set.seed(123)
n_obs <- 100
n_rep <- 100
phi_true <- -0.191 # parameter AR(1)
#Hasil estimasi
est_normal <- numeric(n_rep)
est_outlier <- numeric(n_rep)
est_missing <- numeric(n_rep)
est_missing_baru <- numeric(n_rep)
Membangkitkan Data
data_gen <- arima.sim(
n = n_obs,
list(order = c(1,1,0), ar = phi_true)
)
Estimasi Data Normal
model_normal <- arima(data_gen, order = c(1,1,0))
coef(model_normal)
## ar1
## -0.1776056
plot(data_gen, main = "Simulasi Data ARIMA(1,1,0) - BBCA",
ylab = "Nilai", xlab = "Waktu")
Skenario 1 (Data Pencilan)
data_outlier <- data_gen
# Menambahkan nilai ekstrem (5x standar deviasi)
data_outlier[50] <- data_outlier[50] + (5 * sd(data_gen))
model_outlier <- arima(data_outlier, order = c(1,1,0))
coef(model_outlier)
## ar1
## -0.4740628
plot(data_outlier, main = "Simulasi Data Outlier")
Skenario 2 (Missing Value)
data_missing <- data_gen
# Menghapus 10% data secara acak
idx_missing <- sample(1:n_obs, 10)
data_missing[idx_missing] <- NA
# Interpolasi linear
data_fixed <- approx(data_missing, xout = 1:n_obs)$y
model_missing <- arima(data_fixed, order = c(1,1,0))
coef(model_missing)
## ar1
## -0.06006856
plot(data_fixed, type = "l",
main = "Simulasi Data Missing (Interpolasi)",
ylab = "Nilai", xlab = "Waktu")
library(forecast)
## Warning: package 'forecast' was built under R version 4.4.3
data_missing_baru <- data_gen
n_obs <- length(data_missing_baru)
# Menghapus 10% data secara acak
n_missing <- round(0.1 * n_obs)
idx_missing_baru <- sample(1:n_obs, n_missing)
data_missing_baru[idx_missing_baru] <- NA
# Model langsung tanpa interpolasi
model_missing_baru <- Arima(data_missing_baru, order = c(1,1,0))
coef(model_missing_baru)
## ar1
## -0.275261
# Plot data missing
plot(data_missing_baru, type = "l",
main = "Simulasi Data Missing",
ylab = "Nilai", xlab = "Waktu")
par(mfrow = c(2,2))
plot(data_gen, type="l", main="Normal")
plot(data_outlier, type="l", main="Outlier")
plot(data_fixed, type="l", main="Missing (Interpolasi)")
plot(data_missing_baru, type="l", main="Missing")
Simulasi Replikasi
for(i in 1:n_rep) {
# Data Normal
data_gen <- arima.sim(
n = n_obs,
list(order = c(1,1,0), ar = phi_true)
)
model_normal <- arima(data_gen, order = c(1,1,0))
est_normal[i] <- coef(model_normal)["ar1"]
# Data Outlier
data_outlier <- data_gen
data_outlier[50] <- data_outlier[50] + (5 * sd(data_gen))
model_outlier <- arima(data_outlier, order = c(1,1,0))
est_outlier[i] <- coef(model_outlier)["ar1"]
# Data Missing dengan Interpolasi
data_missing <- data_gen
data_missing[sample(1:n_obs, 10)] <- NA
data_fixed <- approx(data_missing, xout = 1:n_obs)$y
model_missing <- arima(data_fixed, order = c(1,1,0))
est_missing[i] <- coef(model_missing)["ar1"]
# Data Missing Value tanpa Interpolasi
data_missing <- data_gen
data_missing[sample(1:n_obs, 10)] <- NA
model_missing_baru <- Arima(data_missing, order = c(1,1,0))
est_missing_baru[i] <- coef(model_missing_baru)["ar1"]
}
data_gen
## Time Series:
## Start = 1
## End = 102
## Frequency = 1
## [1] 0.00000000 -0.88193660 -1.78919290 -3.50821414 -2.85653910 -2.26345968
## [7] -1.48434582 -1.03272956 -0.11382655 1.02656733 0.34433159 -0.32207147
## [13] 0.58943525 2.22217386 2.00578919 2.94045137 3.75307492 3.13527657
## [19] 3.39846839 3.78544600 4.41115082 3.85640191 2.74338027 3.62648304
## [25] 1.95070954 1.79813968 2.84018926 2.15793736 2.48699646 1.56967224
## [31] 2.03124661 2.67668544 3.69979564 4.09232980 3.89433341 3.05359878
## [37] 2.94339599 3.68362610 5.27896299 5.23355434 4.72163331 3.66975551
## [43] 3.53439925 5.13932163 3.37283665 2.70431582 3.14553230 -0.03955549
## [49] 1.95407390 1.31003669 1.19826008 1.78659648 4.42781714 2.92295804
## [55] 2.54031858 3.17471080 1.47801958 1.76234411 1.93297091 2.14858020
## [61] 2.16135019 2.85913684 2.34839960 2.68085398 3.56179691 3.97827095
## [67] 4.11378842 4.18823178 6.58831881 5.86761095 5.76517769 6.02460917
## [73] 6.94702961 6.76239294 6.83781949 6.05494267 7.59703500 6.89675599
## [79] 7.34451107 8.45834548 6.59717850 8.30711660 8.53860986 8.24162183
## [85] 8.93765563 8.22829239 8.35435246 7.51367725 8.15529536 7.76870894
## [91] 7.61232439 9.04589941 10.25119000 9.32223454 10.36057669 10.65236005
## [97] 11.33710028 11.83535543 11.14535914 11.27923998 10.59746041 10.42196759
data_outlier
## Time Series:
## Start = 1
## End = 102
## Frequency = 1
## [1] 0.00000000 -0.88193660 -1.78919290 -3.50821414 -2.85653910 -2.26345968
## [7] -1.48434582 -1.03272956 -0.11382655 1.02656733 0.34433159 -0.32207147
## [13] 0.58943525 2.22217386 2.00578919 2.94045137 3.75307492 3.13527657
## [19] 3.39846839 3.78544600 4.41115082 3.85640191 2.74338027 3.62648304
## [25] 1.95070954 1.79813968 2.84018926 2.15793736 2.48699646 1.56967224
## [31] 2.03124661 2.67668544 3.69979564 4.09232980 3.89433341 3.05359878
## [37] 2.94339599 3.68362610 5.27896299 5.23355434 4.72163331 3.66975551
## [43] 3.53439925 5.13932163 3.37283665 2.70431582 3.14553230 -0.03955549
## [49] 1.95407390 18.66430436 1.19826008 1.78659648 4.42781714 2.92295804
## [55] 2.54031858 3.17471080 1.47801958 1.76234411 1.93297091 2.14858020
## [61] 2.16135019 2.85913684 2.34839960 2.68085398 3.56179691 3.97827095
## [67] 4.11378842 4.18823178 6.58831881 5.86761095 5.76517769 6.02460917
## [73] 6.94702961 6.76239294 6.83781949 6.05494267 7.59703500 6.89675599
## [79] 7.34451107 8.45834548 6.59717850 8.30711660 8.53860986 8.24162183
## [85] 8.93765563 8.22829239 8.35435246 7.51367725 8.15529536 7.76870894
## [91] 7.61232439 9.04589941 10.25119000 9.32223454 10.36057669 10.65236005
## [97] 11.33710028 11.83535543 11.14535914 11.27923998 10.59746041 10.42196759
data_missing
## Time Series:
## Start = 1
## End = 102
## Frequency = 1
## [1] 0.00000000 -0.88193660 NA -3.50821414 -2.85653910 NA
## [7] -1.48434582 -1.03272956 -0.11382655 1.02656733 0.34433159 -0.32207147
## [13] 0.58943525 2.22217386 2.00578919 NA NA 3.13527657
## [19] 3.39846839 3.78544600 4.41115082 3.85640191 2.74338027 3.62648304
## [25] 1.95070954 1.79813968 2.84018926 2.15793736 2.48699646 1.56967224
## [31] 2.03124661 2.67668544 3.69979564 4.09232980 3.89433341 NA
## [37] NA 3.68362610 5.27896299 5.23355434 4.72163331 3.66975551
## [43] 3.53439925 5.13932163 3.37283665 2.70431582 3.14553230 -0.03955549
## [49] NA 1.31003669 1.19826008 1.78659648 4.42781714 2.92295804
## [55] 2.54031858 3.17471080 1.47801958 1.76234411 1.93297091 2.14858020
## [61] 2.16135019 2.85913684 2.34839960 2.68085398 3.56179691 3.97827095
## [67] 4.11378842 4.18823178 6.58831881 5.86761095 5.76517769 6.02460917
## [73] 6.94702961 6.76239294 6.83781949 6.05494267 7.59703500 6.89675599
## [79] NA 8.45834548 6.59717850 8.30711660 8.53860986 8.24162183
## [85] 8.93765563 8.22829239 8.35435246 7.51367725 8.15529536 7.76870894
## [91] 7.61232439 9.04589941 10.25119000 9.32223454 NA NA
## [97] 11.33710028 11.83535543 11.14535914 11.27923998 10.59746041 10.42196759
data_missing_baru
## Time Series:
## Start = 1
## End = 101
## Frequency = 1
## [1] 0.000000000 1.681918503 1.821588275 0.529850114 0.089719251
## [6] -0.271877725 1.021269095 NA 1.513314178 1.551565435
## [11] 0.988418310 2.882892548 3.018898447 1.026304164 2.108245573
## [16] 1.428803356 0.490753114 0.451945795 -0.566646455 -1.100986565
## [21] -1.623966871 -3.210770944 -2.069904321 -2.134436728 -3.260247976
## [26] -1.791403106 -1.645488255 -1.968429474 -1.011622040 -0.316238773
## [31] 0.372524105 0.929610649 1.377124773 1.229737865 0.951926100
## [36] 0.624517146 -0.007654722 -0.094827174 -1.343573587 1.063892943
## [41] 1.812028834 0.546026296 0.384947945 NA 0.812278548
## [46] NA 0.864767598 0.778780814 0.752333832 2.125987490
## [51] 1.637848655 3.247553777 1.391347295 2.330496483 NA
## [56] 2.501519741 2.837888841 2.271318889 2.046326366 1.070724555
## [61] 0.185273275 0.657923111 1.015856771 1.000495668 1.925697107
## [66] NA 2.950223250 0.803183783 2.219006845 NA
## [71] 0.738483248 NA 1.360796144 0.235374156 0.631633235
## [76] 0.417056389 NA 0.840156216 0.397613054 1.126515347
## [81] 0.766808447 1.167294429 2.187640620 2.427935988 NA
## [86] 3.275934754 4.036451697 4.439589921 4.601322255 3.942525303
## [91] 5.429007969 4.544830193 6.901041141 7.983615476 7.541143419
## [96] 6.599234682 6.068732687 6.426942277 NA 5.824475760
## [101] 4.927742305
Fungsi Evaluasi dan Hasil
hitung_evaluasi <- function(est_list, true_val) {
rata_est <- mean(est_list)
bias <- rata_est - true_val
mse <- mean((est_list - true_val)^2)
return(c(rata_est, bias, mse))
}
hasil_normal <- hitung_evaluasi(est_normal, phi_true)
hasil_outlier <- hitung_evaluasi(est_outlier, phi_true)
hasil_missing <- hitung_evaluasi(est_missing, phi_true)
hasil_missing_baru <- hitung_evaluasi(est_missing_baru, phi_true)
Tabel Ringkasan
tabel_evaluasi <- data.frame(
Skenario = c("Normal", "Outlier", "Interpolasi", "Missing Values"),
Rata_Rata_Estimasi = c(hasil_normal[1], hasil_outlier[1], hasil_missing[1], hasil_missing_baru[1]),
Bias = c(hasil_normal[2], hasil_outlier[2], hasil_missing[2], hasil_missing_baru[2]),
MSE = c(hasil_normal[3], hasil_outlier[3], hasil_missing[3], hasil_missing_baru[3])
)
print(tabel_evaluasi)
## Skenario Rata_Rata_Estimasi Bias MSE
## 1 Normal -0.1982989 -0.007298890 0.009412451
## 2 Outlier -0.4263324 -0.235332367 0.059313651
## 3 Interpolasi -0.1357730 0.055226950 0.013782576
## 4 Missing Values -0.1923917 -0.001391667 0.010933616
Visualisasi
barplot(tabel_evaluasi$MSE,
names.arg = tabel_evaluasi$Skenario,
main = "Perbandingan MSE antar Skenario",
ylab = "MSE",
col = c("#A3B18A", "#E27396", "#AEC6CF", "#F4F1DE"))
