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':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Loading required package: greybox## Package "greybox", v1.0.6 loaded.## This is package "smooth", v3.1.6##
## Attaching package: 'smooth'## The following object is masked from 'package:TTR':
##
## lags## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast##
## Attaching package: 'TSA'## The following object is masked from 'package:readr':
##
## spec## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tar##
## Attaching package: 'MLmetrics'## The following objects are masked from 'package:greybox':
##
## MAE, MAPE, MSE## The following object is masked from 'package:base':
##
## Recall##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combine##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2## Warning: package 'lubridate' was built under R version 4.2.3##
## Attaching package: 'lubridate'## The following object is masked from 'package:cowplot':
##
## stamp## The following object is masked from 'package:greybox':
##
## hm## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union## Loading required package: lattice## Registered S3 method overwritten by 'lava':
## method from
## print.pcor greybox##
## Attaching package: 'caret'## The following objects are masked from 'package:MLmetrics':
##
## MAE, RMSE## The following object is masked from 'package:greybox':
##
## 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
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ lubridate::as.difftime() masks base::as.difftime()
## ✖ gridExtra::combine() masks dplyr::combine()
## ✖ lubridate::date() masks base::date()
## ✖ dplyr::filter() masks stats::filter()
## ✖ lubridate::hm() masks greybox::hm()
## ✖ lubridate::intersect() masks base::intersect()
## ✖ dplyr::lag() masks stats::lag()
## ✖ purrr::lift() masks caret::lift()
## ✖ MASS::select() masks dplyr::select()
## ✖ lubridate::setdiff() masks base::setdiff()
## ✖ TSA::spec() masks readr::spec()
## ✖ tidyr::spread() masks greybox::spread()
## ✖ lubridate::stamp() masks cowplot::stamp()
## ✖ lubridate::union() masks base::union()## [1] "dplyr" "stats" "graphics" "grDevices" "utils" "datasets"
## [7] "methods" "base"df = read_xlsx('C:/Users/User/Downloads/data indri.xlsx')
data2 = df$Jumlah_PNP# Menghitung rata-rata
rata_rata <- mean(data2)
# Menghitung median
median_data <- median(data2)
# Menemukan nilai minimum
nilai_minimum <- min(data2)
# Menemukan nilai maksimum
nilai_maksimum <- max(data2)
# Mencetak hasil
cat("Rata-rata:", rata_rata, "\n")## Rata-rata: 546531.3cat("Median:", median_data, "\n")## Median: 526712.3cat("Nilai minimum:", nilai_minimum, "\n")## Nilai minimum: 40511.1cat("Nilai maksimum:", nilai_maksimum, "\n")## Nilai maksimum: 975271data.ts<-ts(data2, frequency = 365, start = c(2021,1,1))
length(data.ts)## [1] 973# Box-Cox
#lambda <- BoxCox.lambda(data.ts)
#data.ts <- BoxCox(data.ts, lambda)
#Plot semua data
plot(data.ts,xlab ="Bulan", ylab = "Jumlah Penumpang", col="black", main = "Plot Deret Waktu Data")
points(data.ts)
model <- lm(df$Jumlah_PNP ~ df$Tanggal, data = df)
# Melakukan uji Breusch-Pagan
bp_test <- bptest(model)
bp_test##
## studentized Breusch-Pagan test
##
## data: model
## BP = 3.3165, df = 1, p-value = 0.06859# Asumsi bahwa data.ts adalah time series data yang tersedia
# Split data into training and testing
n <- length(data.ts)
data.train <- data.ts[1:778]
data.test <- data.ts[779:n]
training.ts<-ts(data.train,frequency=365)
length(training.ts)## [1] 778testing.ts<-ts(data.test,frequency=365)
length(testing.ts)## [1] 195#Plot Data
#Plot semua data
plot(data.ts,xlab ="Bulan", ylab = "Jumlah Penumpang", col="black", main = "Plot Deret Waktu Data")
points(data.ts)
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(data.train, col = "blue")
lines(data.test, col="Red")
legend("bottomleft",c("Data Training","Data Testing"),
lty=1, col=c("blue","red"), cex=0.8)
abline(v=2022.25, col=c("black"), lty=1, lwd=1)
# Plot
plot(data.train, xlab = "Periode", ylab ="Jumlah Kedatangan", col = "blue",
main = "Plot Deret Waktu Data Jumlah Penumpang Transjakarta")
lines(data.test, col = "red")
legend("bottomleft", c("Data Training", "Data Testing"),
lty = 1, col = c("blue", "red"), cex = 0.8)
abline(v = time(data.test)[1], col = "black", lty = 1, lwd = 1)
acf(data.train, lag.max = 48, main = "Plot ACF")
pacf(data.train, lag.max = 48, main = "Plot PACF")
adf.test(data.train)##
## Augmented Dickey-Fuller Test
##
## data: data.train
## Dickey-Fuller = -2.8346, Lag order = 9, p-value = 0.225
## alternative hypothesis: stationary# DIFFERENCING NON MUSIMAN
data.dif<- diff(data.train, differences = 1)
plot.ts(ts(data.dif,frequency=365, start = c(2021,1), end = c(2023,8)),lty=1,xlab = "Periode", ylab= "Jumlah Penumpang", main=" ")
adf.test(data.dif)## Warning in adf.test(data.dif): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: data.dif
## Dickey-Fuller = -9.6878, Lag order = 9, p-value = 0.01
## alternative hypothesis: stationaryacf(data.dif, lag.max = 48, main = "Plot ACF Setelah Differencing satu kali")
pacf(data.dif, lag.max = 50, main = "Plot PACF Setelah Differencing satu kali")
# DIFFERENCING NON MUSIMAN
data.dif2 <- diff(data.dif, lag = 7)
plot.ts(ts(data.dif2,frequency=365, start = c(2021,1), end = c(2023,8)),lty=1,xlab = "Periode", ylab= "Jumlah Penumpang", main=" ")
acf(data.dif2, lag.max = 48, main = " ")
pacf(data.dif2, lag.max = 50)
Plot————-Non Musiman————–Musiman PACF P(AR) = 3 P(SAR) = 3 Differencing d = 1 D = 1 ACF q(MA) = 1 Q(SMA) = 3
ARIMA(2,0,0)(0,1,0)[365]
##PENAKSIRAN PARAMETER (4,1,2)(5,1,1)7
model=Arima(data.train, order=c(3,1,1),seasonal=list(order=c(3,1,3),period=7))
model1=Arima(data.train, order=c(3,1,0),seasonal=list(order=c(3,1,3),period=7))
model2=Arima(data.train, order=c(0,1,1),seasonal=list(order=c(3,1,3),period=7))summary(model)## Series: data.train
## ARIMA(3,1,1)(3,1,3)[7]
##
## Coefficients:
## ar1 ar2 ar3 ma1 sar1 sar2 sar3 sma1
## 0.0823 -0.0108 0.0468 -0.6853 -1.7142 -0.9511 -0.0063 0.7956
## s.e. 0.1741 0.1101 0.0830 0.1678 0.0857 0.1253 0.0450 0.0891
## sma2 sma3
## -0.5984 -0.880
## s.e. 0.0384 0.088
##
## sigma^2 = 1.566e+09: log likelihood = -9246.94
## AIC=18515.88 AICc=18516.23 BIC=18567
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -717.4737 39117.24 24527.09 -1.306128 6.928985 0.3973808
## ACF1
## Training set 0.006318749coeftest(model)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 0.0823395 0.1741413 0.4728 0.6363
## ar2 -0.0108136 0.1101304 -0.0982 0.9218
## ar3 0.0468240 0.0830067 0.5641 0.5727
## ma1 -0.6852821 0.1677892 -4.0842 4.423e-05 ***
## sar1 -1.7142492 0.0856577 -20.0128 < 2.2e-16 ***
## sar2 -0.9511145 0.1252835 -7.5917 3.157e-14 ***
## sar3 -0.0063492 0.0449617 -0.1412 0.8877
## sma1 0.7955639 0.0890640 8.9325 < 2.2e-16 ***
## sma2 -0.5983823 0.0383610 -15.5987 < 2.2e-16 ***
## sma3 -0.8799662 0.0879876 -10.0010 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model1)## Series: data.train
## ARIMA(3,1,0)(3,1,3)[7]
##
## Coefficients:
## ar1 ar2 ar3 sar1 sar2 sar3 sma1 sma2
## -0.5813 -0.3707 -0.1546 -1.6971 -0.9266 -0.0029 0.7790 -0.5969
## s.e. 0.0362 0.0399 0.0360 0.1106 0.1542 0.0436 0.1087 0.0414
## sma3
## -0.8565
## s.e. 0.1047
##
## sigma^2 = 1.588e+09: log likelihood = -9251.95
## AIC=18523.91 AICc=18524.2 BIC=18570.37
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -718.6889 39417.27 24770.89 -1.309296 6.956565 0.4013307
## ACF1
## Training set -0.003752709coeftest(model1)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 -0.5812566 0.0362074 -16.0535 < 2.2e-16 ***
## ar2 -0.3707417 0.0398896 -9.2942 < 2.2e-16 ***
## ar3 -0.1545860 0.0359746 -4.2971 1.731e-05 ***
## sar1 -1.6971283 0.1105695 -15.3490 < 2.2e-16 ***
## sar2 -0.9266272 0.1541524 -6.0111 1.843e-09 ***
## sar3 -0.0028622 0.0436493 -0.0656 0.9477
## sma1 0.7789655 0.1087325 7.1641 7.833e-13 ***
## sma2 -0.5969277 0.0413676 -14.4298 < 2.2e-16 ***
## sma3 -0.8564555 0.1046732 -8.1822 2.787e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model2)## Series: data.train
## ARIMA(0,1,1)(3,1,3)[7]
##
## Coefficients:
## ma1 sar1 sar2 sar3 sma1 sma2 sma3
## -0.6273 -1.7152 -0.9560 -0.0090 0.7969 -0.5931 -0.8779
## s.e. 0.0297 0.0990 0.1384 0.0423 0.1021 0.0391 0.0983
##
## sigma^2 = 1.566e+09: log likelihood = -9248.13
## AIC=18512.26 AICc=18512.45 BIC=18549.43
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -719.5041 39186.51 24586.57 -1.30618 6.949063 0.3983444 0.02890199coeftest(model2)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 -0.627281 0.029738 -21.0935 < 2.2e-16 ***
## sar1 -1.715199 0.098972 -17.3302 < 2.2e-16 ***
## sar2 -0.956021 0.138405 -6.9074 4.935e-12 ***
## sar3 -0.008979 0.042341 -0.2121 0.8321
## sma1 0.796853 0.102057 7.8079 5.816e-15 ***
## sma2 -0.593104 0.039115 -15.1631 < 2.2e-16 ***
## sma3 -0.877902 0.098292 -8.9316 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Overfitting
#ARIMA(0,1,1)(3,1,3)[7]
model2c <- Arima(data.train, order=c(0,1,2),seasonal=list(order=c(3,1,3),period=7))
model2b1 <- Arima(data.train, order=c(0,1,1),seasonal=list(order=c(4,1,3),period=7))
model2c1 <- Arima(data.train, order=c(0,1,1),seasonal=list(order=c(3,1,4),period=7))summary(model2c)## Series: data.train
## ARIMA(0,1,2)(3,1,3)[7]
##
## Coefficients:
## ma1 ma2 sar1 sar2 sar3 sma1 sma2 sma3
## -0.6023 -0.0404 -1.714 -0.9527 -0.0067 0.7957 -0.5967 -0.8805
## s.e. 0.0374 0.0390 0.087 0.1250 0.0423 0.0881 0.0380 0.0855
##
## sigma^2 = 1.565e+09: log likelihood = -9247.59
## AIC=18513.19 AICc=18513.42 BIC=18555
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -716.4644 39151.67 24481.08 -1.302816 6.915972 0.3966352
## ACF1
## Training set 0.005777293coeftest(model2c)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 -0.6023453 0.0374050 -16.1033 < 2.2e-16 ***
## ma2 -0.0404224 0.0389842 -1.0369 0.2998
## sar1 -1.7140206 0.0869529 -19.7121 < 2.2e-16 ***
## sar2 -0.9527439 0.1249995 -7.6220 2.498e-14 ***
## sar3 -0.0066731 0.0423249 -0.1577 0.8747
## sma1 0.7956911 0.0880812 9.0336 < 2.2e-16 ***
## sma2 -0.5966909 0.0380019 -15.7016 < 2.2e-16 ***
## sma3 -0.8805475 0.0854521 -10.3046 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model2b1)## Series: data.train
## ARIMA(0,1,1)(4,1,3)[7]
##
## Coefficients:
## ma1 sar1 sar2 sar3 sar4 sma1 sma2 sma3
## -0.6231 -0.5118 -0.7089 0.0480 0.1182 -0.4189 0.3223 -0.7343
## s.e. 0.0305 0.2020 0.1618 0.0481 0.0399 0.2023 0.1748 0.1419
##
## sigma^2 = 1.575e+09: log likelihood = -9248.72
## AIC=18515.44 AICc=18515.68 BIC=18557.26
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -710.5854 39282.02 24357.74 -1.301483 6.937928 0.3946369
## ACF1
## Training set 0.02782729coeftest(model2b1)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 -0.623126 0.030523 -20.4148 < 2.2e-16 ***
## sar1 -0.511847 0.202016 -2.5337 0.011287 *
## sar2 -0.708930 0.161822 -4.3809 1.182e-05 ***
## sar3 0.048024 0.048133 0.9977 0.318413
## sar4 0.118232 0.039927 2.9612 0.003065 **
## sma1 -0.418894 0.202330 -2.0703 0.038420 *
## sma2 0.322285 0.174798 1.8438 0.065218 .
## sma3 -0.734287 0.141926 -5.1737 2.295e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(model2c)## Series: data.train
## ARIMA(0,1,2)(3,1,3)[7]
##
## Coefficients:
## ma1 ma2 sar1 sar2 sar3 sma1 sma2 sma3
## -0.6023 -0.0404 -1.714 -0.9527 -0.0067 0.7957 -0.5967 -0.8805
## s.e. 0.0374 0.0390 0.087 0.1250 0.0423 0.0881 0.0380 0.0855
##
## sigma^2 = 1.565e+09: log likelihood = -9247.59
## AIC=18513.19 AICc=18513.42 BIC=18555
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -716.4644 39151.67 24481.08 -1.302816 6.915972 0.3966352
## ACF1
## Training set 0.005777293coeftest(model2c)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 -0.6023453 0.0374050 -16.1033 < 2.2e-16 ***
## ma2 -0.0404224 0.0389842 -1.0369 0.2998
## sar1 -1.7140206 0.0869529 -19.7121 < 2.2e-16 ***
## sar2 -0.9527439 0.1249995 -7.6220 2.498e-14 ***
## sar3 -0.0066731 0.0423249 -0.1577 0.8747
## sma1 0.7956911 0.0880812 9.0336 < 2.2e-16 ***
## sma2 -0.5966909 0.0380019 -15.7016 < 2.2e-16 ***
## sma3 -0.8805475 0.0854521 -10.3046 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tetap menggunakan model -> ARIMA(3,0,3)
#Diagnostik Sisaan
sisaan <- model2$residuals
#kenormalan
shapiro.test(sisaan)##
## Shapiro-Wilk normality test
##
## data: sisaan
## W = 0.83991, p-value < 2.2e-16#sisaan saling bebas
Box.test(sisaan, type = "Ljung")##
## Box-Ljung test
##
## data: sisaan
## X-squared = 0.65239, df = 1, p-value = 0.4193data ga normal (bisa di abaikan) data gaada autokol
# Forecasting
#ARIMA(0,1,1)(3,1,3)[7]
#ramalan <- forecast(Arima(data.ts, order=c(3,1,3),method="ML",include.drift = TRUE),h = length(data.test))
# Forecast
forecast_length <- length(data.test) # Length of the test data
ramalan <- forecast::forecast(model2, h = forecast_length)
data.ramalan <- ramalan$mean
data.ramalan.ts <- ts(data.ramalan, start = 2021, frequency = 365)
plot(ramalan,col="black",col.sub ="black",col.axis="black",
col.lab="black",col.main="black",lwd=2)
box(col="black",lwd=2)
# Plot the forecast
plot(ramalan)
# Contoh tanggal dalam format "dd/mm/yyyy"
start_date <- as.Date("01/09/2023", format="%d/%m/%Y")
# Membuat vektor tanggal untuk forecast dengan asumsi bahwa forecast dimulai pada hari berikutnya
forecast_dates <- seq(from=start_date, length.out=195, by="day")
# Menambahkan vektor tanggal ke hasil forecast
hasilforecast <- matrix(data=data.ramalan[1:195], nrow=195, ncol=1)
colnames(hasilforecast) <- c("Hasil Forecast")
hasilforecast <- cbind(ForecastDate = forecast_dates, hasilforecast)
# Mengubah matrix menjadi data frame
hasilforecast_df <- as.data.frame(hasilforecast)
# If it's a character string in the format "yyyy-mm-dd"
# Mengkonversi angka menjadi tanggal
hasilforecast_df$ForecastDate <- as.Date(hasilforecast_df$ForecastDate, origin = "1970-01-01")
# Menampilkan hasil forecast dengan tanggal yang benar
print(hasilforecast_df)## ForecastDate Hasil Forecast
## 1 2023-09-01 673589.8
## 2 2023-09-02 610586.8
## 3 2023-09-03 802230.5
## 4 2023-09-04 805759.3
## 5 2023-09-05 808909.1
## 6 2023-09-06 806781.0
## 7 2023-09-07 811663.1
## 8 2023-09-08 675257.6
## 9 2023-09-09 601929.1
## 10 2023-09-10 824182.1
## 11 2023-09-11 809150.2
## 12 2023-09-12 791408.8
## 13 2023-09-13 805356.9
## 14 2023-09-14 820520.4
## 15 2023-09-15 683227.6
## 16 2023-09-16 620955.4
## 17 2023-09-17 816918.3
## 18 2023-09-18 811788.2
## 19 2023-09-19 816397.3
## 20 2023-09-20 815919.6
## 21 2023-09-21 819020.6
## 22 2023-09-22 681552.3
## 23 2023-09-23 609910.2
## 24 2023-09-24 822626.9
## 25 2023-09-25 817957.0
## 26 2023-09-26 804272.4
## 27 2023-09-27 813097.0
## 28 2023-09-28 827245.1
## 29 2023-09-29 690836.0
## 30 2023-09-30 624787.7
## 31 2023-10-01 833627.3
## 32 2023-10-02 818868.5
## 33 2023-10-03 815381.2
## 34 2023-10-04 821897.6
## 35 2023-10-05 828537.4
## 36 2023-10-06 690487.4
## 37 2023-10-07 623703.1
## 38 2023-10-08 823411.6
## 39 2023-10-09 825428.5
## 40 2023-10-10 821739.3
## 41 2023-10-11 823451.1
## 42 2023-10-12 832516.2
## 43 2023-10-13 696269.6
## 44 2023-10-14 625484.0
## 45 2023-10-15 844410.3
## 46 2023-10-16 827294.6
## 47 2023-10-17 814367.2
## 48 2023-10-18 826443.0
## 49 2023-10-19 838427.1
## 50 2023-10-20 700646.5
## 51 2023-10-21 637377.3
## 52 2023-10-22 832105.7
## 53 2023-10-23 831858.8
## 54 2023-10-24 834878.3
## 55 2023-10-25 833791.8
## 56 2023-10-26 838517.9
## 57 2023-10-27 701659.1
## 58 2023-10-28 629329.7
## 59 2023-10-29 847271.7
## 60 2023-10-30 836231.9
## 61 2023-10-31 820733.1
## 62 2023-11-01 832357.5
## 63 2023-11-02 846720.1
## 64 2023-11-03 709730.6
## 65 2023-11-04 645791.3
## 66 2023-11-05 846878.5
## 67 2023-11-06 838395.5
## 68 2023-11-07 839496.7
## 69 2023-11-08 841809.7
## 70 2023-11-09 846556.4
## 71 2023-11-10 708923.6
## 72 2023-11-11 639187.9
## 73 2023-11-12 847209.0
## 74 2023-11-13 844507.4
## 75 2023-11-14 834696.9
## 76 2023-11-15 840947.1
## 77 2023-11-16 853039.5
## 78 2023-11-17 716626.8
## 79 2023-11-18 648893.4
## 80 2023-11-19 860926.5
## 81 2023-11-20 845961.2
## 82 2023-11-21 839162.7
## 83 2023-11-22 847447.6
## 84 2023-11-23 856047.2
## 85 2023-11-24 718158.0
## 86 2023-11-25 652456.4
## 87 2023-11-26 851130.5
## 88 2023-11-27 851649.7
## 89 2023-11-28 849967.8
## 90 2023-11-29 851082.4
## 91 2023-11-30 858736.5
## 92 2023-12-01 722219.1
## 93 2023-12-02 651170.4
## 94 2023-12-03 868860.1
## 95 2023-12-04 854492.7
## 96 2023-12-05 841253.2
## 97 2023-12-06 852685.8
## 98 2023-12-07 865234.8
## 99 2023-12-08 727765.0
## 100 2023-12-09 663927.3
## 101 2023-12-10 861736.9
## 102 2023-12-11 858209.7
## 103 2023-12-12 859875.1
## 104 2023-12-13 860447.0
## 105 2023-12-14 865535.5
## 106 2023-12-15 728401.1
## 107 2023-12-16 657288.7
## 108 2023-12-17 871137.3
## 109 2023-12-18 863109.9
## 110 2023-12-19 850213.8
## 111 2023-12-20 859614.1
## 112 2023-12-21 872827.7
## 113 2023-12-22 736016.3
## 114 2023-12-23 670535.5
## 115 2023-12-24 875709.1
## 116 2023-12-25 865170.6
## 117 2023-12-26 863104.8
## 118 2023-12-27 867653.0
## 119 2023-12-28 874019.0
## 120 2023-12-29 736341.4
## 121 2023-12-30 668091.3
## 122 2023-12-31 872989.1
## 123 2024-01-01 870962.6
## 124 2024-01-02 864108.0
## 125 2024-01-03 868635.9
## 126 2024-01-04 879046.2
## 127 2024-01-05 742542.4
## 128 2024-01-06 673723.6
## 129 2024-01-07 887243.9
## 130 2024-01-08 873058.7
## 131 2024-01-09 864194.7
## 132 2024-01-10 873316.9
## 133 2024-01-11 883263.8
## 134 2024-01-12 745571.9
## 135 2024-01-13 680325.5
## 136 2024-01-14 879398.1
## 137 2024-01-15 877952.4
## 138 2024-01-16 877015.9
## 139 2024-01-17 878320.9
## 140 2024-01-18 885257.6
## 141 2024-01-19 748489.1
## 142 2024-01-20 677683.9
## 143 2024-01-21 893296.4
## 144 2024-01-22 881547.5
## 145 2024-01-23 868977.7
## 146 2024-01-24 879298.7
## 147 2024-01-25 891805.2
## 148 2024-01-26 754578.2
## 149 2024-01-27 689897.3
## 150 2024-01-28 890875.4
## 151 2024-01-29 884728.5
## 152 2024-01-30 884551.2
## 153 2024-01-31 886840.2
## 154 2024-02-01 892675.4
## 155 2024-02-02 755362.7
## 156 2024-02-03 685459.7
## 157 2024-02-04 895855.9
## 158 2024-02-05 889836.1
## 159 2024-02-06 879453.7
## 160 2024-02-07 886969.9
## 161 2024-02-08 898949.9
## 162 2024-02-09 762214.3
## 163 2024-02-10 695463.1
## 164 2024-02-11 903547.8
## 165 2024-02-12 892046.8
## 166 2024-02-13 887425.2
## 167 2024-02-14 893573.5
## 168 2024-02-15 901341.8
## 169 2024-02-16 763702.5
## 170 2024-02-17 696482.6
## 171 2024-02-18 899659.6
## 172 2024-02-19 897388.1
## 173 2024-02-20 892530.7
## 174 2024-02-21 896100.0
## 175 2024-02-22 905277.5
## 176 2024-02-23 768637.3
## 177 2024-02-24 699255.0
## 178 2024-02-25 912974.9
## 179 2024-02-26 900112.0
## 180 2024-02-27 890243.3
## 181 2024-02-28 899496.8
## 182 2024-02-29 910228.6
## 183 2024-03-01 772733.4
## 184 2024-03-02 707480.0
## 185 2024-03-03 907829.3
## 186 2024-03-04 904358.4
## 187 2024-03-05 903258.7
## 188 2024-03-06 905240.5
## 189 2024-03-07 911997.0
## 190 2024-03-08 775021.2
## 191 2024-03-09 704757.5
## 192 2024-03-10 918004.9
## 193 2024-03-11 908467.6
## 194 2024-03-12 897120.2
## 195 2024-03-13 906163.4# Validasi model
## Hitung error
## Hitung error
error <- data.frame(data.test)-data.frame(data.ramalan[1:195])
## 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 1.950499e+12
## 2 MSE 1.000256e+10
## 3 MAPE 1.011910e+01
## 4 RMSE 1.296567e+01
## 5 MAD 6.431735e+04MAPE 10% RMSE 13%
residu <- residuals(model2)
# Melakukan uji Jarque-Bera
jarque.bera.test(residu)##
## Jarque Bera Test
##
## data: residu
## X-squared = 2838.3, df = 2, p-value < 2.2e-16# Melakukan uji Ljung-Box pada residuals
Box.test(residu, type = "Ljung-Box")##
## Box-Ljung test
##
## data: residu
## X-squared = 0.65239, df = 1, p-value = 0.4193# Uji Shapiro-Wilk untuk residuals
shapiro.test(residu)##
## Shapiro-Wilk normality test
##
## data: residu
## W = 0.83991, p-value < 2.2e-16# Membuat plot dasar untuk residuals
plot(residu, main="Residuals dari Model ARIMA", xlab="Waktu", ylab="Residuals")
# Membuat plot density untuk residuals
# Hal ini membantu dalam memeriksa distribusi normal dari residuals
hist(residu, breaks=30, probability=TRUE, main="Density Plot dari Residuals ARIMA", xlab="Residuals")
lines(density(residu), col="blue")
# Membuat correlogram (ACF Plot) untuk residuals
# Ini membantu dalam memeriksa adanya autokorelasi pada residuals
acf(residu, main="Correlogram dari Residuals ARIMA")