai untuk meramal cuaca di Delhi.
Package
Package yang digunakan yakni dLagM, dynlm, MLmetrics, car, dan readxl.
library(dLagM)## Warning: package 'dLagM' was built under R version 4.1.3## Loading required package: nardl## Warning: package 'nardl' was built under R version 4.1.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Loading required package: dynlm## Warning: package 'dynlm' was built under R version 4.1.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 4.1.3##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(dynlm)
library(MLmetrics)## Warning: package 'MLmetrics' was built under R version 4.1.3##
## Attaching package: 'MLmetrics'## The following object is masked from 'package:dLagM':
##
## MAPE## The following object is masked from 'package:base':
##
## Recalllibrary(lmtest)## Warning: package 'lmtest' was built under R version 4.1.3library(car)## Loading required package: carDatalibrary(readxl)Read dan Splitting Data
Data yang digunakan Merupakan data cuaca Delhi dari tahun 2013 hingga 2017. Pada data ini, terdapat 4 peubah yang dicatat setiap hari, yakni suhu rata-rata, kelembapan, kecepatan angin, dan tekanan rata-rata.
A<-read.csv("C:\\Users\\Alam\\Downloads\\archive\\DailyDelhiClimateTrain.csv")
B<-read.csv("C:\\Users\\Alam\\Downloads\\archive\\DailyDelhiClimateTest.csv")
data<- rbind(A,B)
head(data)## date Meantemp humidity wind_speed meanpressure
## 1 2013-01-01 10.000000 84.50000 0.000000 1015.667
## 2 2013-01-02 7.400000 92.00000 2.980000 1017.800
## 3 2013-01-03 7.166667 87.00000 4.633333 1018.667
## 4 2013-01-04 8.666667 71.33333 1.233333 1017.167
## 5 2013-01-05 6.000000 86.83333 3.700000 1016.500
## 6 2013-01-06 7.000000 82.80000 1.480000 1018.000Pada dataset tersebut, akan suhu rata-rata (meantemp) akan digunakan sebagai variabel respon, sementara kelembapan (humidity) akan digunakan sebagai variabel penjelas.
#data time series
data$Yt <- data$Meantemp
data$Xt <- data$humidity
train <- data[1:1462,]
test <- data[1463:1576,]
train.ts<-ts(train)
test.ts<-ts(test)
data.ts<-ts(data)
Yt.ts <- data$Yt
Xt.ts <- data$XtEksplorasi Data
par(mfrow = c(2,1))
plot.ts(Yt.ts, ylab = "Suhu")
plot.ts(Xt.ts, ylab = "Kelembapan")
Berdasarkan kedua grafik time series tersebut, kedua peubah memiliki pola musiman.
MODEL KOYCK
Digunakan syntax koyckDlm untuk mendapatkan model koyck, yakni:
model.koyck = dLagM::koyckDlm(x = train$Xt, y = train$Yt)
summary(model.koyck)##
## Call:
## "Y ~ (Intercept) + Y.1 + X.t"
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.70363 -0.89800 0.05309 1.04736 6.88622
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.308579 0.383286 -0.805 0.42090
## Y.1 0.986820 0.007629 129.355 < 2e-16 ***
## X.t 0.010612 0.003799 2.793 0.00529 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.714 on 1458 degrees of freedom
## Multiple R-Squared: 0.9455, Adjusted R-squared: 0.9455
## Wald test: 1.27e+04 on 2 and 1458 DF, p-value: < 2.2e-16
##
## Diagnostic tests:
## NULL
##
## alpha beta phi
## Geometric coefficients: -23.41311 0.01061212 0.9868202AIC dan BIC
Sementara itu, didapatkan AIC dan BIC dari model sebesar:
AIC(model.koyck)## [1] 5725.577BIC(model.koyck)## [1] 5746.725Peramalan
Dilaksanakan peramalan data training sebagai pendugaan terhadap data testing.
#Ramalan
(fore.koyck <- forecast(model = model.koyck, x=test$Xt, h=114))## $forecasts
## [1] 10.47088 10.84379 11.26131 11.54768 11.88223 12.25878 12.80563 13.21466
## [9] 13.58948 13.86527 14.13921 14.43572 14.64851 14.93514 15.19979 15.52340
## [17] 15.90636 16.21942 16.49450 16.67395 16.89769 17.17547 17.44704 17.63153
## [25] 17.83299 18.26190 18.53021 18.85580 19.16654 19.42838 19.67026 19.93681
## [33] 20.07166 20.32821 20.57521 20.81929 20.97563 21.06712 21.20675 21.34427
## [41] 21.51610 21.60311 21.75664 21.87232 21.97057 22.09101 22.09352 22.17717
## [49] 22.32711 22.42563 22.45954 22.59160 22.59149 22.44015 22.26428 22.19742
## [57] 22.22240 22.24042 22.18701 22.09457 22.07050 21.92205 21.78219 21.62428
## [65] 21.48112 21.32983 21.29967 21.44337 21.57114 21.61923 21.62662 21.55654
## [73] 21.56167 21.54992 21.47944 21.52131 21.42051 21.38439 21.37410 21.30381
## [81] 21.19199 21.13206 20.94469 20.77791 20.58920 20.41915 20.27301 20.06336
## [89] 19.88148 19.71015 19.51454 19.30693 19.05960 18.83799 18.76929 18.48925
## [97] 18.25402 18.01659 17.69474 17.35912 17.01012 16.75327 16.53281 16.40562
## [105] 16.20389 16.04522 15.93314 15.70463 15.44509 15.22478 15.13339 15.05939
## [113] 14.84417 14.62799
##
## $call
## forecast.koyckDlm(model = model.koyck, x = test$Xt, h = 114)
##
## attr(,"class")
## [1] "forecast.koyckDlm" "dLagM"MAPE
Dihitung MAPE dari antara data forecast dan data testing serta data training dan model. Kemudian, kedua data dibandingkan.
mape.koyck <- MAPE(fore.koyck$forecasts, test$Yt)
mape_train <- dLagM::GoF(model.koyck)["MAPE"]
c("MAPE_testing" = mape.koyck, "MAPE_taining" = mape_train)## $MAPE_testing
## [1] 0.2420774
##
## $MAPE_taining.MAPE
## [1] 0.05559705Regression with distributed lag
Digunakan syntax dlm dengan nilai lag = 2 untuk membuat sebuah model regresi with distributed lag sebagai berikut:
model.dlm = dLagM::dlm(x = train$Xt,y = train$Yt, q=2)
summary(model.dlm)##
## Call:
## lm(formula = model.formula, data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.109 -4.670 -0.306 5.541 12.179
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 41.858693 0.618846 67.640 < 2e-16 ***
## x.t -0.176868 0.019496 -9.072 < 2e-16 ***
## x.1 -0.002206 0.025355 -0.087 0.931
## x.2 -0.089981 0.019515 -4.611 4.36e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.952 on 1456 degrees of freedom
## Multiple R-squared: 0.3415, Adjusted R-squared: 0.3401
## F-statistic: 251.6 on 3 and 1456 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 9357.638 9384.069AIC dan BIC
Sementara itu, didapatkan AIC dan BIC dari model sebesar:
AIC(model.koyck)## [1] 5725.577BIC(model.koyck)## [1] 5746.725Peramalan
Dilaksanakan peramalan data training sebagai pendugaan terhadap data testing.
#Ramalan
(fore.dlm <- forecast(model = model.dlm, x=test$Xt, h=114))#meramalkan 23 periode ke depan## $forecasts
## [1] 18.62214 19.01300 19.47816 22.33988 21.08042 21.36132 17.99026 19.73699
## [9] 18.75861 21.43995 21.67449 22.03533 23.34496 21.86229 22.82632 21.13950
## [17] 20.22059 20.75871 20.79710 22.88732 22.41604 22.23654 21.87160 22.78077
## [25] 22.49613 19.36520 21.73522 18.80275 20.27991 20.51319 20.88716 20.80624
## [33] 23.07690 20.80925 21.97341 20.92206 22.38308 23.44428 23.35159 23.87814
## [41] 22.85794 24.22832 22.81176 24.09448 23.79360 23.70896 25.77828 24.25018
## [49] 24.09677 24.21845 24.71253 23.50152 26.19185 27.90326 29.48289 28.99247
## [57] 27.67923 26.86624 27.28284 28.01600 27.50885 29.90994 29.25602 30.64355
## [65] 30.38019 30.71331 28.62217 25.79162 24.97904 24.81127 25.61407 27.57342
## [73] 26.69111 27.61182 27.96706 26.26466 29.10956 27.13839 27.90775 28.36754
## [81] 28.87256 28.55115 31.03776 30.33485 31.82073 31.40231 31.24255 32.19151
## [89] 31.60450 32.01837 32.24675 32.42636 33.36182 33.12000 30.97552 34.29124
## [97] 32.37827 34.25777 35.36936 35.73260 36.77557 35.47276 35.05534 32.80030
## [105] 33.77159 32.34826 32.24411 33.85763 34.07218 34.48211 32.66305 32.06344
## [113] 33.36158 33.31709
##
## $call
## forecast.dlm(model = model.dlm, x = test$Xt, h = 114)
##
## attr(,"class")
## [1] "forecast.dlm" "dLagM"MAPE
Dihitung MAPE dari antara data forecast dan data testing serta data training dan model. Kemudian, kedua data dibandingkan.
mape.dlm <- MAPE(fore.dlm$forecasts,test$Yt)
mape_train <- GoF(model.dlm)["MAPE"]
c("MAPE_testing" = mape.dlm, "MAPE_training" = mape_train)## $MAPE_testing
## [1] 0.2740091
##
## $MAPE_training.MAPE
## [1] 0.2415499Regression with Distributed Lag Optimum
Penentuan lag optimum
Untuk menentukan nilai lag optimum, digunakan syntax finiteDLMauto.
finiteDLMauto(formula = Yt ~ Xt,
data = data.frame(train),q.min = 1,q.max = 650,
model.type = "dlm",error.type = "AIC", trace = FALSE)## q - k MASE AIC BIC GMRAE MBRAE R.Adj.Sq Ljung-Box
## 650 650 0.81706 3957.241 7026.014 1.50518 1.19092 0.85271 0model dlm dengan lag optimum
Setelah didapatkan lag optimum sebesar 650, nilai lag optimum dimasukkan ke dalam fungsi dlm.
model.dlm2 = dLagM::dlm(x = train$Xt,y = train$Yt, q= 650)
summary(model.dlm2)##
## Call:
## lm(formula = model.formula, data = design)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1502 -0.7755 0.0799 0.8270 3.8529
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.275e+02 1.217e+01 10.482 < 2e-16 ***
## x.t -1.644e-01 2.489e-02 -6.605 5.59e-10 ***
## x.1 1.952e-02 3.146e-02 0.621 0.5358
## x.2 -2.392e-02 3.136e-02 -0.763 0.4468
## x.3 -1.054e-02 3.126e-02 -0.337 0.7364
## x.4 -2.115e-02 3.120e-02 -0.678 0.4990
## x.5 5.448e-03 3.121e-02 0.175 0.8616
## x.6 4.830e-03 3.131e-02 0.154 0.8776
## x.7 1.434e-02 3.121e-02 0.459 0.6465
## x.8 -2.875e-02 3.135e-02 -0.917 0.3604
## x.9 -2.754e-02 3.136e-02 -0.878 0.3812
## x.10 -1.744e-03 3.146e-02 -0.055 0.9559
## x.11 -5.970e-03 3.163e-02 -0.189 0.8505
## x.12 -1.551e-02 3.177e-02 -0.488 0.6261
## x.13 3.851e-03 3.169e-02 0.122 0.9034
## x.14 -6.185e-03 3.167e-02 -0.195 0.8454
## x.15 -9.444e-03 3.166e-02 -0.298 0.7659
## x.16 -1.334e-02 3.159e-02 -0.422 0.6734
## x.17 -2.724e-02 3.163e-02 -0.861 0.3905
## x.18 -1.004e-02 3.179e-02 -0.316 0.7526
## x.19 2.751e-03 3.205e-02 0.086 0.9317
## x.20 -2.320e-03 3.201e-02 -0.072 0.9423
## x.21 -5.342e-03 3.172e-02 -0.168 0.8665
## x.22 -2.230e-02 3.155e-02 -0.707 0.4807
## x.23 1.164e-02 3.197e-02 0.364 0.7162
## x.24 -1.924e-02 3.215e-02 -0.599 0.5503
## x.25 -1.581e-02 3.219e-02 -0.491 0.6240
## x.26 1.300e-03 3.194e-02 0.041 0.9676
## x.27 1.302e-02 3.183e-02 0.409 0.6830
## x.28 -1.343e-02 3.173e-02 -0.423 0.6728
## x.29 1.251e-02 3.169e-02 0.395 0.6936
## x.30 1.118e-02 3.192e-02 0.350 0.7266
## x.31 -1.051e-03 3.174e-02 -0.033 0.9736
## x.32 8.259e-03 3.184e-02 0.259 0.7957
## x.33 -9.028e-03 3.184e-02 -0.284 0.7771
## x.34 -7.597e-03 3.155e-02 -0.241 0.8100
## x.35 6.858e-03 3.139e-02 0.218 0.8273
## x.36 1.770e-02 3.135e-02 0.565 0.5731
## x.37 7.008e-03 3.155e-02 0.222 0.8245
## x.38 -3.308e-03 3.159e-02 -0.105 0.9167
## x.39 3.310e-03 3.193e-02 0.104 0.9176
## x.40 -1.273e-02 3.205e-02 -0.397 0.6918
## x.41 -1.195e-02 3.203e-02 -0.373 0.7095
## x.42 -2.215e-02 3.203e-02 -0.691 0.4903
## x.43 -3.813e-04 3.214e-02 -0.012 0.9905
## x.44 1.203e-03 3.207e-02 0.038 0.9701
## x.45 -1.641e-03 3.206e-02 -0.051 0.9592
## x.46 -1.502e-02 3.185e-02 -0.471 0.6380
## x.47 -9.078e-03 3.176e-02 -0.286 0.7754
## x.48 1.265e-02 3.203e-02 0.395 0.6934
## x.49 7.919e-03 3.204e-02 0.247 0.8051
## x.50 -2.028e-02 3.209e-02 -0.632 0.5282
## x.51 -6.813e-03 3.230e-02 -0.211 0.8332
## x.52 -4.512e-03 3.233e-02 -0.140 0.8892
## x.53 1.255e-02 3.220e-02 0.390 0.6971
## x.54 -2.155e-02 3.212e-02 -0.671 0.5033
## x.55 -6.532e-03 3.212e-02 -0.203 0.8391
## x.56 5.830e-03 3.215e-02 0.181 0.8563
## x.57 -7.233e-03 3.218e-02 -0.225 0.8224
## x.58 -5.216e-03 3.196e-02 -0.163 0.8706
## x.59 -1.105e-02 3.205e-02 -0.345 0.7306
## x.60 6.583e-03 3.222e-02 0.204 0.8384
## x.61 -3.893e-03 3.216e-02 -0.121 0.9038
## x.62 -1.561e-02 3.213e-02 -0.486 0.6278
## x.63 -9.642e-03 3.244e-02 -0.297 0.7667
## x.64 7.635e-03 3.249e-02 0.235 0.8145
## x.65 2.382e-03 3.249e-02 0.073 0.9416
## x.66 -2.049e-02 3.280e-02 -0.625 0.5330
## x.67 -5.242e-03 3.285e-02 -0.160 0.8734
## x.68 5.874e-03 3.298e-02 0.178 0.8589
## x.69 1.767e-02 3.307e-02 0.534 0.5940
## x.70 -6.656e-03 3.297e-02 -0.202 0.8403
## x.71 -3.081e-03 3.298e-02 -0.093 0.9257
## x.72 2.775e-04 3.251e-02 0.009 0.9932
## x.73 -3.941e-03 3.215e-02 -0.123 0.9026
## x.74 -2.077e-02 3.231e-02 -0.643 0.5212
## x.75 -4.388e-02 3.234e-02 -1.357 0.1769
## x.76 -6.140e-03 3.227e-02 -0.190 0.8493
## x.77 -1.680e-02 3.241e-02 -0.518 0.6050
## x.78 -3.549e-02 3.249e-02 -1.092 0.2764
## x.79 -1.042e-02 3.254e-02 -0.320 0.7493
## x.80 -8.399e-03 3.271e-02 -0.257 0.7977
## x.81 1.033e-02 3.276e-02 0.315 0.7529
## x.82 7.430e-04 3.273e-02 0.023 0.9819
## x.83 -6.809e-04 3.274e-02 -0.021 0.9834
## x.84 1.533e-03 3.320e-02 0.046 0.9632
## x.85 6.133e-03 3.328e-02 0.184 0.8540
## x.86 2.502e-02 3.323e-02 0.753 0.4526
## x.87 -9.718e-03 3.351e-02 -0.290 0.7722
## x.88 -8.840e-03 3.360e-02 -0.263 0.7928
## x.89 1.291e-02 3.364e-02 0.384 0.7016
## x.90 6.012e-03 3.343e-02 0.180 0.8575
## x.91 1.663e-04 3.368e-02 0.005 0.9961
## x.92 -9.690e-03 3.382e-02 -0.287 0.7748
## x.93 1.369e-02 3.364e-02 0.407 0.6845
## x.94 3.427e-03 3.351e-02 0.102 0.9187
## x.95 -1.603e-02 3.358e-02 -0.477 0.6339
## x.96 -1.445e-02 3.352e-02 -0.431 0.6669
## x.97 -8.747e-03 3.325e-02 -0.263 0.7929
## x.98 9.607e-03 3.343e-02 0.287 0.7742
## x.99 -7.369e-03 3.351e-02 -0.220 0.8262
## x.100 -1.098e-02 3.361e-02 -0.327 0.7443
## x.101 -6.421e-03 3.363e-02 -0.191 0.8488
## x.102 -1.548e-03 3.365e-02 -0.046 0.9634
## x.103 -4.849e-04 3.360e-02 -0.014 0.9885
## x.104 -1.080e-02 3.342e-02 -0.323 0.7469
## x.105 6.472e-03 3.342e-02 0.194 0.8467
## x.106 -9.149e-03 3.352e-02 -0.273 0.7852
## x.107 -1.307e-02 3.374e-02 -0.387 0.6991
## x.108 -1.739e-02 3.369e-02 -0.516 0.6064
## x.109 -1.436e-03 3.355e-02 -0.043 0.9659
## x.110 3.072e-03 3.367e-02 0.091 0.9274
## x.111 -5.785e-03 3.362e-02 -0.172 0.8636
## x.112 -1.591e-02 3.349e-02 -0.475 0.6355
## x.113 -1.609e-02 3.333e-02 -0.483 0.6299
## x.114 -4.691e-03 3.363e-02 -0.139 0.8892
## x.115 1.256e-02 3.381e-02 0.371 0.7108
## x.116 4.628e-04 3.387e-02 0.014 0.9891
## x.117 3.807e-03 3.368e-02 0.113 0.9101
## x.118 1.012e-03 3.338e-02 0.030 0.9758
## x.119 1.649e-03 3.327e-02 0.050 0.9605
## x.120 -2.167e-02 3.274e-02 -0.662 0.5090
## x.121 -9.651e-04 3.245e-02 -0.030 0.9763
## x.122 -6.911e-04 3.263e-02 -0.021 0.9831
## x.123 2.000e-02 3.284e-02 0.609 0.5433
## x.124 -7.552e-03 3.278e-02 -0.230 0.8181
## x.125 -5.877e-03 3.280e-02 -0.179 0.8580
## x.126 1.451e-02 3.288e-02 0.441 0.6596
## x.127 -9.350e-04 3.278e-02 -0.029 0.9773
## x.128 -3.218e-02 3.267e-02 -0.985 0.3260
## x.129 -1.873e-02 3.291e-02 -0.569 0.5701
## x.130 8.408e-03 3.299e-02 0.255 0.7992
## x.131 -1.217e-02 3.289e-02 -0.370 0.7119
## x.132 -8.035e-03 3.272e-02 -0.246 0.8063
## x.133 -6.742e-03 3.265e-02 -0.207 0.8366
## x.134 -1.224e-02 3.262e-02 -0.375 0.7080
## x.135 -9.837e-04 3.236e-02 -0.030 0.9758
## x.136 -1.485e-03 3.228e-02 -0.046 0.9634
## x.137 -1.691e-03 3.234e-02 -0.052 0.9584
## x.138 -7.050e-03 3.235e-02 -0.218 0.8278
## x.139 -1.638e-02 3.234e-02 -0.506 0.6133
## x.140 -1.889e-02 3.253e-02 -0.581 0.5622
## x.141 1.152e-03 3.262e-02 0.035 0.9719
## x.142 1.390e-02 3.254e-02 0.427 0.6697
## x.143 9.742e-03 3.264e-02 0.299 0.7657
## x.144 -2.692e-02 3.238e-02 -0.831 0.4070
## x.145 4.409e-03 3.195e-02 0.138 0.8904
## x.146 9.409e-04 3.189e-02 0.030 0.9765
## x.147 -3.082e-03 3.192e-02 -0.097 0.9232
## x.148 -4.517e-03 3.178e-02 -0.142 0.8872
## x.149 4.538e-03 3.177e-02 0.143 0.8866
## x.150 -1.286e-02 3.198e-02 -0.402 0.6881
## x.151 6.695e-03 3.202e-02 0.209 0.8346
## x.152 -4.569e-03 3.200e-02 -0.143 0.8866
## x.153 1.664e-04 3.216e-02 0.005 0.9959
## x.154 6.599e-03 3.213e-02 0.205 0.8375
## x.155 -7.856e-03 3.220e-02 -0.244 0.8076
## x.156 -4.836e-03 3.212e-02 -0.151 0.8805
## x.157 -2.354e-02 3.213e-02 -0.733 0.4647
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## x.465 1.618e-03 2.990e-02 0.054 0.9569
## x.466 -6.829e-03 2.995e-02 -0.228 0.8199
## x.467 -2.988e-03 2.974e-02 -0.100 0.9201
## x.468 -6.087e-03 2.932e-02 -0.208 0.8358
## x.469 -1.316e-02 2.924e-02 -0.450 0.6532
## x.470 -1.345e-02 2.920e-02 -0.461 0.6457
## x.471 -9.406e-03 2.916e-02 -0.323 0.7474
## x.472 -5.301e-03 2.924e-02 -0.181 0.8564
## x.473 -3.756e-03 2.928e-02 -0.128 0.8981
## x.474 1.277e-02 2.912e-02 0.438 0.6617
## x.475 -4.859e-03 2.905e-02 -0.167 0.8674
## x.476 -1.254e-02 2.893e-02 -0.434 0.6652
## x.477 -6.872e-03 2.885e-02 -0.238 0.8120
## x.478 -1.195e-02 2.869e-02 -0.416 0.6777
## x.479 3.320e-03 2.872e-02 0.116 0.9081
## x.480 -2.157e-03 2.868e-02 -0.075 0.9401
## x.481 1.670e-02 2.857e-02 0.584 0.5597
## x.482 -4.213e-03 2.895e-02 -0.146 0.8845
## x.483 9.303e-03 2.946e-02 0.316 0.7526
## x.484 -2.033e-02 2.911e-02 -0.698 0.4859
## x.485 5.559e-03 2.874e-02 0.193 0.8469
## x.486 1.215e-02 2.870e-02 0.423 0.6727
## x.487 3.118e-05 2.870e-02 0.001 0.9991
## x.488 -9.009e-04 2.842e-02 -0.032 0.9748
## x.489 -1.694e-02 2.842e-02 -0.596 0.5521
## x.490 -1.427e-02 2.860e-02 -0.499 0.6184
## x.491 2.825e-03 2.857e-02 0.099 0.9213
## x.492 1.892e-02 2.832e-02 0.668 0.5051
## x.493 6.617e-03 2.842e-02 0.233 0.8162
## x.494 -5.591e-03 2.832e-02 -0.197 0.8438
## x.495 -7.208e-03 2.826e-02 -0.255 0.7990
## x.496 -1.246e-02 2.834e-02 -0.440 0.6607
## x.497 -1.109e-02 2.851e-02 -0.389 0.6980
## x.498 1.187e-02 2.851e-02 0.416 0.6777
## x.499 4.173e-03 2.851e-02 0.146 0.8838
## x.500 -6.824e-03 2.860e-02 -0.239 0.8117
## x.501 1.569e-02 2.861e-02 0.548 0.5841
## x.502 -1.038e-02 2.840e-02 -0.366 0.7152
## x.503 1.556e-03 2.798e-02 0.056 0.9557
## x.504 4.436e-03 2.783e-02 0.159 0.8736
## x.505 -1.132e-02 2.786e-02 -0.406 0.6852
## x.506 -1.513e-02 2.786e-02 -0.543 0.5879
## x.507 -4.365e-03 2.806e-02 -0.156 0.8766
## x.508 9.225e-03 2.803e-02 0.329 0.7425
## x.509 6.054e-03 2.799e-02 0.216 0.8290
## x.510 -2.561e-03 2.775e-02 -0.092 0.9266
## x.511 1.441e-02 2.761e-02 0.522 0.6023
## x.512 1.019e-02 2.761e-02 0.369 0.7126
## x.513 -6.206e-03 2.763e-02 -0.225 0.8226
## x.514 -1.666e-02 2.773e-02 -0.601 0.5489
## x.515 -5.097e-03 2.785e-02 -0.183 0.8550
## x.516 2.421e-03 2.798e-02 0.087 0.9311
## x.517 8.367e-03 2.774e-02 0.302 0.7633
## x.518 1.159e-02 2.772e-02 0.418 0.6765
## x.519 1.321e-03 2.771e-02 0.048 0.9620
## x.520 -7.029e-03 2.778e-02 -0.253 0.8006
## x.521 -2.348e-03 2.760e-02 -0.085 0.9323
## x.522 5.920e-03 2.757e-02 0.215 0.8302
## x.523 3.600e-03 2.743e-02 0.131 0.8957
## x.524 1.778e-03 2.733e-02 0.065 0.9482
## x.525 2.750e-03 2.734e-02 0.101 0.9200
## x.526 -1.174e-03 2.739e-02 -0.043 0.9659
## x.527 2.401e-03 2.742e-02 0.088 0.9303
## x.528 1.609e-02 2.730e-02 0.589 0.5565
## x.529 -6.955e-03 2.736e-02 -0.254 0.7996
## x.530 -1.734e-03 2.731e-02 -0.064 0.9494
## x.531 -3.126e-03 2.721e-02 -0.115 0.9087
## x.532 3.256e-04 2.729e-02 0.012 0.9905
## x.533 1.152e-02 2.732e-02 0.422 0.6737
## x.534 8.839e-04 2.747e-02 0.032 0.9744
## x.535 1.455e-02 2.770e-02 0.525 0.6000
## x.536 7.180e-03 2.791e-02 0.257 0.7973
## x.537 -1.298e-02 2.789e-02 -0.466 0.6422
## x.538 -5.609e-03 2.781e-02 -0.202 0.8404
## x.539 1.117e-02 2.774e-02 0.403 0.6877
## x.540 -2.655e-03 2.764e-02 -0.096 0.9236
## x.541 -1.356e-02 2.743e-02 -0.494 0.6217
## x.542 -2.105e-02 2.750e-02 -0.766 0.4450
## x.543 -8.146e-03 2.747e-02 -0.297 0.7672
## x.544 7.990e-03 2.760e-02 0.289 0.7726
## x.545 6.675e-03 2.763e-02 0.242 0.8094
## x.546 -1.742e-03 2.780e-02 -0.063 0.9501
## x.547 -5.886e-03 2.805e-02 -0.210 0.8340
## x.548 1.458e-02 2.803e-02 0.520 0.6037
## x.549 -6.183e-03 2.815e-02 -0.220 0.8264
## x.550 -3.954e-03 2.810e-02 -0.141 0.8883
## x.551 1.775e-02 2.801e-02 0.634 0.5271
## x.552 -9.965e-03 2.801e-02 -0.356 0.7225
## x.553 1.459e-02 2.800e-02 0.521 0.6031
## x.554 3.091e-03 2.796e-02 0.111 0.9121
## x.555 -1.837e-03 2.786e-02 -0.066 0.9475
## x.556 1.230e-02 2.791e-02 0.441 0.6601
## x.557 -9.979e-03 2.821e-02 -0.354 0.7240
## x.558 -6.752e-03 2.837e-02 -0.238 0.8122
## x.559 6.199e-03 2.836e-02 0.219 0.8272
## x.560 -9.772e-03 2.841e-02 -0.344 0.7313
## x.561 1.451e-03 2.865e-02 0.051 0.9597
## x.562 1.048e-02 2.894e-02 0.362 0.7178
## x.563 -4.316e-04 2.902e-02 -0.015 0.9882
## x.564 1.145e-02 2.889e-02 0.396 0.6923
## x.565 6.120e-03 2.863e-02 0.214 0.8310
## x.566 8.170e-03 2.860e-02 0.286 0.7755
## x.567 -1.162e-02 2.856e-02 -0.407 0.6847
## x.568 2.029e-04 2.886e-02 0.007 0.9944
## x.569 4.179e-03 2.878e-02 0.145 0.8847
## x.570 -5.684e-03 2.872e-02 -0.198 0.8434
## x.571 -1.166e-02 2.874e-02 -0.406 0.6856
## x.572 3.423e-03 2.854e-02 0.120 0.9047
## x.573 -8.365e-03 2.842e-02 -0.294 0.7689
## x.574 1.686e-02 2.842e-02 0.593 0.5538
## x.575 8.869e-04 2.839e-02 0.031 0.9751
## x.576 1.658e-02 2.838e-02 0.584 0.5600
## x.577 2.157e-03 2.828e-02 0.076 0.9393
## x.578 5.082e-03 2.821e-02 0.180 0.8572
## x.579 -1.864e-03 2.821e-02 -0.066 0.9474
## x.580 -6.852e-03 2.822e-02 -0.243 0.8085
## x.581 1.280e-03 2.840e-02 0.045 0.9641
## x.582 -6.421e-03 2.883e-02 -0.223 0.8240
## x.583 -2.362e-02 2.970e-02 -0.795 0.4275
## x.584 4.754e-03 3.026e-02 0.157 0.8754
## x.585 1.392e-02 3.034e-02 0.459 0.6470
## x.586 1.374e-02 3.011e-02 0.456 0.6488
## x.587 1.387e-02 3.008e-02 0.461 0.6454
## x.588 -2.758e-03 3.022e-02 -0.091 0.9274
## x.589 -3.250e-04 3.047e-02 -0.011 0.9915
## x.590 6.662e-03 3.056e-02 0.218 0.8277
## x.591 4.733e-03 3.064e-02 0.154 0.8774
## x.592 -1.339e-02 3.055e-02 -0.438 0.6618
## x.593 1.323e-03 3.059e-02 0.043 0.9656
## x.594 3.913e-03 3.060e-02 0.128 0.8984
## x.595 -1.646e-02 3.080e-02 -0.534 0.5938
## x.596 -8.222e-03 3.083e-02 -0.267 0.7901
## x.597 -5.754e-03 3.088e-02 -0.186 0.8524
## x.598 4.853e-03 3.090e-02 0.157 0.8754
## x.599 -3.038e-03 3.100e-02 -0.098 0.9220
## x.600 -9.799e-03 3.115e-02 -0.315 0.7535
## x.601 -2.812e-03 3.074e-02 -0.091 0.9272
## x.602 -1.125e-02 3.060e-02 -0.368 0.7137
## x.603 5.334e-03 3.069e-02 0.174 0.8623
## x.604 -1.290e-03 3.070e-02 -0.042 0.9665
## x.605 1.560e-03 3.065e-02 0.051 0.9595
## x.606 1.498e-02 3.096e-02 0.484 0.6290
## x.607 -7.031e-03 3.125e-02 -0.225 0.8223
## x.608 -1.704e-02 3.125e-02 -0.546 0.5862
## x.609 4.279e-03 3.127e-02 0.137 0.8913
## x.610 2.148e-02 3.106e-02 0.691 0.4903
## x.611 2.333e-02 3.064e-02 0.761 0.4476
## x.612 1.419e-02 3.088e-02 0.460 0.6465
## x.613 -1.728e-02 3.092e-02 -0.559 0.5771
## x.614 5.685e-03 3.074e-02 0.185 0.8535
## x.615 5.719e-03 3.031e-02 0.189 0.8506
## x.616 6.956e-03 3.000e-02 0.232 0.8169
## x.617 -1.146e-03 2.980e-02 -0.038 0.9694
## x.618 2.106e-03 2.980e-02 0.071 0.9438
## x.619 1.095e-02 2.987e-02 0.367 0.7143
## x.620 -1.050e-02 2.979e-02 -0.353 0.7249
## x.621 5.692e-03 2.963e-02 0.192 0.8479
## x.622 5.261e-03 2.966e-02 0.177 0.8594
## x.623 2.158e-02 2.975e-02 0.725 0.4694
## x.624 -4.649e-03 2.960e-02 -0.157 0.8754
## x.625 -1.769e-02 2.955e-02 -0.599 0.5504
## x.626 5.397e-03 2.953e-02 0.183 0.8552
## x.627 1.726e-02 2.960e-02 0.583 0.5605
## x.628 8.361e-03 2.950e-02 0.283 0.7772
## x.629 3.760e-03 2.947e-02 0.128 0.8986
## x.630 1.088e-02 2.970e-02 0.366 0.7145
## x.631 -1.052e-02 2.968e-02 -0.354 0.7236
## x.632 -1.395e-02 2.928e-02 -0.476 0.6344
## x.633 -1.170e-02 2.839e-02 -0.412 0.6807
## x.634 -1.062e-02 2.819e-02 -0.377 0.7068
## x.635 -2.456e-03 2.803e-02 -0.088 0.9303
## x.636 1.387e-02 2.777e-02 0.500 0.6181
## x.637 8.769e-03 2.738e-02 0.320 0.7491
## x.638 -2.273e-02 2.763e-02 -0.823 0.4119
## x.639 -6.757e-03 2.797e-02 -0.242 0.8094
## x.640 3.412e-03 2.786e-02 0.122 0.9027
## x.641 -1.779e-03 2.802e-02 -0.064 0.9494
## x.642 -9.022e-03 2.797e-02 -0.323 0.7474
## x.643 -3.532e-03 2.793e-02 -0.126 0.8995
## x.644 7.414e-03 2.798e-02 0.265 0.7914
## x.645 -1.363e-02 2.797e-02 -0.487 0.6268
## x.646 -1.121e-02 2.770e-02 -0.405 0.6863
## x.647 8.640e-05 2.774e-02 0.003 0.9975
## x.648 9.681e-03 2.780e-02 0.348 0.7281
## x.649 8.141e-04 2.789e-02 0.029 0.9767
## x.650 -3.953e-02 2.249e-02 -1.757 0.0808 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.789 on 160 degrees of freedom
## Multiple R-squared: 0.9709, Adjusted R-squared: 0.8527
## F-statistic: 8.212 on 651 and 160 DF, p-value: < 2.2e-16
##
## AIC and BIC values for the model:
## AIC BIC
## 1 3957.241 7026.014AIC dan BIC
Sementara itu, didapatkan AIC dan BIC dari model sebesar:
AIC(model.koyck)## [1] 5725.577BIC(model.koyck)## [1] 5746.725Peramalan
Dilaksanakan peramalan data training sebagai pendugaan terhadap data testing.
#ramalan
(fore.dlm2 <- forecast(model = model.dlm2, x=test$Xt, h=114))## $forecasts
## [1] 11.31206 10.98702 12.14416 15.60685 16.93620 16.93603 12.87922 12.54258
## [9] 12.65955 16.67661 16.91704 16.91685 17.52297 15.73263 12.13883 11.00255
## [17] 12.06509 13.15564 13.35670 16.99182 17.03518 19.05521 20.57817 18.66082
## [25] 15.18932 11.85439 16.22820 18.81620 22.04180 22.85480 17.29696 14.56926
## [33] 19.29066 16.55770 17.24138 18.36060 20.15353 19.00494 19.28363 17.37932
## [41] 19.60706 20.45030 18.84035 21.81238 24.59455 23.67775 24.68985 21.86081
## [49] 20.61181 20.09093 20.77335 19.50663 24.88105 28.31558 30.95553 25.85282
## [57] 24.79303 27.10157 33.16992 35.41543 32.37798 35.65620 35.88797 34.33741
## [65] 35.04541 33.76446 34.85782 25.53758 27.24421 30.71931 32.41774 30.83419
## [73] 27.42919 28.21596 30.62852 28.59840 31.50338 29.87132 34.57387 33.80257
## [81] 33.21206 33.10488 35.48321 35.40198 35.42947 35.99700 33.79028 34.79783
## [89] 31.52644 30.53271 33.89635 35.69509 36.55309 37.07682 36.64029 39.63537
## [97] 37.07629 37.17804 37.97017 38.11849 39.50345 40.02351 40.73627 41.35786
## [105] 42.74578 36.84543 36.23000 39.71194 38.81476 41.70264 39.84441 40.81602
## [113] 39.84777 37.70464
##
## $call
## forecast.dlm(model = model.dlm2, x = test$Xt, h = 114)
##
## attr(,"class")
## [1] "forecast.dlm" "dLagM"MAPE
Dihitung MAPE dari antara data forecast dan data testing serta data training dan model. Kemudian, kedua data dibandingkan.
mape.dlm2 <- MAPE(fore.dlm2$forecast, test$Yt)
mape_train <- GoF(model.dlm2)["MAPE"]
c("MAPE_testing" = mape.dlm2,"MAPE_training" = mape_train)## $MAPE_testing
## [1] 0.2788194
##
## $MAPE_training.MAPE
## [1] 0.04285742Model Autoregressive/Dynamic Regression
Digunakan syntax ardlDlm untuk membuat model autoregresive dengan nilai lag x = 1, dan nilai lag y = 1
#MODEL AUTOREGRESSIVE
model.ardl = ardlDlm(x = train$Xt, y = train$Yt, p =1, q =1)
summary(model.ardl)##
## Time series regression with "ts" data:
## Start = 2, End = 1462
##
## Call:
## dynlm(formula = as.formula(model.text), data = data, start = 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.7218 -0.6964 0.1028 0.7305 6.2173
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.270489 0.256393 4.955 8.07e-07 ***
## X.t -0.136302 0.004090 -33.322 < 2e-16 ***
## X.1 0.126140 0.004240 29.747 < 2e-16 ***
## Y.1 0.974448 0.005432 179.375 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.249 on 1457 degrees of freedom
## Multiple R-squared: 0.9711, Adjusted R-squared: 0.9711
## F-statistic: 1.633e+04 on 3 and 1457 DF, p-value: < 2.2e-16AIC dan BIC
Didapatkan AIC dan BIC dari model sebesar:
AIC(model.ardl)## [1] 4801.104BIC(model.ardl)## [1] 4827.538Peramalan
Dilaksanakan peramalan data training sebagai pendugaan terhadap data testing.
#ramalan
(fore.ardl <- forecast(model = model.ardl, x=test$Xt,h=114))## $forecasts
## [1] 11.92475 13.19657 12.70902 14.43626 13.95888 13.51494 11.38298 13.06620
## [9] 13.52431 14.83635 14.97390 14.79259 15.95222 15.14936 15.51163 14.84622
## [17] 14.12307 15.00750 15.53334 16.82493 16.39081 15.79028 15.91523 17.07936
## [25] 16.97170 14.14215 16.11015 15.40492 15.57623 16.19317 16.47377 16.19320
## [33] 17.89738 16.44823 16.58323 16.63709 17.77919 18.69386 18.20503 18.31865
## [41] 17.96241 19.10462 18.36764 18.91364 19.22443 19.03625 20.62665 19.75066
## [49] 18.99651 19.69766 20.60636 19.47283 21.21570 23.30587 23.88589 22.76542
## [57] 21.77343 21.97317 23.00334 23.67125 22.98750 24.72086 24.84259 25.29562
## [65] 25.33775 25.65820 24.32103 22.20648 22.38774 23.39950 23.97283 25.04919
## [73] 24.22416 24.51901 25.36308 24.05432 25.92889 25.25251 25.02087 25.86886
## [81] 26.52560 26.01357 27.76077 27.70628 28.17876 28.14434 28.02487 29.00653
## [89] 28.86396 28.91770 29.40767 29.75720 30.46956 30.37065 28.61485 31.41275
## [97] 31.08819 31.32886 32.62480 33.07820 33.53483 32.64355 32.39165 31.37817
## [105] 32.44324 32.05665 31.58825 33.17537 33.75769 33.46041 31.97786 31.82324
## [113] 33.69139 33.87021
##
## $call
## forecast.ardlDlm(model = model.ardl, x = test$Xt, h = 114)
##
## attr(,"class")
## [1] "forecast.ardlDlm" "dLagM"#Akurasi testing
mape.ardl <- MAPE(fore.ardl$forecasts, test$Yt)
#Akurasi data training
mape_train <- GoF(model.ardl)["MAPE"]
c("MAPE_testing" = mape.ardl, "MAPE_training" = mape_train) ## $MAPE_testing
## [1] 0.1220792
##
## $MAPE_training.MAPE
## [1] 0.04222255Penentuan Lag Optimum
Digunakna fungsi ardlBoundOrders untuk menentukan for nilai lag optimum dalam model autoregressive
ardlBoundOrders(data = data.frame(data), formula = Yt ~ Xt)## $p
## Xt
## 1 4
##
## $q
## [1] 15
##
## $Stat.table
## q = 1 q = 2 q = 3 q = 4 q = 5 q = 6 q = 7 q = 8
## p = 1 5223.217 5211.007 5189.278 5182.436 5172.609 5166.250 5162.958 5154.423
## p = 2 5219.151 5188.993 5172.795 5166.931 5157.776 5152.441 5149.223 5140.990
## p = 3 5187.419 5187.419 5155.695 5152.130 5144.025 5138.806 5136.212 5128.058
## p = 4 5152.696 5154.681 5154.681 5150.529 5143.672 5138.673 5136.112 5127.917
## p = 5 5153.613 5152.585 5149.404 5149.404 5144.741 5140.174 5137.687 5129.666
## p = 6 5154.942 5149.371 5141.774 5143.771 5143.771 5139.153 5137.246 5129.479
## p = 7 5152.980 5145.930 5134.796 5136.634 5138.632 5138.632 5138.876 5131.247
## p = 8 5149.276 5140.069 5126.202 5126.939 5127.982 5128.591 5128.591 5124.947
## p = 9 5141.508 5132.056 5118.446 5119.259 5119.921 5120.763 5121.845 5121.845
## p = 10 5132.247 5121.789 5107.697 5108.488 5109.007 5109.320 5110.841 5112.739
## p = 11 5134.875 5122.972 5107.530 5107.894 5107.994 5107.695 5109.669 5110.583
## p = 12 5144.593 5129.415 5111.614 5110.843 5109.873 5108.420 5110.344 5109.329
## p = 13 5148.172 5132.296 5113.326 5112.021 5110.878 5108.947 5110.798 5109.302
## p = 14 5148.628 5133.113 5113.784 5112.107 5110.643 5108.577 5110.363 5108.656
## p = 15 5149.312 5133.492 5113.861 5111.848 5109.646 5107.279 5108.835 5106.620
## q = 9 q = 10 q = 11 q = 12 q = 13 q = 14 q = 15
## p = 1 5145.935 5136.347 5134.315 5130.707 5129.409 5128.840 5120.189
## p = 2 5132.787 5123.270 5121.325 5117.716 5116.681 5116.178 5107.683
## p = 3 5119.634 5111.347 5109.194 5105.608 5104.914 5104.347 5095.587
## p = 4 5119.513 5111.333 5109.331 5105.618 5104.987 5104.458 5095.374
## p = 5 5121.383 5113.215 5111.222 5107.552 5106.936 5106.410 5097.344
## p = 6 5121.087 5112.920 5110.941 5107.317 5106.741 5106.217 5097.295
## p = 7 5122.924 5114.861 5112.869 5109.247 5108.669 5108.158 5099.241
## p = 8 5118.128 5110.525 5108.872 5105.071 5104.514 5104.005 5095.680
## p = 9 5119.193 5111.887 5110.263 5106.606 5106.088 5105.583 5097.222
## p = 10 5112.739 5113.602 5112.000 5108.373 5107.855 5107.353 5098.994
## p = 11 5111.980 5111.980 5113.974 5110.328 5109.801 5109.287 5100.905
## p = 12 5109.073 5110.326 5110.326 5112.037 5111.572 5111.074 5102.782
## p = 13 5108.566 5109.982 5111.724 5111.724 5113.557 5113.069 5104.781
## p = 14 5107.752 5109.144 5110.888 5112.882 5112.882 5114.880 5106.197
## p = 15 5105.342 5106.548 5108.438 5110.328 5112.183 5112.183 5104.190
##
## $min.Stat
## [1] 5095.374Dengan nilai P dan Q sama dengan 15, dibuat 4 model DLM dan ARDL dengan library dynlm sebagai berikut:
#PEMODELAN DLM dan ARDL dengan library dynlm
#sama dengan model dlm p=1
cons_lm1 <- dynlm(Yt ~ Xt+L(Xt),data = train.ts)
#sama dengan model ardl p=0 q=1
cons_lm2 <- dynlm(Yt ~ Xt+L(Yt),data = train.ts)
#sama dengan ardl p=1 q=1
cons_lm3 <- dynlm(Yt ~ Xt+L(Xt)+L(Yt),data = train.ts)
#sama dengan dlm p=2
cons_lm4 <- dynlm(Yt ~ Xt+L(Xt)+L(Xt,2),data = train.ts)Ringkasan dari model-model berikut yakni:
summary(cons_lm1)##
## Time series regression with "ts" data:
## Start = 2, End = 1462
##
## Call:
## dynlm(formula = Yt ~ Xt + L(Xt), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.0061 -4.8229 -0.0874 5.6174 12.3816
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 41.26800 0.60783 67.894 < 2e-16 ***
## Xt -0.18283 0.01961 -9.325 < 2e-16 ***
## L(Xt) -0.07662 0.01963 -3.903 9.93e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.997 on 1458 degrees of freedom
## Multiple R-squared: 0.3332, Adjusted R-squared: 0.3323
## F-statistic: 364.3 on 2 and 1458 DF, p-value: < 2.2e-16summary(cons_lm2)##
## Time series regression with "ts" data:
## Start = 2, End = 1462
##
## Call:
## dynlm(formula = Yt ~ Xt + L(Yt), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.0376 -0.8761 0.0372 0.9540 6.2722
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.909006 0.304880 12.82 <2e-16 ***
## Xt -0.035529 0.002905 -12.23 <2e-16 ***
## L(Yt) 0.931372 0.006636 140.36 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.583 on 1458 degrees of freedom
## Multiple R-squared: 0.9536, Adjusted R-squared: 0.9535
## F-statistic: 1.497e+04 on 2 and 1458 DF, p-value: < 2.2e-16summary(cons_lm3)##
## Time series regression with "ts" data:
## Start = 2, End = 1462
##
## Call:
## dynlm(formula = Yt ~ Xt + L(Xt) + L(Yt), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.7218 -0.6964 0.1028 0.7305 6.2173
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.270489 0.256393 4.955 8.07e-07 ***
## Xt -0.136302 0.004090 -33.322 < 2e-16 ***
## L(Xt) 0.126140 0.004240 29.747 < 2e-16 ***
## L(Yt) 0.974448 0.005432 179.375 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.249 on 1457 degrees of freedom
## Multiple R-squared: 0.9711, Adjusted R-squared: 0.9711
## F-statistic: 1.633e+04 on 3 and 1457 DF, p-value: < 2.2e-16summary(cons_lm4)##
## Time series regression with "ts" data:
## Start = 3, End = 1462
##
## Call:
## dynlm(formula = Yt ~ Xt + L(Xt) + L(Xt, 2), data = train.ts)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.109 -4.670 -0.306 5.541 12.179
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 41.858693 0.618846 67.640 < 2e-16 ***
## Xt -0.176868 0.019496 -9.072 < 2e-16 ***
## L(Xt) -0.002206 0.025355 -0.087 0.931
## L(Xt, 2) -0.089981 0.019515 -4.611 4.36e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.952 on 1456 degrees of freedom
## Multiple R-squared: 0.3415, Adjusted R-squared: 0.3401
## F-statistic: 251.6 on 3 and 1456 DF, p-value: < 2.2e-16Sementara itu, didapatkan jumlah kuadrat galat yakni:
deviance(cons_lm1)## [1] 52440.98deviance(cons_lm2)## [1] 3651.525deviance(cons_lm3)## [1] 2271.808deviance(cons_lm4)## [1] 51575.73Uji Diagnostik Model
Uji Non Autokorelasi
Uji model
if(require("lmtest"))encomptest(cons_lm1, cons_lm2)## Encompassing test
##
## Model 1: Yt ~ Xt + L(Xt)
## Model 2: Yt ~ Xt + L(Yt)
## Model E: Yt ~ Xt + L(Xt) + L(Yt)
## Res.Df Df F Pr(>F)
## M1 vs. ME 1457 -1 32175.47 < 2.2e-16 ***
## M2 vs. ME 1457 -1 884.87 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Uji Durbin-Watson
dwtest(cons_lm1)##
## Durbin-Watson test
##
## data: cons_lm1
## DW = 0.061873, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm2)##
## Durbin-Watson test
##
## data: cons_lm2
## DW = 2.1257, p-value = 0.9908
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm3)##
## Durbin-Watson test
##
## data: cons_lm3
## DW = 2.0043, p-value = 0.5142
## alternative hypothesis: true autocorrelation is greater than 0dwtest(cons_lm4)##
## Durbin-Watson test
##
## data: cons_lm4
## DW = 0.05825, p-value < 2.2e-16
## alternative hypothesis: true autocorrelation is greater than 0Uji Heterogenitas
Uji Breusch-Pagan
bptest(cons_lm1)##
## studentized Breusch-Pagan test
##
## data: cons_lm1
## BP = 244.48, df = 2, p-value < 2.2e-16bptest(cons_lm2)##
## studentized Breusch-Pagan test
##
## data: cons_lm2
## BP = 24.477, df = 2, p-value = 4.84e-06bptest(cons_lm3)##
## studentized Breusch-Pagan test
##
## data: cons_lm3
## BP = 8.3324, df = 3, p-value = 0.03962bptest(cons_lm4)##
## studentized Breusch-Pagan test
##
## data: cons_lm4
## BP = 301.05, df = 3, p-value < 2.2e-16Uji Normalitas
Uji Shapiro-Wilk
shapiro.test(residuals(cons_lm1))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm1)
## W = 0.96906, p-value < 2.2e-16shapiro.test(residuals(cons_lm2))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm2)
## W = 0.9858, p-value = 8.871e-11shapiro.test(residuals(cons_lm3))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm3)
## W = 0.96764, p-value < 2.2e-16shapiro.test(residuals(cons_lm4))##
## Shapiro-Wilk normality test
##
## data: residuals(cons_lm4)
## W = 0.9698, p-value < 2.2e-16Perbandingan Akurasi
Dibuat perbandingan akurasi antara model koyck, kedua model DLM, dan model ARDL
akurasi <- matrix(c(mape.koyck, mape.dlm, mape.dlm2, mape.ardl))
row.names(akurasi) <- c("Koyck","DLM 1","DLM 2","Autoregressive")
colnames(akurasi) <- c("MAPE")
akurasi## MAPE
## Koyck 0.2420774
## DLM 1 0.2740091
## DLM 2 0.2788194
## Autoregressive 0.1220792#Plot
par(mfrow=c(1,1))
plot(test$Xt, test$Yt, col="black", ylim=c(0,40), ylab = "Suhu", xlab = "Kelembapan")
abline(lm(test$Yt~test$Xt))
points(test$Xt, fore.koyck$forecasts,col="red")
abline(lm(fore.koyck$forecasts~test$Xt), col = "red")
points(test$Xt, fore.dlm$forecasts,col="blue")
abline(lm(fore.dlm$forecasts~test$Xt), col = "blue")
points(test$Xt, fore.dlm2$forecasts,col="orange")
abline(lm(fore.dlm2$forecasts~test$Xt), col = "orange")
points(test$Xt, fore.ardl$forecasts,col="green")
abline(lm(fore.ardl$forecasts~test$Xt), col = "green")
legend("topleft",c("aktual", "koyck","DLM 1","DLM 2", "autoregressive"), lty=1, col=c("black","red","blue","orange","green"), cex=0.8)
Terlihat bahwa autoregressive memiliki garis regresi yang paling mendekati dengan garis aktual.
Kesimpulan
Di antara model-model yang telah dibuat, didapatkan bahwa MAPE terkecil dimiliki oleh model autoregressive, yang dapat dilihat pada grafik memiliki garis paling dekat dengan garis aktual.
Sumber data: https://www.kaggle.com/datasets/sumanthvrao/daily-climate-time-series-data?resource=download