Transjakarta
Maulana Ahsan Fadillah
2023-11-26
lapply(c("dplyr","readxl","forecast","TTR","graphics","smooth","Mcomp","knitr","tseries",
"readr","TSA","ggplot2","MLmetrics","cowplot","gridExtra","gtable","grid","MASS",
"lmtest","GGally", "lubridate", "caret", "tseries", "tidyverse"), library, character.only = T)[[1]]##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## fitted.Arima forecast
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## MAE## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ tibble 3.1.8 ✔ stringr 1.5.0
## ✔ tidyr 1.2.1 ✔ forcats 0.5.2
## ✔ purrr 0.3.5
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## [7] "methods" "base"library(forecast)
df = read_xlsx('C:/Users/User/Downloads/transjakarta.xlsx')
data2 = log(df$jumlah_penumpang)
data2## [1] 15.98315 15.84764 16.05450 15.99394 16.01666 15.97798 15.84576 15.99056
## [9] 15.95034 15.98233 15.95758 15.95750 15.95687 15.91303 16.01367 16.02729
## [17] 16.12029 16.13874 16.03085 16.26482 16.26063 16.32560 16.30448 16.30435
## [25] 16.28332 16.18019 16.33996 16.25726 16.30975 16.11033 16.29947 16.35696
## [33] 16.31470 16.41047 16.39616 16.37732 16.42954 16.32791 16.48530 16.50934
## [41] 16.49848 16.29646 16.59809 16.69724 16.70136 16.75402 16.71063 16.72194
## [49] 16.73473 16.66313 16.83519 16.80522 16.81111 16.72296 16.96402 16.97368
## [57] 17.01629 17.09415 17.06536 17.09271 17.07603 17.01717 16.62855 14.73414
## [65] 14.66134 15.27831 15.93798 15.93746 15.93772 15.99542 16.02307 16.07617
## [73] 16.09762 16.05425 16.26609 16.26864 16.19722 16.21764 15.70002 15.68704
## [81] 15.95928 16.18260 16.33469 16.24407data.ts<-ts(data2, frequency = 12, start = c(2015,1), end = c(2021,12))
# Box-Cox
#lambda <- BoxCox.lambda(data.ts)
# data.ts <- BoxCox(data.ts, lambda)
#Plot semua data
plot(data.ts,xlab ="Bulan", ylab = "Jumlah Penumpang", col="black", main = "Plot Deret Waktu Data")
points(data.ts)
data.train <- ts(data.ts[1:63])
data.test <- ts(data.ts[64:84])
#Time Series Data
training.ts<-ts(data.train,frequency=12, start = c(2015,1), end = c(2020,3))
testing.ts<-ts(data.test,frequency=12, start = c(2020,4), end = c(2021,12))#Plot Data
plot(training.ts, xlab ="Periode", ylab = "Jumlah Kedatangan", col="red", main = "Plot Data Training")
points(training.ts)
plot(testing.ts, xlab ="Periode", ylab = "Jumlah Kedatangan", col="red", main = "Plot Data Testing")
points(testing.ts)
## Plot Data Training dan testing Inflasi
ts.plot(data.ts, xlab = "Periode", ylab ="Jumlah Kedatangan",
main = "Plot Deret Waktu Data Jumlah Penumpang Transjakarta")
lines(training.ts, col = "blue")
lines(testing.ts, col="Red")
legend("bottomleft",c("Data Training","Data Testing"),
lty=1, col=c("blue","red"), cex=0.8)
abline(v=2020.25, col=c("black"), lty=1, lwd=1)
acf(data.train, lag.max = 24, main = "Plot ACF")
pacf(data.train, lag.max = 24, main = "Plot PACF")
adf.test(data.train)##
## Augmented Dickey-Fuller Test
##
## data: data.train
## Dickey-Fuller = -2.9329, Lag order = 3, p-value = 0.1971
## alternative hypothesis: stationary# DIFFERENCING
data.dif<-diff(data.train,differences = 1)
plot.ts(ts(data.dif,frequency=12, start = c(2015,1), end = c(2021,12)),lty=1,xlab = "Periode", ylab= "Data Inflasi Pembedaan 1", main="Plot Differencing Data Inflasi")
adf.test(data.dif)##
## Augmented Dickey-Fuller Test
##
## data: data.dif
## Dickey-Fuller = -3.491, Lag order = 3, p-value = 0.04983
## alternative hypothesis: stationaryacf(data.dif, lag.max = 36, main = "Plot ACF Setelah Differencing satu kali")
pacf(data.dif, lag.max = 48, main = "Plot PACF Setelah Differencing satu kali")
eacf(data.dif)## AR/MA
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13
## 0 x o o o o o o o o o o x o o
## 1 o o o o o o o o o o o x o o
## 2 x o o o o o o o o o o x o o
## 3 x o o o o o o o o o o x o o
## 4 o o o o o o o o o o o x o o
## 5 x o o o o o o o o o o x o o
## 6 o x o o o o o o o o o o o o
## 7 o x o o o o o o o o o o o oARIMA(0,1,1) ARIMA(0,1,2) ARIMA(0,1,3) ARIMA(1,1,0) ARIMA(1,1,1) ARIMA(1,1,2) ARIMA(1,1,3) ARIMA(2,1,1) ARIMA(2,1,2) ARIMA(2,1,3) ARIMA(3,1,1) ARIMA(3,1,2) ARIMA(3,1,3)
auto.arima(data.dif)## Series: data.dif
## ARIMA(0,0,1) with non-zero mean
##
## Coefficients:
## ma1 mean
## -0.4811 0.0145
## s.e. 0.1530 0.0071
##
## sigma^2 = 0.01115: log likelihood = 52.29
## AIC=-98.57 AICc=-98.16 BIC=-92.19model <- Arima(data.dif, order=c(0,0,1), method="ML")
model1 <- Arima(data.dif, order=c(0,0,2), method="ML")
model2 <- Arima(data.dif, order=c(0,0,3), method="ML")
model3 <- Arima(data.dif, order=c(1,0,0), method="ML")
model4 <- Arima(data.dif, order=c(1,0,1), method="ML")
model5 <- Arima(data.dif, order=c(1,0,2), method="ML")
model6 <- Arima(data.dif, order=c(1,0,3), method="ML")
model7 <- Arima(data.dif, order=c(2,0,1), method="ML")
model8 <- Arima(data.dif, order=c(2,0,2), method="ML")
model9 <- Arima(data.dif, order=c(2,0,3), method="ML")
model10 <- Arima(data.dif, order=c(3,0,1), method="ML")
model11 <- Arima(data.dif, order=c(3,0,2), method="ML")
model12 <- Arima(data.dif, order=c(3,0,3), method="ML")summary(model)## Series: data.dif
## ARIMA(0,0,1) with non-zero mean
##
## Coefficients:
## ma1 mean
## -0.4811 0.0145
## s.e. 0.1530 0.0071
##
## sigma^2 = 0.01115: log likelihood = 52.29
## AIC=-98.57 AICc=-98.16 BIC=-92.19
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.0006470904 0.1038929 0.07376048 978.0486 1038.697 0.538449
## ACF1
## Training set -0.001874654coeftest(model)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 -0.4811094 0.1529869 -3.1448 0.001662 **
## intercept 0.0144688 0.0070803 2.0435 0.041000 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model1)## Series: data.dif
## ARIMA(0,0,2) with non-zero mean
##
## Coefficients:
## ma1 ma2 mean
## -0.4813 0.004 0.0144
## s.e. 0.1535 0.172 0.0073
##
## sigma^2 = 0.01134: log likelihood = 52.29
## AIC=-96.57 AICc=-95.87 BIC=-88.07
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.0006476582 0.1038943 0.0737577 980.2098 1041.306 0.5384286
## ACF1
## Training set -0.001116443coeftest(model1)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 -0.4813236 0.1535053 -3.1356 0.001715 **
## ma2 0.0039747 0.1720249 0.0231 0.981566
## intercept 0.0144373 0.0072661 1.9869 0.046930 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model2)## Series: data.dif
## ARIMA(0,0,3) with non-zero mean
##
## Coefficients:
## ma1 ma2 ma3 mean
## -0.5800 -0.0769 -0.3431 0.0184
## s.e. 0.1635 0.1658 0.1283 0.0012
##
## sigma^2 = 0.01065: log likelihood = 53.2
## AIC=-96.4 AICc=-95.33 BIC=-85.76
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.01174072 0.09983093 0.07413183 1446.955 1909.065 0.5411598
## ACF1
## Training set 0.03368266coeftest(model2)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 -0.5800339 0.1635496 -3.5465 0.0003903 ***
## ma2 -0.0768714 0.1658073 -0.4636 0.6429208
## ma3 -0.3430888 0.1283104 -2.6739 0.0074975 **
## intercept 0.0184438 0.0012004 15.3649 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model3)## Series: data.dif
## ARIMA(1,0,0) with non-zero mean
##
## Coefficients:
## ar1 mean
## -0.4058 0.0130
## s.e. 0.1336 0.0095
##
## sigma^2 = 0.01132: log likelihood = 51.87
## AIC=-97.74 AICc=-97.32 BIC=-91.35
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.0007694027 0.1046679 0.07439282 993.7082 1077.506 0.543065
## ACF1
## Training set -0.02347896coeftest(model3)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.4057506 0.1335927 -3.0372 0.002388 **
## intercept 0.0129731 0.0095205 1.3627 0.172990
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model4)## Series: data.dif
## ARIMA(1,0,1) with non-zero mean
##
## Coefficients:
## ar1 ma1 mean
## -0.0166 -0.4651 0.0144
## s.e. 0.5208 0.5281 0.0074
##
## sigma^2 = 0.01134: log likelihood = 52.29
## AIC=-96.57 AICc=-95.87 BIC=-88.07
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.00063722 0.1038953 0.07375324 982.1883 1043.767 0.5383961
## ACF1
## Training set -0.0002651442coeftest(model4)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.0165633 0.5207727 -0.0318 0.97463
## ma1 -0.4651211 0.5280534 -0.8808 0.37841
## intercept 0.0144019 0.0074363 1.9367 0.05278 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model5)## Series: data.dif
## ARIMA(1,0,2) with non-zero mean
##
## Coefficients:
## ar1 ma1 ma2 mean
## -0.5276 0.0391 -0.2022 0.0142
## s.e. 0.7482 0.7564 0.4002 0.0075
##
## sigma^2 = 0.01152: log likelihood = 52.34
## AIC=-94.68 AICc=-93.6 BIC=-84.04
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.0006672126 0.1038164 0.07374 1041.672 1112.115 0.5382995
## ACF1
## Training set 0.01002608coeftest(model5)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.5276473 0.7482448 -0.7052 0.48070
## ma1 0.0390563 0.7564460 0.0516 0.95882
## ma2 -0.2022184 0.4001846 -0.5053 0.61334
## intercept 0.0142398 0.0074653 1.9075 0.05646 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model6)## Series: data.dif
## ARIMA(1,0,3) with non-zero mean
##
## Coefficients:
## ar1 ma1 ma2 ma3 mean
## 0.691 -1.2696 0.3894 -0.1198 0.0178
## s.e. 0.230 0.2707 0.2615 0.1576 0.0019
##
## sigma^2 = 0.01059: log likelihood = 54.29
## AIC=-96.57 AICc=-95.04 BIC=-83.81
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.007186347 0.09868318 0.07103453 1483.329 1547.874 0.5185496
## ACF1
## Training set 0.004768468coeftest(model6)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.6909591 0.2300028 3.0041 0.002663 **
## ma1 -1.2696124 0.2706797 -4.6905 2.726e-06 ***
## ma2 0.3894380 0.2614915 1.4893 0.136410
## ma3 -0.1197902 0.1576058 -0.7601 0.447217
## intercept 0.0177728 0.0018617 9.5466 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model7)## Series: data.dif
## ARIMA(2,0,1) with non-zero mean
##
## Coefficients:
## ar1 ar2 ma1 mean
## 0.4146 0.2381 -1.000 0.0177
## s.e. 0.1464 0.1453 0.048 0.0019
##
## sigma^2 = 0.01041: log likelihood = 54.31
## AIC=-98.61 AICc=-97.54 BIC=-87.98
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.006941607 0.09870595 0.07114576 1479.191 1546.267 0.5193616
## ACF1
## Training set 0.01176516coeftest(model7)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.4145611 0.1464177 2.8314 0.004635 **
## ar2 0.2380787 0.1453428 1.6381 0.101411
## ma1 -1.0000000 0.0480123 -20.8280 < 2.2e-16 ***
## intercept 0.0177064 0.0018985 9.3264 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model8)## Series: data.dif
## ARIMA(2,0,2) with non-zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2 mean
## 0.2584 0.3202 -0.8359 -0.1639 0.0178
## s.e. 0.5653 0.3094 0.5879 0.5857 0.0018
##
## sigma^2 = 0.01057: log likelihood = 54.34
## AIC=-96.69 AICc=-95.16 BIC=-83.92
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.007196214 0.09859786 0.07142285 1502.572 1575.874 0.5213843
## ACF1
## Training set 0.006837753coeftest(model8)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.2583955 0.5652661 0.4571 0.6476
## ar2 0.3202129 0.3094055 1.0349 0.3007
## ma1 -0.8359356 0.5879301 -1.4218 0.1551
## ma2 -0.1638972 0.5857315 -0.2798 0.7796
## intercept 0.0177774 0.0018454 9.6333 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model9)## Series: data.dif
## ARIMA(2,0,3) with non-zero mean
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3 mean
## 0.2618 0.3148 -0.8383 -0.1561 -0.0056 0.0178
## s.e. 0.6452 0.4753 0.6581 0.8114 0.2772 0.0019
##
## sigma^2 = 0.01076: log likelihood = 54.34
## AIC=-94.69 AICc=-92.61 BIC=-79.8
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.007207981 0.09858895 0.07141248 1499.05 1572.595 0.5213086
## ACF1
## Training set 0.006057755coeftest(model9)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.2618493 0.6452077 0.4058 0.6849
## ar2 0.3147763 0.4752605 0.6623 0.5078
## ma1 -0.8382652 0.6580790 -1.2738 0.2027
## ma2 -0.1560986 0.8113665 -0.1924 0.8474
## ma3 -0.0055903 0.2771593 -0.0202 0.9839
## intercept 0.0177810 0.0018597 9.5614 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model10)## Series: data.dif
## ARIMA(3,0,1) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1 mean
## 0.4233 0.2535 -0.0415 -1.0000 0.0178
## s.e. 0.1497 0.1563 0.1562 0.0489 0.0019
##
## sigma^2 = 0.01057: log likelihood = 54.34
## AIC=-96.68 AICc=-95.16 BIC=-83.92
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.00723574 0.09858138 0.07134105 1491.254 1564.862 0.5207872
## ACF1
## Training set 0.006289166coeftest(model10)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.4233245 0.1497170 2.8275 0.004691 **
## ar2 0.2534887 0.1562520 1.6223 0.104738
## ar3 -0.0415071 0.1562355 -0.2657 0.790493
## ma1 -0.9999986 0.0488781 -20.4590 < 2.2e-16 ***
## intercept 0.0177894 0.0018517 9.6073 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model11)## Series: data.dif
## ARIMA(3,0,2) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 mean
## 0.2946 0.3063 -0.0103 -0.8712 -0.1288 0.0178
## s.e. 2.1692 0.9042 0.5497 2.1623 2.1616 0.0019
##
## sigma^2 = 0.01076: log likelihood = 54.34
## AIC=-94.69 AICc=-92.61 BIC=-79.8
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.007191589 0.09858895 0.07141256 1498.963 1572.465 0.5213092
## ACF1
## Training set 0.006204726coeftest(model11)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.2945631 2.1692247 0.1358 0.8920
## ar2 0.3063095 0.9042278 0.3388 0.7348
## ar3 -0.0102628 0.5497105 -0.0187 0.9851
## ma1 -0.8711709 2.1623050 -0.4029 0.6870
## ma2 -0.1287918 2.1616164 -0.0596 0.9525
## intercept 0.0177784 0.0018599 9.5587 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model12)## Series: data.dif
## ARIMA(3,0,3) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 ma3 mean
## -1.0538 0.1836 0.6339 0.6839 -0.6839 -1.0000 0.0177
## s.e. 0.1272 0.2111 0.1297 0.0917 0.0932 0.0904 0.0018
##
## sigma^2 = 0.008958: log likelihood = 58.44
## AIC=-100.88 AICc=-98.17 BIC=-83.87
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.006359759 0.08914422 0.06605995 1568.965 1720.922 0.4822353
## ACF1
## Training set 0.03893473coeftest(model12)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -1.0538331 0.1272500 -8.2816 < 2.2e-16 ***
## ar2 0.1836456 0.2110524 0.8701 0.3842
## ar3 0.6338810 0.1297301 4.8862 1.028e-06 ***
## ma1 0.6838572 0.0917202 7.4559 8.925e-14 ***
## ma2 -0.6838524 0.0931722 -7.3397 2.141e-13 ***
## ma3 -0.9999937 0.0903916 -11.0629 < 2.2e-16 ***
## intercept 0.0177425 0.0018007 9.8532 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1ARIMA(0,1,1) ARIMA(0,1,2) ARIMA(0,1,3) ARIMA(1,1,0) ARIMA(1,1,1) ARIMA(1,1,2) ARIMA(1,1,3) ARIMA(2,1,1) ARIMA(2,1,2) ARIMA(2,1,3) ARIMA(3,1,1) ARIMA(3,1,2) ARIMA(3,1,3)
#Overfitting
model12b <- Arima(data.dif, order=c(4,0,3), method="ML")
model12c <- Arima(data.dif, order=c(3,0,4), method = "ML")summary(model12b)## Series: data.dif
## ARIMA(4,0,3) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ar4 ma1 ma2 ma3 mean
## -1.0170 0.1957 0.5684 -0.0628 0.6860 -0.6860 -1.0000 0.0178
## s.e. 0.1576 0.2122 0.2115 0.1611 0.0933 0.0949 0.0931 0.0017
##
## sigma^2 = 0.009046: log likelihood = 58.52
## AIC=-99.04 AICc=-95.57 BIC=-79.89
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.006810885 0.08876458 0.06581016 1534.649 1686.456 0.4804119
## ACF1
## Training set 0.02214229coeftest(model12b)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -1.0169676 0.1575784 -6.4537 1.091e-10 ***
## ar2 0.1956820 0.2121533 0.9224 0.356340
## ar3 0.5683667 0.2114786 2.6876 0.007197 **
## ar4 -0.0628191 0.1610932 -0.3900 0.696570
## ma1 0.6860261 0.0932989 7.3530 1.938e-13 ***
## ma2 -0.6860227 0.0948837 -7.2301 4.825e-13 ***
## ma3 -0.9999889 0.0931261 -10.7380 < 2.2e-16 ***
## intercept 0.0178463 0.0017233 10.3556 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model12c)## Series: data.dif
## ARIMA(3,0,4) with non-zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1 ma2 ma3 ma4 mean
## -0.6747 0.2762 0.5270 0.2544 -0.6269 -0.8754 0.2479 0.0178
## s.e. 0.3057 0.2797 0.1566 0.3406 0.1579 0.1728 0.3144 0.0019
##
## sigma^2 = 0.009422: log likelihood = 57.57
## AIC=-97.15 AICc=-93.69 BIC=-78
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.006464599 0.09058627 0.06930584 2063.158 2171.524 0.5059302
## ACF1
## Training set 0.01357103coeftest(model12c)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.674698 0.305692 -2.2071 0.0273059 *
## ar2 0.276248 0.279725 0.9876 0.3233634
## ar3 0.527050 0.156642 3.3647 0.0007663 ***
## ma1 0.254411 0.340615 0.7469 0.4551138
## ma2 -0.626866 0.157910 -3.9698 7.194e-05 ***
## ma3 -0.875449 0.172783 -5.0667 4.047e-07 ***
## ma4 0.247917 0.314448 0.7884 0.4304506
## intercept 0.017757 0.001869 9.5009 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tetap menggunakan model -> ARIMA(3,0,3)
#Diagnostik Sisaan
sisaan <- model12$residuals
#kenormalan
shapiro.test(sisaan)##
## Shapiro-Wilk normality test
##
## data: sisaan
## W = 0.9439, p-value = 0.006859#sisaan saling bebas
Box.test(sisaan, type = "Ljung")##
## Box-Ljung test
##
## data: sisaan
## X-squared = 0.098609, df = 1, p-value = 0.7535data ga normal (bisa di abaikan) data gaada autokol
# Forecasting
ramalan <- forecast(Arima(data.ts, order=c(3,1,3),method="ML",include.drift = TRUE),h = length(data.test))
data.ramalan <- ramalan$mean
data.ramalan.ts <- ts(data.ramalan, start = 2015, frequency = 12)
plot(ramalan,col="black",col.sub ="black",col.axis="black",
col.lab="black",col.main="black",lwd=2)
box(col="black",lwd=2)
hasilforecast<-matrix(data=c(data.ramalan[1:12]), nrow = 12, ncol = 1)
colnames(hasilforecast)<-c("Hasil Forecast")
head(hasilforecast)## Hasil Forecast
## [1,] 16.24902
## [2,] 16.28519
## [3,] 16.31182
## [4,] 16.31766
## [5,] 16.32478
## [6,] 16.33799hasilforecast <- matrix(data=exp(data.ramalan[1:12]), nrow=12, ncol=1)
colnames(hasilforecast) <- c("Hasil Forecast")
# Menampilkan baris pertama dari hasil forecast yang telah dikembalikan ke skala asli
hasilforecast## Hasil Forecast
## [1,] 11398849
## [2,] 11818694
## [3,] 12137584
## [4,] 12208745
## [5,] 12295926
## [6,] 12459493
## [7,] 12573797
## [8,] 12626475
## [9,] 12686542
## [10,] 12759114
## [11,] 12813773
## [12,] 12853363# Contoh tanggal dalam format "dd/mm/yyyy"
start_date <- as.Date("01/01/2022", format="%d/%m/%Y")
# Membuat vektor tanggal untuk forecast dengan asumsi bahwa forecast dimulai pada bulan berikutnya
forecast_dates <- seq(from=start_date, length.out=24, by="month")
# Menambahkan vektor tanggal ke hasil forecast
hasilforecast <- matrix(data=exp(data.ramalan[1:24]), nrow=24, ncol=1)
colnames(hasilforecast) <- c("Hasil Forecast")
hasilforecast <- cbind(ForecastDate = forecast_dates, hasilforecast)
# Mengubah matrix menjadi data frame
hasilforecast_df <- as.data.frame(hasilforecast)
# Mengkonversi angka menjadi tanggal
hasilforecast_df$ForecastDate <- as.Date(hasilforecast_df$ForecastDate, origin = "1970-01-01")
# Menampilkan hasil forecast dengan tanggal yang benar
print(hasilforecast_df)## ForecastDate Hasil Forecast
## 1 2022-01-01 11398849
## 2 2022-02-01 11818694
## 3 2022-03-01 12137584
## 4 2022-04-01 12208745
## 5 2022-05-01 12295926
## 6 2022-06-01 12459493
## 7 2022-07-01 12573797
## 8 2022-08-01 12626475
## 9 2022-09-01 12686542
## 10 2022-10-01 12759114
## 11 2022-11-01 12813773
## 12 2022-12-01 12853363
## 13 2023-01-01 12894816
## 14 2023-02-01 12937200
## 15 2023-03-01 12973744
## 16 2023-04-01 13006533
## 17 2023-05-01 13039554
## 18 2023-06-01 13072143
## 19 2023-07-01 13102933
## 20 2023-08-01 13132755
## 21 2023-09-01 13162525
## 22 2023-10-01 NA
## 23 2023-11-01 NA
## 24 2023-12-01 NA# Validasi model
## Hitung error
## Hitung error
error <- data.frame(data.test)-data.frame(data.ramalan[1:21])
## SSE (Sum Square Error)
SSE <- sum(error^2, na.rm = T)
## MSE (Mean Squared Error)
MSE<- sapply(error^2, mean, na.rm = T)
## RMSE (Root Mean Square Error)
RMSE1 <- sqrt(MSE)
# Menghitung rata-rata dari nilai aktual
mean_actual <- mean(data.test, na.rm = TRUE)
# Menghitung persentase RMSE
RMSE <- (RMSE1 / mean_actual) * 100
## MAD (Mean Absolute Deviation)
MAD <- sapply(abs(error), mean, na.rm = T)
## MAPE (Mean Absolute Percentage Error)
r.error <- (error/data.frame(data.test))*100 # Relative Error
MAPE <- sapply(abs(r.error), mean, na.rm = T)akurasifarima <- data.frame(
"Ukuran Keakuratan" = c("SSE", "MSE", "MAPE", "RMSE", "MAD"),
"Forecasting" = c(SSE, MSE, MAPE, RMSE, MAD))
akurasifarima## Ukuran.Keakuratan Forecasting
## 1 SSE 8.2085322
## 2 MSE 0.3908825
## 3 MAPE 2.9695864
## 4 RMSE 3.9333999
## 5 MAD 0.4588478MAPE 3% RMSE 3.93% model baik