## ============================================================
## UAS ANALISIS RUNTUN WAKTU TERAPAN — STUDI KASUS 1
## Volatilitas return harian saham ITMG dengan model ARCH/GARCH
## ============================================================
# install.packages(c("quantmod","tseries","FinTS","rugarch",
# "PerformanceAnalytics","forecast"))
library(quantmod)
## Loading required package: xts
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: TTR
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(tseries)
library(FinTS) # ArchTest
library(rugarch)
## Loading required package: parallel
library(PerformanceAnalytics) # skewness, kurtosis
##
## Attaching package: 'PerformanceAnalytics'
## The following object is masked from 'package:graphics':
##
## legend
# Harga penutupan harian ITMG (Bursa Efek Indonesia), via Yahoo Finance
KODE_SAHAM <- "ITMG.JK"
getSymbols(KODE_SAHAM, src = "yahoo",
from = "2021-01-01", to = "2026-09-01", auto.assign = TRUE)
## Warning: ITMG.JK contains missing values. Some functions will not work if
## objects contain missing values in the middle of the series. Consider using
## na.omit(), na.approx(), na.fill(), etc to remove or replace them.
## [1] "ITMG.JK"
harga <- na.omit(Cl(get(KODE_SAHAM)))
names(harga) <- "Close"
# --- Cadangan jika tidak ada internet: baca dari CSV ---
# df <- read.csv("data_ITMG.csv"); df$Date <- as.Date(df$Date)
# harga <- xts(df$Close, order.by = df$Date); names(harga) <- "Close"
plot(harga, main = "Harga Penutupan Saham ITMG")
return_log <- na.omit(diff(log(harga)))
names(return_log) <- "Return"
length(return_log)
## [1] 1363
plot(return_log, main = "Return Log Harian ITMG")
summary(as.numeric(return_log))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -0.1118781 -0.0098787 0.0000000 0.0004742 0.0100503 0.1489084
sd(return_log)
## [1] 0.02201398
skewness(return_log)
## [1] 0.3290638
kurtosis(return_log) # EXCESS kurtosis (> 0 berarti fat tail)
## [1] 4.463372
jarque.bera.test(return_log)
##
## Jarque Bera Test
##
## data: return_log
## X-squared = 1156, df = 2, p-value < 2.2e-16
adf.test(return_log)
## Warning in adf.test(return_log): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: return_log
## Dickey-Fuller = -10.087, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationary
pp.test(return_log)
## Warning in pp.test(return_log): p-value smaller than printed p-value
##
## Phillips-Perron Unit Root Test
##
## data: return_log
## Dickey-Fuller Z(alpha) = -1382.4, Truncation lag parameter = 7, p-value
## = 0.01
## alternative hypothesis: stationary
acf(return_log, main = "ACF Return")
pacf(return_log, main = "PACF Return")
model_mean <- tryCatch({
library(forecast)
auto.arima(return_log, max.d = 0, seasonal = FALSE)
}, error = function(e) arima(return_log, order = c(0, 0, 0)))
##
## Attaching package: 'forecast'
## The following object is masked from 'package:FinTS':
##
## Acf
model_mean
## Series: return_log
## ARIMA(0,0,0) with zero mean
##
## sigma^2 = 0.0004845: log likelihood = 3267.48
## AIC=-6532.97 AICc=-6532.97 BIC=-6527.75
resid_mean <- residuals(model_mean)
acf(as.numeric(resid_mean)^2, main = "ACF Residual Kuadrat")
ArchTest(resid_mean, lags = 12) # H0: tidak ada efek ARCH
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: resid_mean
## Chi-squared = 61.236, df = 12, p-value = 1.342e-08
## ============================================================
## 7. TRIAL AND ERROR SPESIFIKASI MODEL
## ============================================================
coba_model <- function(nama, vmodel, order, arma = c(0, 0), dist = "std",
submodel = NULL, archm = FALSE) {
vm <- list(model = vmodel, garchOrder = order)
if (!is.null(submodel)) vm$submodel <- submodel
spec <- ugarchspec(
variance.model = vm,
mean.model = list(armaOrder = arma, include.mean = TRUE,
archm = archm, archpow = 1),
distribution.model = dist)
fit <- tryCatch(ugarchfit(spec, data = return_log, solver = "hybrid"),
error = function(e) NULL)
arma_txt <- paste0("(", arma[1], ",", arma[2], ")")
if (is.null(fit) || convergence(fit) != 0) {
return(data.frame(Model = nama, ARMA = arma_txt, Dist = dist,
LogLik = NA, AIC = NA, BIC = NA, Persistensi = NA,
Param_tdk_sig = "gagal konvergen",
LB_z2_p = NA, ARCHLM_p = NA, Layak = FALSE))
}
ic <- infocriteria(fit)
mc <- fit@fit$matcoef
par_cek <- rownames(mc)[!grepl("^(mu|ar[0-9]+|ma[0-9]+|shape|skew)$", rownames(mc))]
tdk_sig <- par_cek[which(!(mc[par_cek, 4] <= 0.05))]
z <- as.numeric(residuals(fit, standardize = TRUE))
lb <- Box.test(z^2, lag = 12, type = "Ljung-Box")$p.value
alm <- ArchTest(z, lags = 12)$p.value
pers <- persistence(fit)
# Layak: parameter varians (kecuali omega) signifikan, residual bersih
# dari efek ARCH, persistensi < 1 (kecuali IGARCH)
layak <- length(setdiff(tdk_sig, "omega")) == 0 &&
lb > 0.05 && alm > 0.05 && (pers < 1 || vmodel == "iGARCH")
data.frame(Model = nama, ARMA = arma_txt, Dist = dist,
LogLik = round(likelihood(fit), 2),
AIC = round(ic[1], 4), BIC = round(ic[2], 4),
Persistensi = round(pers, 4),
Param_tdk_sig = ifelse(length(tdk_sig) == 0, "-", paste(tdk_sig, collapse = ",")),
LB_z2_p = round(lb, 4), ARCHLM_p = round(alm, 4),
Layak = layak)
}
spesifikasi <- list(
"ARCH(1)" = list("sGARCH", c(1, 0)),
"ARCH(2)" = list("sGARCH", c(2, 0)),
"ARCH(3)" = list("sGARCH", c(3, 0)),
"GARCH(1,1)" = list("sGARCH", c(1, 1)),
"GARCH(1,2)" = list("sGARCH", c(1, 2)),
"GARCH(2,1)" = list("sGARCH", c(2, 1)),
"GARCH(2,2)" = list("sGARCH", c(2, 2)),
"GARCH-M(1,1)" = list("sGARCH", c(1, 1), archm = TRUE),
"IGARCH(1,1)" = list("iGARCH", c(1, 1)),
"EGARCH(1,1)" = list("eGARCH", c(1, 1)),
"EGARCH(1,2)" = list("eGARCH", c(1, 2)),
"EGARCH(2,1)" = list("eGARCH", c(2, 1)),
"EGARCH-M(1,1)" = list("eGARCH", c(1, 1), archm = TRUE),
"GJR-GARCH(1,1)" = list("gjrGARCH", c(1, 1)),
"GJR-GARCH(2,1)" = list("gjrGARCH", c(2, 1)),
"TGARCH(1,1)" = list("fGARCH", c(1, 1), submodel = "TGARCH"))
coba_dari_nama <- function(nama, arma = c(0, 0), dist = "std") {
s <- spesifikasi[[nama]]
coba_model(nama, s[[1]], s[[2]], arma = arma, dist = dist,
submodel = s$submodel, archm = isTRUE(s$archm))
}
## Tahap 1 — jenis model & orde (mean konstanta, Student-t)
tahap1 <- do.call(rbind, lapply(names(spesifikasi), coba_dari_nama))
tahap1 <- tahap1[order(tahap1$AIC), ]
print(tahap1, row.names = FALSE)
## Model ARMA Dist LogLik AIC BIC Persistensi
## EGARCH(1,1) (0,0) std 3506.10 -5.1359 -5.1129 0.9898
## EGARCH(1,2) (0,0) std 3506.74 -5.1353 -5.1085 0.9874
## EGARCH(2,1) (0,0) std 3507.61 -5.1352 -5.1045 0.9917
## EGARCH-M(1,1) (0,0) std 3506.53 -5.1350 -5.1082 0.9884
## TGARCH(1,1) (0,0) std 3504.10 -5.1329 -5.1100 0.9911
## GJR-GARCH(1,1) (0,0) std 3500.00 -5.1269 -5.1040 0.9990
## GJR-GARCH(2,1) (0,0) std 3501.50 -5.1262 -5.0956 0.9990
## IGARCH(1,1) (0,0) std 3495.09 -5.1227 -5.1073 1.0000
## GARCH(1,1) (0,0) std 3495.06 -5.1211 -5.1020 0.9990
## GARCH-M(1,1) (0,0) std 3495.60 -5.1205 -5.0975 0.9990
## GARCH(1,2) (0,0) std 3495.40 -5.1202 -5.0972 0.9990
## GARCH(2,1) (0,0) std 3495.29 -5.1200 -5.0970 0.9990
## GARCH(2,2) (0,0) std 3495.40 -5.1187 -5.0919 0.9990
## ARCH(3) (0,0) std 3448.70 -5.0517 -5.0287 0.9374
## ARCH(2) (0,0) std 3442.66 -5.0443 -5.0251 0.8763
## ARCH(1) (0,0) std 3426.80 -5.0224 -5.0071 0.6502
## Param_tdk_sig LB_z2_p ARCHLM_p Layak
## - 0.4291 0.4243 TRUE
## - 0.4362 0.4268 TRUE
## alpha1,alpha2,gamma2 0.3047 0.3069 FALSE
## archm 0.4489 0.4431 FALSE
## omega 0.5266 0.5261 TRUE
## omega 0.2894 0.2739 TRUE
## omega,alpha1,alpha2,gamma1,gamma2 0.2325 0.2284 FALSE
## omega 0.5193 0.5201 TRUE
## omega 0.5176 0.5186 TRUE
## archm,omega 0.5315 0.5317 FALSE
## omega,beta2 0.5250 0.5274 FALSE
## omega,alpha1,alpha2 0.5181 0.5193 FALSE
## omega,alpha1,alpha2,beta2 0.5250 0.5274 FALSE
## - 0.0029 0.0022 FALSE
## - 0.0000 0.0001 FALSE
## - 0.0000 0.0000 FALSE
## Tahap 2 — distribusi error untuk 3 model layak terbaik
kandidat <- head(tahap1[tahap1$Layak, ], 3)
if (nrow(kandidat) == 0) kandidat <- head(tahap1, 3)
tahap2 <- do.call(rbind, lapply(kandidat$Model, function(m)
do.call(rbind, lapply(c("norm", "std", "sstd", "ged"), function(d)
coba_dari_nama(m, dist = d)))))
tahap2 <- tahap2[order(tahap2$AIC), ]
print(tahap2, row.names = FALSE)
## Model ARMA Dist LogLik AIC BIC Persistensi Param_tdk_sig
## EGARCH(1,1) (0,0) ged 3507.09 -5.1373 -5.1144 0.9905 omega,gamma1
## EGARCH(1,2) (0,0) ged 3507.97 -5.1371 -5.1104 0.9877 omega
## EGARCH(1,1) (0,0) std 3506.10 -5.1359 -5.1129 0.9898 -
## EGARCH(1,2) (0,0) std 3506.74 -5.1353 -5.1085 0.9874 -
## TGARCH(1,1) (0,0) ged 3505.50 -5.1350 -5.1120 0.9914 omega
## EGARCH(1,1) (0,0) sstd 3506.45 -5.1349 -5.1081 0.9894 -
## EGARCH(1,2) (0,0) sstd 3507.11 -5.1344 -5.1038 0.9869 -
## TGARCH(1,1) (0,0) std 3504.10 -5.1329 -5.1100 0.9911 omega
## TGARCH(1,1) (0,0) sstd 3504.46 -5.1320 -5.1052 0.9910 omega
## EGARCH(1,2) (0,0) norm 3428.88 -5.0226 -4.9996 0.9881 omega
## EGARCH(1,1) (0,0) norm 3426.50 -5.0205 -5.0014 0.9909 -
## TGARCH(1,1) (0,0) norm 3424.45 -5.0175 -4.9984 0.9990 -
## LB_z2_p ARCHLM_p Layak
## 0.3933 0.3817 FALSE
## 0.4086 0.3922 TRUE
## 0.4291 0.4243 TRUE
## 0.4362 0.4268 TRUE
## 0.4798 0.4726 TRUE
## 0.4345 0.4310 TRUE
## 0.4404 0.4321 TRUE
## 0.5266 0.5261 TRUE
## 0.5292 0.5296 TRUE
## 0.3962 0.3748 TRUE
## 0.3733 0.3563 TRUE
## 0.4333 0.4196 TRUE
## Tahap 3 — mean model ARMA untuk kombinasi layak terbaik tahap 2
terbaik2 <- head(tahap2[tahap2$Layak, ], 1)
if (nrow(terbaik2) == 0) terbaik2 <- head(tahap2, 1)
tahap3 <- do.call(rbind, lapply(list(c(0, 0), c(1, 0), c(0, 1), c(1, 1)), function(a)
coba_dari_nama(terbaik2$Model, arma = a, dist = terbaik2$Dist)))
tahap3 <- tahap3[order(tahap3$AIC), ]
print(tahap3, row.names = FALSE)
## Model ARMA Dist LogLik AIC BIC Persistensi Param_tdk_sig
## EGARCH(1,2) (1,0) ged 3509.02 -5.1372 -5.1066 0.9873 omega
## EGARCH(1,2) (0,1) ged 3508.99 -5.1372 -5.1066 0.9873 omega
## EGARCH(1,2) (0,0) ged 3507.97 -5.1371 -5.1104 0.9877 omega
## EGARCH(1,2) (1,1) ged 3509.16 -5.1360 -5.1015 0.9872 omega
## LB_z2_p ARCHLM_p Layak
## 0.4273 0.4077 TRUE
## 0.4268 0.4072 TRUE
## 0.4086 0.3922 TRUE
## 0.4197 0.4020 TRUE
## Rekap seluruh percobaan
semua <- unique(rbind(tahap1, tahap2, tahap3))
semua <- semua[order(!semua$Layak, semua$AIC), ]
print(semua, row.names = FALSE)
## Model ARMA Dist LogLik AIC BIC Persistensi
## EGARCH(1,2) (1,0) ged 3509.02 -5.1372 -5.1066 0.9873
## EGARCH(1,2) (0,1) ged 3508.99 -5.1372 -5.1066 0.9873
## EGARCH(1,2) (0,0) ged 3507.97 -5.1371 -5.1104 0.9877
## EGARCH(1,2) (1,1) ged 3509.16 -5.1360 -5.1015 0.9872
## EGARCH(1,1) (0,0) std 3506.10 -5.1359 -5.1129 0.9898
## EGARCH(1,2) (0,0) std 3506.74 -5.1353 -5.1085 0.9874
## TGARCH(1,1) (0,0) ged 3505.50 -5.1350 -5.1120 0.9914
## EGARCH(1,1) (0,0) sstd 3506.45 -5.1349 -5.1081 0.9894
## EGARCH(1,2) (0,0) sstd 3507.11 -5.1344 -5.1038 0.9869
## TGARCH(1,1) (0,0) std 3504.10 -5.1329 -5.1100 0.9911
## TGARCH(1,1) (0,0) sstd 3504.46 -5.1320 -5.1052 0.9910
## GJR-GARCH(1,1) (0,0) std 3500.00 -5.1269 -5.1040 0.9990
## IGARCH(1,1) (0,0) std 3495.09 -5.1227 -5.1073 1.0000
## GARCH(1,1) (0,0) std 3495.06 -5.1211 -5.1020 0.9990
## EGARCH(1,2) (0,0) norm 3428.88 -5.0226 -4.9996 0.9881
## EGARCH(1,1) (0,0) norm 3426.50 -5.0205 -5.0014 0.9909
## TGARCH(1,1) (0,0) norm 3424.45 -5.0175 -4.9984 0.9990
## EGARCH(1,1) (0,0) ged 3507.09 -5.1373 -5.1144 0.9905
## EGARCH(2,1) (0,0) std 3507.61 -5.1352 -5.1045 0.9917
## EGARCH-M(1,1) (0,0) std 3506.53 -5.1350 -5.1082 0.9884
## GJR-GARCH(2,1) (0,0) std 3501.50 -5.1262 -5.0956 0.9990
## GARCH-M(1,1) (0,0) std 3495.60 -5.1205 -5.0975 0.9990
## GARCH(1,2) (0,0) std 3495.40 -5.1202 -5.0972 0.9990
## GARCH(2,1) (0,0) std 3495.29 -5.1200 -5.0970 0.9990
## GARCH(2,2) (0,0) std 3495.40 -5.1187 -5.0919 0.9990
## ARCH(3) (0,0) std 3448.70 -5.0517 -5.0287 0.9374
## ARCH(2) (0,0) std 3442.66 -5.0443 -5.0251 0.8763
## ARCH(1) (0,0) std 3426.80 -5.0224 -5.0071 0.6502
## Param_tdk_sig LB_z2_p ARCHLM_p Layak
## omega 0.4273 0.4077 TRUE
## omega 0.4268 0.4072 TRUE
## omega 0.4086 0.3922 TRUE
## omega 0.4197 0.4020 TRUE
## - 0.4291 0.4243 TRUE
## - 0.4362 0.4268 TRUE
## omega 0.4798 0.4726 TRUE
## - 0.4345 0.4310 TRUE
## - 0.4404 0.4321 TRUE
## omega 0.5266 0.5261 TRUE
## omega 0.5292 0.5296 TRUE
## omega 0.2894 0.2739 TRUE
## omega 0.5193 0.5201 TRUE
## omega 0.5176 0.5186 TRUE
## omega 0.3962 0.3748 TRUE
## - 0.3733 0.3563 TRUE
## - 0.4333 0.4196 TRUE
## omega,gamma1 0.3933 0.3817 FALSE
## alpha1,alpha2,gamma2 0.3047 0.3069 FALSE
## archm 0.4489 0.4431 FALSE
## omega,alpha1,alpha2,gamma1,gamma2 0.2325 0.2284 FALSE
## archm,omega 0.5315 0.5317 FALSE
## omega,beta2 0.5250 0.5274 FALSE
## omega,alpha1,alpha2 0.5181 0.5193 FALSE
## omega,alpha1,alpha2,beta2 0.5250 0.5274 FALSE
## - 0.0029 0.0022 FALSE
## - 0.0000 0.0001 FALSE
## - 0.0000 0.0000 FALSE
## ============================================================
## 8. MODEL TERPILIH: EGARCH(1,1), Student-t, mean konstanta
## ============================================================
# Dasar pemilihan: model layak dengan BIC terkecil, seluruh parameter
# signifikan, selisih AIC dengan model ber-AIC terkecil < 2 (skala total),
# dan uji LR menolak tambahan orde (lihat di bawah).
spec_terbaik <- ugarchspec(
variance.model = list(model = "eGARCH", garchOrder = c(1, 1)),
mean.model = list(armaOrder = c(0, 0), include.mean = TRUE),
distribution.model = "std")
model_terbaik <- ugarchfit(spec_terbaik, data = return_log, solver = "hybrid")
model_terbaik
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : eGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000539 0.000380 1.4162 0.156727
## omega -0.079796 0.009286 -8.5935 0.000000
## alpha1 0.046223 0.017175 2.6913 0.007117
## beta1 0.989760 0.001418 698.1868 0.000000
## gamma1 0.160712 0.018735 8.5779 0.000000
## shape 3.794807 0.420207 9.0308 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000539 0.000370 1.4549 0.145685
## omega -0.079796 0.016234 -4.9155 0.000001
## alpha1 0.046223 0.020372 2.2690 0.023269
## beta1 0.989760 0.002038 485.6377 0.000000
## gamma1 0.160712 0.019282 8.3348 0.000000
## shape 3.794807 0.413841 9.1697 0.000000
##
## LogLikelihood : 3506.096
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.1359
## Bayes -5.1129
## Shibata -5.1359
## Hannan-Quinn -5.1273
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.09786 0.7544
## Lag[2*(p+q)+(p+q)-1][2] 0.28434 0.8045
## Lag[4*(p+q)+(p+q)-1][5] 1.91209 0.6393
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4897 0.4841
## Lag[2*(p+q)+(p+q)-1][5] 1.6173 0.7110
## Lag[4*(p+q)+(p+q)-1][9] 3.4699 0.6795
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.8847 0.500 2.000 0.3469
## ARCH Lag[5] 1.8854 1.440 1.667 0.4971
## ARCH Lag[7] 2.8033 2.315 1.543 0.5514
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.9132
## Individual Statistics:
## mu 0.03921
## omega 0.41886
## alpha1 0.71538
## beta1 0.39108
## gamma1 0.46362
## shape 0.22102
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.5094 0.1314
## Negative Sign Bias 0.9280 0.3536
## Positive Sign Bias 0.3323 0.7397
## Joint Effect 2.4746 0.4799
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 17.53 0.5541
## 2 30 28.42 0.4954
## 3 40 43.28 0.2936
## 4 50 36.74 0.9016
##
##
## Elapsed time : 0.287107
# Uji likelihood ratio: EGARCH(1,2) vs EGARCH(1,1), keduanya Student-t
fit_e12 <- ugarchfit(ugarchspec(
variance.model = list(model = "eGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(0, 0), include.mean = TRUE),
distribution.model = "std"), data = return_log, solver = "hybrid")
LR <- 2 * (likelihood(fit_e12) - likelihood(model_terbaik))
c(LR = LR, p_value = 1 - pchisq(LR, df = 1))
## LR p_value
## 1.2812604 0.2576648
# Selisih AIC skala total terhadap model layak ber-AIC terkecil
n_obs <- length(return_log)
(semua$AIC[semua$Layak][1] - infocriteria(model_terbaik)[1]) * n_obs # |nilai| < 2 -> setara
## [1] -1.811155
resid_std <- residuals(model_terbaik, standardize = TRUE)
Box.test(resid_std, lag = 12, type = "Ljung-Box")
##
## Box-Ljung test
##
## data: resid_std
## X-squared = 15.783, df = 12, p-value = 0.2014
Box.test(resid_std^2, lag = 12, type = "Ljung-Box")
##
## Box-Ljung test
##
## data: resid_std^2
## X-squared = 12.208, df = 12, p-value = 0.4291
ArchTest(resid_std, lags = 12)
##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: resid_std
## Chi-squared = 12.269, df = 12, p-value = 0.4243
signbias(model_terbaik)
## t-value prob sig
## Sign Bias 1.5093632 0.1314386
## Negative Sign Bias 0.9279730 0.3535865
## Positive Sign Bias 0.3322576 0.7397460
## Joint Effect 2.4746365 0.4798923
nyblom(model_terbaik)
## $IndividualStat
## [,1]
## mu 0.03921336
## omega 0.41885730
## alpha1 0.71538248
## beta1 0.39108187
## gamma1 0.46362332
## shape 0.22101987
##
## $JointStat
## [1] 1.913167
##
## $IndividualCritical
## 10% 5% 1%
## 0.353 0.470 0.748
##
## $JointCritical
## 10% 5% 1%
## 1.49 1.68 2.12
ni <- newsimpact(model_terbaik)
plot(ni$zx, ni$zy, type = "l", lwd = 2,
xlab = "Guncangan (z)", ylab = "Varians bersyarat",
main = "News Impact Curve - EGARCH(1,1)")
abline(v = 0, lty = 2)
# Kurva lebih tinggi di sisi kanan -> guncangan positif menaikkan
# volatilitas lebih besar (inverse leverage effect)
sigma_t <- sigma(model_terbaik)
plot(sigma_t, main = "Volatilitas Kondisional (Conditional SD)")
forecast_vol <- ugarchforecast(model_terbaik, n.ahead = 20)
sigma(forecast_vol)
## 2026-08-31
## T+1 0.01596296
## T+2 0.01600246
## T+3 0.01604165
## T+4 0.01608054
## T+5 0.01611912
## T+6 0.01615740
## T+7 0.01619537
## T+8 0.01623304
## T+9 0.01627042
## T+10 0.01630749
## T+11 0.01634427
## T+12 0.01638076
## T+13 0.01641695
## T+14 0.01645285
## T+15 0.01648846
## T+16 0.01652378
## T+17 0.01655881
## T+18 0.01659356
## T+19 0.01662802
## T+20 0.01666220
plot(forecast_vol, which = 3)
coef(model_terbaik)
## mu omega alpha1 beta1 gamma1
## 0.0005386905 -0.0797955852 0.0462228653 0.9897596471 0.1607120291
## shape
## 3.7948065787
persistence(model_terbaik) # untuk EGARCH = beta1
## [1] 0.9897596
halflife(model_terbaik) # hari perdagangan
## [1] 67.34065
b <- coef(model_terbaik)
sqrt(exp(b["omega"] / (1 - b["beta1"]))) # volatilitas harian jangka panjang (aprox.)
## omega
## 0.02032031