# ============================================================
# ANALISIS VOLATILITAS SAHAM HRUM
# Model: ARCH / GARCH
# ============================================================
# 1. BACA DATA
library(readxl)
## Warning: package 'readxl' was built under R version 4.5.3
data <- read_excel("C:/ARW/UAS_ARW/Data_Saham_Soal Nomor 1.xlsx", sheet = "Saham")
head(data)
## # A tibble: 6 × 2
## Date Close
## <dttm> <dbl>
## 1 2021-01-04 15:00:00 610
## 2 2021-01-05 15:00:00 610
## 3 2021-01-06 15:00:00 592
## 4 2021-01-07 16:00:00 670
## 5 2021-01-08 16:00:00 780
## 6 2021-01-11 15:00:00 826
# 2. BERSIHKAN DATA
# cek tipe data kolom date
str(data$Date)
## POSIXct[1:1378], format: "2021-01-04 15:00:00" "2021-01-05 15:00:00" "2021-01-06 15:00:00" ...
# Konversi ke numerik lalu ke date
data$Date <- as.numeric(data$Date)
data$Date <- as.Date(data$Date, origin = "1899-12-30")
# cek range tanggal
range(data$Date, na.rm = TRUE)
## [1] "4409307-02-17" "4903717-04-13"
# Cek beberapa tangga pertama
head(data$Date, 10)
## [1] "4409307-02-17" "4409543-09-08" "4409780-03-28" "4410026-08-26"
## [5] "4410263-03-17" "4410963-01-06" "4411199-07-28" "4411436-02-16"
## [9] "4411672-09-05" "4411909-03-28"
# Bersihkan kolom close
data$Close <- as.numeric(gsub("COMPUTED_VALUE", NA, data$Close))
data <- na.omit(data)
cat("Jumlah data:", nrow(data), "\n")
## Jumlah data: 1378
# 3. TIME SERIES & RETURN
library(xts)
## Warning: package 'xts' was built under R version 4.5.2
## Loading required package: zoo
## Warning: package 'zoo' was built under R version 4.5.2
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
harga <- xts(data$Close, order.by = data$Date)
plot(harga, main = "Harga Saham HRUM", col = "blue", ylab = "Harga")
return_xts <- diff(log(harga))
return_xts <- na.omit(return_xts)
plot(return_xts, main = "Return Saham HRUM", col = "darkgreen", ylab = "Return")
# Konversi ke vektor numerik
return <- as.numeric(return_xts)
# 4. UJI STASIONER (ADF)
library(urca)
## Warning: package 'urca' was built under R version 4.5.3
adf <- ur.df(return, type = "drift", lags = 2)
summary(adf)
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.128963 -0.018381 -0.000819 0.016041 0.180869
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0001944 0.0009124 0.213 0.831
## z.lag.1 -0.9985271 0.0469335 -21.275 <2e-16 ***
## z.diff.lag1 0.0125424 0.0377798 0.332 0.740
## z.diff.lag2 -0.0348510 0.0268698 -1.297 0.195
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03382 on 1370 degrees of freedom
## Multiple R-squared: 0.4982, Adjusted R-squared: 0.4971
## F-statistic: 453.4 on 3 and 1370 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -21.2754 226.3239
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.43 -2.86 -2.57
## phi1 6.43 4.59 3.78
# 5. MODEL ARIMA (MEAN)
library(forecast)
## Warning: package 'forecast' was built under R version 4.5.3
auto.arima(return, trace = TRUE)
##
## Fitting models using approximations to speed things up...
##
## ARIMA(2,0,2) with non-zero mean : -5404.354
## ARIMA(0,0,0) with non-zero mean : -5403.453
## ARIMA(1,0,0) with non-zero mean : -5400.57
## ARIMA(0,0,1) with non-zero mean : -5401.584
## ARIMA(0,0,0) with zero mean : -5405.377
## ARIMA(1,0,1) with non-zero mean : -5399.704
##
## Now re-fitting the best model(s) without approximations...
##
## ARIMA(0,0,0) with zero mean : -5405.377
##
## Best model: ARIMA(0,0,0) with zero mean
## Series: return
## ARIMA(0,0,0) with zero mean
##
## sigma^2 = 0.001154: log likelihood = 2703.69
## AIC=-5405.38 AICc=-5405.38 BIC=-5400.15
model_arima <- Arima(return_xts, order = c(1,0,0), include.mean = TRUE)
summary(model_arima)
## Series: return_xts
## ARIMA(1,0,0) with non-zero mean
##
## Coefficients:
## ar1 mean
## 0.0096 3e-04
## s.e. 0.0269 9e-04
##
## sigma^2 = 0.001155: log likelihood = 2703.79
## AIC=-5401.59 AICc=-5401.57 BIC=-5385.9
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set -3.741311e-08 0.03396319 0.02432459 NaN Inf 1.002017 0.0004568386
resid <- residuals(model_arima)
# 6. UJI EFEK ARCH
library(nortsTest)
## Warning: package 'nortsTest' was built under R version 4.5.3
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## Registered S3 methods overwritten by 'nortsTest':
## method from
## autoplot.ts forecast
## fortify.ts forecast
arch.test(resid)
##
## Box-Ljung test
##
## data: y^2
## X-squared = 52.137, df = 2, p-value = 4.772e-12
## alternative hypothesis: y is heteroscedastic
# 7. ESTIMASI MODEL ARCH/GARCH
library(rugarch)
## Warning: package 'rugarch' was built under R version 4.5.3
## Loading required package: parallel
spec1 <- ugarchspec(
variance.model = list(model = "sGARCH", garchOrder = c(1,0)),
mean.model = list(armaOrder = c(1,0), include.mean = TRUE)
)
fit1 <- ugarchfit(spec1, data = return)
fit1
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,0)
## Mean Model : ARFIMA(1,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000248 0.000859 0.28896 0.772611
## ar1 -0.026799 0.031019 -0.86396 0.387612
## omega 0.000988 0.000046 21.34214 0.000000
## alpha1 0.138411 0.034446 4.01819 0.000059
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000248 0.000839 0.29595 0.76726
## ar1 -0.026799 0.025705 -1.04255 0.29716
## omega 0.000988 0.000087 11.34181 0.00000
## alpha1 0.138411 0.040384 3.42733 0.00061
##
## LogLikelihood : 2726.633
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.9544
## Bayes -3.9393
## Shibata -3.9545
## Hannan-Quinn -3.9488
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4375 0.5083
## Lag[2*(p+q)+(p+q)-1][2] 2.0156 0.2081
## Lag[4*(p+q)+(p+q)-1][5] 4.4130 0.1670
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1100 0.74014
## Lag[2*(p+q)+(p+q)-1][2] 0.7947 0.56990
## Lag[4*(p+q)+(p+q)-1][5] 6.8052 0.05781
## d.o.f=1
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[2] 1.365 0.500 2.000 0.242605
## ARCH Lag[4] 5.615 1.397 1.611 0.062306
## ARCH Lag[6] 11.820 2.222 1.500 0.004902
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.5843
## Individual Statistics:
## mu 0.23257
## ar1 0.05856
## omega 0.88604
## alpha1 1.19356
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.4869 0.6264
## Negative Sign Bias 0.4839 0.6285
## Positive Sign Bias 0.1459 0.8840
## Joint Effect 0.3068 0.9588
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 97.55 1.482e-12
## 2 30 109.51 2.783e-11
## 3 40 159.88 1.424e-16
## 4 50 185.71 8.741e-18
##
##
## Elapsed time : 1.408073
spec2 <- ugarchspec(
variance.model = list(model = "sGARCH", garchOrder = c(2,0)),
mean.model = list(armaOrder = c(1,0), include.mean = TRUE)
)
fit2 <- ugarchfit(spec2, data = return)
fit2
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(2,0)
## Mean Model : ARFIMA(1,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000327 0.000847 0.38637 0.699220
## ar1 -0.030349 0.031124 -0.97511 0.329505
## omega 0.000905 0.000052 17.49048 0.000000
## alpha1 0.133904 0.033973 3.94150 0.000081
## alpha2 0.084363 0.035318 2.38866 0.016910
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000327 0.000802 0.40796 0.683303
## ar1 -0.030349 0.027298 -1.11179 0.266230
## omega 0.000905 0.000101 8.99333 0.000000
## alpha1 0.133904 0.040538 3.30316 0.000956
## alpha2 0.084363 0.048903 1.72509 0.084511
##
## LogLikelihood : 2731.015
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.9594
## Bayes -3.9404
## Shibata -3.9594
## Hannan-Quinn -3.9523
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7494 0.3867
## Lag[2*(p+q)+(p+q)-1][2] 1.8295 0.2773
## Lag[4*(p+q)+(p+q)-1][5] 3.6778 0.2815
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1617 0.68756
## Lag[2*(p+q)+(p+q)-1][5] 4.9437 0.15763
## Lag[4*(p+q)+(p+q)-1][9] 11.8086 0.02005
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 3.287 0.500 2.000 0.069827
## ARCH Lag[5] 10.331 1.440 1.667 0.005456
## ARCH Lag[7] 13.053 2.315 1.543 0.003460
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.7094
## Individual Statistics:
## mu 0.23032
## ar1 0.05856
## omega 0.84301
## alpha1 1.22401
## alpha2 0.09558
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.36266 0.7169
## Negative Sign Bias 0.22264 0.8238
## Positive Sign Bias 0.04418 0.9648
## Joint Effect 0.15409 0.9846
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 95.9 2.942e-12
## 2 30 108.6 3.872e-11
## 3 40 150.7 4.780e-15
## 4 50 177.5 1.857e-16
##
##
## Elapsed time : 0.4328799
spec3 <- ugarchspec(
variance.model = list(model = "sGARCH", garchOrder = c(1,1)),
mean.model = list(armaOrder = c(1,0), include.mean = TRUE)
)
fit3 <- ugarchfit(spec3, data = return)
fit3
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(1,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000054 0.000822 -0.065579 0.947713
## ar1 -0.005346 0.029394 -0.181864 0.855690
## omega 0.000065 0.000018 3.568404 0.000359
## alpha1 0.088988 0.018673 4.765535 0.000002
## beta1 0.855167 0.028366 30.148005 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000054 0.000823 -0.065513 0.947765
## ar1 -0.005346 0.026372 -0.202707 0.839364
## omega 0.000065 0.000030 2.173316 0.029757
## alpha1 0.088988 0.026983 3.297891 0.000974
## beta1 0.855167 0.045125 18.951184 0.000000
##
## LogLikelihood : 2764.786
##
## Information Criteria
## ------------------------------------
##
## Akaike -4.0084
## Bayes -3.9894
## Shibata -4.0084
## Hannan-Quinn -4.0013
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1756 0.6752
## Lag[2*(p+q)+(p+q)-1][2] 1.7418 0.3152
## Lag[4*(p+q)+(p+q)-1][5] 3.3990 0.3379
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.852 0.1736
## Lag[2*(p+q)+(p+q)-1][5] 2.466 0.5131
## Lag[4*(p+q)+(p+q)-1][9] 3.131 0.7371
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.6455 0.500 2.000 0.4217
## ARCH Lag[5] 0.8473 1.440 1.667 0.7787
## ARCH Lag[7] 0.9811 2.315 1.543 0.9166
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 0.7056
## Individual Statistics:
## mu 0.2117
## ar1 0.1482
## omega 0.1721
## alpha1 0.2053
## beta1 0.1601
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.34932 0.7269
## Negative Sign Bias 0.07335 0.9415
## Positive Sign Bias 0.23073 0.8176
## Joint Effect 0.41854 0.9364
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 79.08 2.679e-09
## 2 30 105.98 1.055e-10
## 3 40 133.97 2.423e-12
## 4 50 195.44 2.201e-19
##
##
## Elapsed time : 0.4661701
spec4 <- ugarchspec(
variance.model = list(model = "sGARCH", garchOrder = c(1,0)),
mean.model = list(armaOrder = c(1,0), include.mean = TRUE)
)
fit4 <- ugarchfit(spec4, data = return)
fit4
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,0)
## Mean Model : ARFIMA(1,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000248 0.000859 0.28896 0.772611
## ar1 -0.026799 0.031019 -0.86396 0.387612
## omega 0.000988 0.000046 21.34214 0.000000
## alpha1 0.138411 0.034446 4.01819 0.000059
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000248 0.000839 0.29595 0.76726
## ar1 -0.026799 0.025705 -1.04255 0.29716
## omega 0.000988 0.000087 11.34181 0.00000
## alpha1 0.138411 0.040384 3.42733 0.00061
##
## LogLikelihood : 2726.633
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.9544
## Bayes -3.9393
## Shibata -3.9545
## Hannan-Quinn -3.9488
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4375 0.5083
## Lag[2*(p+q)+(p+q)-1][2] 2.0156 0.2081
## Lag[4*(p+q)+(p+q)-1][5] 4.4130 0.1670
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1100 0.74014
## Lag[2*(p+q)+(p+q)-1][2] 0.7947 0.56990
## Lag[4*(p+q)+(p+q)-1][5] 6.8052 0.05781
## d.o.f=1
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[2] 1.365 0.500 2.000 0.242605
## ARCH Lag[4] 5.615 1.397 1.611 0.062306
## ARCH Lag[6] 11.820 2.222 1.500 0.004902
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.5843
## Individual Statistics:
## mu 0.23257
## ar1 0.05856
## omega 0.88604
## alpha1 1.19356
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.4869 0.6264
## Negative Sign Bias 0.4839 0.6285
## Positive Sign Bias 0.1459 0.8840
## Joint Effect 0.3068 0.9588
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 97.55 1.482e-12
## 2 30 109.51 2.783e-11
## 3 40 159.88 1.424e-16
## 4 50 185.71 8.741e-18
##
##
## Elapsed time : 0.4414599
spec5 <- ugarchspec(
variance.model = list(model = "sGARCH", garchOrder = c(0,1)),
mean.model = list(armaOrder = c(1,0), include.mean = TRUE)
)
fit5 <- ugarchfit(spec5, data = return)
fit5
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(0,1)
## Mean Model : ARFIMA(1,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000135 0.000912 1.4826e-01 0.88214
## ar1 0.003898 0.026946 1.4466e-01 0.88498
## omega 0.000002 0.000000 1.2347e+02 0.00000
## beta1 0.997634 0.000015 6.7858e+04 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000135 0.001001 1.3507e-01 0.89256
## ar1 0.003898 0.034842 1.1187e-01 0.91092
## omega 0.000002 0.000000 5.4628e+01 0.00000
## beta1 0.997634 0.000044 2.2922e+04 0.00000
##
## LogLikelihood : 2708.447
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.9280
## Bayes -3.9128
## Shibata -3.9280
## Hannan-Quinn -3.9223
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01037 0.9189
## Lag[2*(p+q)+(p+q)-1][2] 1.59342 0.3872
## Lag[4*(p+q)+(p+q)-1][5] 4.40379 0.1682
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 42.13 8.553e-11
## Lag[2*(p+q)+(p+q)-1][2] 43.15 3.840e-12
## Lag[4*(p+q)+(p+q)-1][5] 51.18 2.909e-14
## d.o.f=1
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[2] 2.040 0.500 2.000 0.1531788
## ARCH Lag[4] 8.956 1.397 1.611 0.0091304
## ARCH Lag[6] 15.798 2.222 1.500 0.0004752
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 22.0039
## Individual Statistics:
## mu 0.2575
## ar1 0.3088
## omega 3.9659
## beta1 0.4731
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.371 1.706e-01
## Negative Sign Bias 1.915 5.571e-02 *
## Positive Sign Bias 5.250 1.762e-07 ***
## Joint Effect 31.397 7.011e-07 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 99.96 5.436e-13
## 2 30 153.83 5.980e-19
## 3 40 192.01 4.243e-22
## 4 50 272.13 1.077e-32
##
##
## Elapsed time : 0.2318211
# 8. BANDINGKAN MODEL
cat("ARCH(1) : AIC =", infocriteria(fit1)[1], "\n")
## ARCH(1) : AIC = -3.954441
cat("ARCH(2) : AIC =", infocriteria(fit2)[1], "\n")
## ARCH(2) : AIC = -3.959353
cat("GARCH(1,1) : AIC =", infocriteria(fit3)[1], "\n")
## GARCH(1,1) : AIC = -4.008403
cat("GARCH(1,0) : AIC =", infocriteria(fit4)[1], "\n")
## GARCH(1,0) : AIC = -3.954441
cat("GARCH(0,1) : AIC =", infocriteria(fit5)[1], "\n")
## GARCH(0,1) : AIC = -3.928028
# 9. PERAMALAN VOLATILITAS
forecast <- ugarchforecast(fit3, n.ahead = 10)
forecast
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: sGARCH
## Horizon: 10
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=1973-10-09]:
## Series Sigma
## T+1 -5.421e-05 0.02686
## T+2 -5.392e-05 0.02732
## T+3 -5.393e-05 0.02774
## T+4 -5.393e-05 0.02814
## T+5 -5.393e-05 0.02851
## T+6 -5.393e-05 0.02885
## T+7 -5.393e-05 0.02917
## T+8 -5.393e-05 0.02947
## T+9 -5.393e-05 0.02975
## T+10 -5.393e-05 0.03002
plot(forecast, which = 1)
# Plot volatilitas bersyarat
plot(fit3, which = 3)
# INTERPRETASI
# Ambil parameter model terbaik (misal GARCH(1,1))
params <- coef(fit3)
omega <- params["omega"]
alpha <- params["alpha1"]
beta <- params["beta1"]
cat("=== INTERPRETASI MODEL GARCH(1,1) ===\n")
## === INTERPRETASI MODEL GARCH(1,1) ===
cat("Omega (volatilitas dasar) :", omega, "\n")
## Omega (volatilitas dasar) : 6.51144e-05
cat("Alpha (efek kejutan) :", alpha, "\n")
## Alpha (efek kejutan) : 0.08898765
cat("Beta (efek volatilitas lalu) :", beta, "\n")
## Beta (efek volatilitas lalu) : 0.8551667
cat("Alpha + Beta :", alpha + beta, "\n")
## Alpha + Beta : 0.9441543
cat("Long-term volatility :", omega / (1 - alpha - beta), "\n")
## Long-term volatility : 0.00116597
if (alpha + beta >= 1) {
cat("Kesimpulan: Volatilitas TIDAK stasioner (shock permanen).\n")
} else if (alpha + beta > 0.9) {
cat("Kesimpulan: Volatilitas PERSISTEN (shock bertahan lama).\n")
} else {
cat("Kesimpulan: Volatilitas CEPAT kembali ke rata-rata.\n")
}
## Kesimpulan: Volatilitas PERSISTEN (shock bertahan lama).
# Tampilkan peramalan
cat("\n=== PERAMALAN VOLATILITAS 10 HARI KE DEPAN ===\n")
##
## === PERAMALAN VOLATILITAS 10 HARI KE DEPAN ===
print(forecast)
##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: sGARCH
## Horizon: 10
## Roll Steps: 0
## Out of Sample: 0
##
## 0-roll forecast [T0=1973-10-09]:
## Series Sigma
## T+1 -5.421e-05 0.02686
## T+2 -5.392e-05 0.02732
## T+3 -5.393e-05 0.02774
## T+4 -5.393e-05 0.02814
## T+5 -5.393e-05 0.02851
## T+6 -5.393e-05 0.02885
## T+7 -5.393e-05 0.02917
## T+8 -5.393e-05 0.02947
## T+9 -5.393e-05 0.02975
## T+10 -5.393e-05 0.03002