ANALISIS DATA SAHAM AMAZON
library yang digunakan
library(readxl)
library(openxlsx)
library(astsa)
library(dynlm) #time series regression ## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(broom) #LM test
library(FinTS) #ARCH test
library(forecast)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo##
## Attaching package: 'forecast'## The following object is masked from 'package:FinTS':
##
## Acf## The following object is masked from 'package:astsa':
##
## gaslibrary(tseries)
library(TTR)
library(TSA)## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast##
## Attaching package: 'TSA'## The following objects are masked from 'package:stats':
##
## acf, arima## The following object is masked from 'package:utils':
##
## tarlibrary(graphics)
library(portes)## Loading required package: parallellibrary(tseries)
library(car)## Loading required package: carDatalibrary(rugarch)##
## Attaching package: 'rugarch'## The following object is masked from 'package:stats':
##
## sigmaData
Data yang digunakan adalah data Saham (Stock) dari perusahaan Amazon dimana data di peroleh dari website Kaggle dengan link: https://www.kaggle.com/datasets/szrlee/stock-time-series-20050101-to-20171231?resource=download&select=AMZN_2006-01-01_to_2018-01-01.csv
Data saham Amazon yang digunakan adalah data terdiri dari 13 Tahun data (2006-01-01 hingga 2018-01-01), dimana data berupa data harian saham yang terdiri dari :
Date - in format: yy-mm-dd
Open - harga awal di pasar saham (this is NYSE data so all in USD)
High - harga tertinggi pada hari itu
Low Close - harga terendah pada hari itu
Volume - Number of shares traded
Name - the stock’s ticker name
yang akan di lakukan dalam pengolahan data untuk model time series menguji efek arch/garch digunakan data “High Close” saja semua data yang terdiri dari 3019 data dari 1 Januari 2006 hingga 1 Januari 2018.
data_amazon<- read.csv("~/Documents/Amazon Stock.csv",sep=",")
head(data_amazon)## Date Open High Low Close Volume Name
## 1 2006-01-03 47.47 47.85 46.25 47.58 7582127 AMZN
## 2 2006-01-04 47.48 47.73 46.69 47.25 7440914 AMZN
## 3 2006-01-05 47.16 48.20 47.11 47.65 5417258 AMZN
## 4 2006-01-06 47.97 48.58 47.32 47.87 6154285 AMZN
## 5 2006-01-09 46.55 47.10 46.40 47.08 8945056 AMZN
## 6 2006-01-10 46.41 46.75 45.36 45.65 9686957 AMZNdata_amazon.ts <- ts(data_amazon[,"Close"],start=1,end=3019)
head(data_amazon.ts)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] 47.58 47.25 47.65 47.87 47.08 45.65Plot Data Time series
plot(data_amazon.ts, type="l",
main="Saham amazon 01/01/2006 - 01/01/2018",
xlab = "Hari ke -",
ylab = "Close Price")
Memeriksa Pola musiman
seasonplot(data_amazon.ts,30,
main="Saham amazon 01/01/2006 - 01/01/2018",
xlab = "Hari ke -",
ylab = "Close Price",
year.labels = TRUE, col=rainbow(18))
dilakukan pengujian pola musiman untuk memastikan apakah data memiliki pola musiman, walaupun secara plot time series tidak ditemukan pola tertentu pada data saham Google ini, dana setelah dilakukan pengujian pola musiman untuk beberapa kali seperti 7 hari, 14 hari dan 30 hari tidak terdapat pola tertentu dalam data (ditampilkan hanya pola untuk 30 hari), sehingga dapat disimpulkan bahwa data tidak memiliki pola musiman.
Membagi Data
Data yang terdiri dari 3019 data akan di bagi menjadi 2 bagian yaitu data training dan data testing, pembagian data dilakukan sekitar 80-20 antara training dan testing, sehingga data training sebanyak 2419 data dan 600 data testing sebagai berikut:
data_amazon.ts.train <- data_amazon.ts[1:2419]
data_amazon.ts.test <- data_amazon.ts[2420:3019]Plot antara data Train dan Testing
plot(data_amazon.ts.train, type="l",
main="Data Training Saham amazon 01/01/2006 - 01/01/2018",
xlab = "Hari ke -",
ylab = "Close Price")
plot(data_amazon.ts.test, type="l",
main="Data Testing Saham amazon 01/01/2006 - 01/01/2018",
xlab = "Hari ke -",
ylab = "Close Price")
Uji Stasioner data Training
acf(data_amazon.ts.train,lag.max = 30)
adf.test(data_amazon.ts.train, alternative=c("stationary"),
k=trunc((length(data_amazon.ts.train)-1)^(1/3)))##
## Augmented Dickey-Fuller Test
##
## data: data_amazon.ts.train
## Dickey-Fuller = -1.437, Lag order = 13, p-value = 0.8167
## alternative hypothesis: stationarydari hasil pengujian dengan plot ACF dan uji ADF untuk data training ddapat disimpulkan bahwa data belum stasioner dengan bentuk lag pada plot ACF yang turun lambat atau eksponensial dan pada uji ADF yang diperoleh nilai p-value yaitu 0.8167 lebih besar dari alpha=0.05.
Differencing Data
Karena data yang belum stasioner maka akan dilakukan differencing untuk membuat data stasioner sebagai berikut :
diff.1.amazon <- diff(data_amazon.ts.train,differences = 1)
plot(diff.1.amazon,type="l",
main="Differencing 1 Data Train Saham",
xlab = "Hari ke -",
ylab = "Close Price")
lalu akan diuji stasioner pada data differencing :
acf(diff.1.amazon,lag.max = 30)
adf.test(diff.1.amazon, alternative=c("stationary"),
k=trunc((length(diff.1.amazon)-1)^(1/3)))## Warning in adf.test(diff.1.amazon, alternative = c("stationary"), k =
## trunc((length(diff.1.amazon) - : p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: diff.1.amazon
## Dickey-Fuller = -13.462, Lag order = 13, p-value = 0.01
## alternative hypothesis: stationarysetelah dilihat dari plot ACF dan uji ADF pada data hasil differencing pertama diperoleh bahwa data telah stasioner dengan plot acf yang telah cut-off setelah lag-2 dan hasil nilai p-value = 0.01 yang lebih kecil dari alpa=0.05. lalu akan dicari model tentatif selanjutnya :
pacf(diff.1.amazon,lag.max = 30)
eacf(diff.1.amazon)## AR/MA
## 0 1 2 3 4 5 6 7 8 9 10 11 12 13
## 0 o x o o o o o o o o o o o o
## 1 x x o o o o o o o o o o o o
## 2 x x o o o o o o o o o o o o
## 3 x x x o o o o o o o o o o o
## 4 x x x x o o o o o o o o o o
## 5 x x x o o o o o o o o o o o
## 6 x x x o o x o o o o o o o o
## 7 x x o o o x x o o o o o o odari plot ACF, PACF dan EACF diperoleh modle tentatif yaitu : 1. Dari plot ACF diperoleh model ARIMA(0,1,2) 2. Dari plot PACF diperoleh model ARIMA(2,1,0) 3. Dari ECAF diperoleh model ARIMA(1,1,2), ARIMA(2,1,2)
Sehingga dari model tentatif diatas akan di pilih model terbaik yang memiliki nilai AIC terkecil yaitu :
Memilih Model Mean Terbaik
ARIMA012 <- arima(diff.1.amazon, order=c(0,0,2), method = "ML")
ARIMA210 <- arima(diff.1.amazon, order=c(2,0,0), method = "ML")
ARIMA112 <- arima(diff.1.amazon, order=c(1,0,2), method = "ML")
ARIMA212 <- arima(diff.1.amazon, order=c(2,0,2), method = "ML")
Model <- c("ARIMA(0,1,2)","ARIMA(2,1,0)","ARIMA(1,1,2)","ARIMA(2,1,2)")
AIC <- c(ARIMA012$aic,ARIMA210$aic,ARIMA112$aic,ARIMA212$aic)
perbandingan_AIC <- as.data.frame(cbind(Model,AIC))
perbandingan_AIC## Model AIC
## 1 ARIMA(0,1,2) 14049.1673390684
## 2 ARIMA(2,1,0) 14049.3359896749
## 3 ARIMA(1,1,2) 14051.1720611438
## 4 ARIMA(2,1,2) 14053.1037022913Dari perbandingan model tentatif diatas diperoleh bahwa model terbaik dengan nilai AIC terkecil yaitu model ARIMA(0,1,2) yaitu 14049.167. Lalu, akan dilakukan pengujian signifikasni parameter model sebagai berikut :
Uji SIgnifikansi Parameter
printstatarima <- function (x, digits = 4,se=TRUE){ if (length(x$coef) > 0) {
cat("\nCoefficients:\n")
coef <- round(x$coef, digits = digits)
if (se && nrow(x$var.coef)) {
ses <- rep(0, length(coef))
ses[x$mask] <- round(sqrt(diag(x$var.coef)), digits = digits)
coef <- matrix(coef, 1, dimnames = list(NULL, names(coef)))
coef <- rbind(coef, s.e. = ses)
statt <- coef[1,]/ses
pval <- 2*pt(abs(statt), df=length(x$residuals)-1, lower.tail = FALSE)
coef <- rbind(coef, t=round(statt,digits=digits),sign.=round(pval,digits=digits))
coef <- t(coef)
}
print.default(coef, print.gap = 2)
}
}
printstatarima(ARIMA012)##
## Coefficients:
## s.e. t sign.
## ma1 -0.0242 0.0203 -1.1921 0.2333
## ma2 -0.0505 0.0204 -2.4755 0.0134
## intercept 0.1994 0.0831 2.3995 0.0165dengan dilihat bahwa sebenarnya model ARIMA(0,1,2) yang memiliki nilai AIC terkecil namun parameternya MA(1) tidak signifikan, sehingga akan dicoba dengan model auto.arima sebagai berikut :
auto.arima(data_amazon.ts.train)## Series: data_amazon.ts.train
## ARIMA(0,1,0) with drift
##
## Coefficients:
## drift
## 0.1994
## s.e. 0.0899
##
## sigma^2 = 19.56: log likelihood = -7025.31
## AIC=14054.62 AICc=14054.62 BIC=14066.2dengan bantuan fungsi auto.arima diperoleh model terbaik yaitu model ARIMA(0,1,0), namun jika dibandingkan nilai AIC kembali masih lebih kecil nilai AIC dari model ARIMA(0,1,2), sehingga disimpulkan model terbaik yaitu ARIMA(0,1,2)
Lalu, akan dilakukan pengujian dignostik model sebagai berikut :
Uji Diagnostik Model
sisaan <- ARIMA012$residuals
# Uji formal normalitas data
qqnorm(sisaan)
qqline(sisaan)
# Uji nilai tengah sisaan
t.test(sisaan, mu = 0, alternative = "two.sided")##
## One Sample t-test
##
## data: sisaan
## t = -0.00086754, df = 2417, p-value = 0.9993
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## -0.1761656 0.1760098
## sample estimates:
## mean of x
## -7.790235e-05# Uji autokorelasi
Box.test(sisaan, lag = 23 ,type = "Ljung")##
## Box-Ljung test
##
## data: sisaan
## X-squared = 24.137, df = 23, p-value = 0.3962Berdasarkan hasil uji dignostik untuk model terbaik ARIMA010 diperoleh sebagai berikut :
Hasil pengujian:
Normalitas Data
Berdasarkan pada Q-Q plot yang diperoleh bahwa residual menyabr pada mengikuti garis lurus, sehingga dapat dikatakan bahwa residual menyebar normal.
Nilai Tengah Sisaan
\(H_0:μ=0\) \(H_1:μ≠0\)
Hasil : \(p−value=0.9993 > α=0.05\) yang berarti TOLAK H0, Nilai tengah sisaan sama dengan 0
Autokorelasi
\(H_0\) : tidak ada autokorelasi \(H_1\) : terdapat autokorelasi
Hasil : \(p−value=0.3962 > α=0.05\) yang berarti TERIMA H0, Tidak terdapat gejala autokorelasi pada sisaan
Kesimpulan : Asumsi terpenuhi untuk residual pada model ARIMA(0,1,2)
Uji sisaan Mean Model
e_topi <- ts(sisaan)
plot.ts(e_topi)
e_topisq <- ts(sisaan^2)
plot.ts(e_topisq)
acf(e_topisq)
pacf(e_topisq)
Uji Efek ARCH
bydArchTest1 <- ArchTest(sisaan, lags=1, demean=TRUE)
bydArchTest1##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: sisaan
## Chi-squared = 9.8042, df = 1, p-value = 0.001741bydArchTest2 <- ArchTest(sisaan, lags=2, demean=TRUE)
bydArchTest2##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: sisaan
## Chi-squared = 10.016, df = 2, p-value = 0.006683bydArchTest3 <- ArchTest(sisaan, lags=3, demean=TRUE)
bydArchTest3##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: sisaan
## Chi-squared = 10.017, df = 3, p-value = 0.01842bydArchTest4 <- ArchTest(sisaan, lags=4, demean=TRUE)
bydArchTest4##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: sisaan
## Chi-squared = 14.705, df = 4, p-value = 0.005355bydArchTest5 <- ArchTest(sisaan, lags=5, demean=TRUE)
bydArchTest5##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: sisaan
## Chi-squared = 17.825, df = 5, p-value = 0.003174bydArchTest6 <- ArchTest(sisaan, lags=6, demean=TRUE)
bydArchTest6##
## ARCH LM-test; Null hypothesis: no ARCH effects
##
## data: sisaan
## Chi-squared = 18.679, df = 6, p-value = 0.004742setelah dilakukan uji efek ARCH untuk 5 lag awal, semua nia p-value menunjukkan signifikan, sehingga akan dicoba dengan GARCH.
#Menentukan model volatilitas jika efek ARCH secara statistik signifikan
#Pendugaan model ARCH/GARCH dengan function garch secara simultan
amazon.arch1 <- garch(data_amazon.ts.train,c(0,1)) #ordo ARCH(1)##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 1.325545e+04 1.000e+00
## 2 5.000000e-02 1.000e+00
##
## IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
## 0 1 1.468e+04
## 1 2 1.353e+04 7.87e-02 8.04e-01 3.8e-05 1.2e+04 1.0e+00 4.75e+03
## 2 3 1.352e+04 2.51e-04 1.27e-04 8.9e-07 0.0e+00 2.9e-02 1.27e-04
## 3 5 1.349e+04 2.12e-03 1.22e-03 8.9e-06 0.0e+00 2.9e-01 1.22e-03
## 4 7 1.348e+04 8.73e-04 1.87e-03 1.0e-05 2.5e+00 2.7e-01 2.11e-03
## 5 8 1.348e+04 2.22e-04 4.13e-04 4.2e-06 0.0e+00 1.1e-01 4.13e-04
## 6 9 1.348e+04 4.43e-05 3.70e-05 1.1e-06 0.0e+00 3.4e-02 3.70e-05
## 7 10 1.348e+04 1.40e-06 1.49e-06 1.0e-06 0.0e+00 2.8e-02 1.49e-06
## 8 11 1.348e+04 4.83e-08 2.72e-08 8.5e-07 0.0e+00 2.2e-02 2.72e-08
## 9 13 1.348e+04 2.68e-07 1.71e-07 7.1e-06 0.0e+00 1.9e-01 1.71e-07
## 10 15 1.348e+04 5.76e-07 3.51e-07 1.9e-05 0.0e+00 5.0e-01 3.51e-07
## 11 17 1.348e+04 1.63e-06 1.01e-06 6.0e-05 0.0e+00 1.6e+00 1.01e-06
## 12 19 1.348e+04 4.12e-06 2.54e-06 1.6e-04 0.0e+00 4.3e+00 2.54e-06
## 13 21 1.348e+04 1.08e-05 6.70e-06 4.4e-04 0.0e+00 1.2e+01 6.70e-06
## 14 23 1.348e+04 2.80e-05 1.72e-05 1.2e-03 0.0e+00 3.1e+01 1.72e-05
## 15 24 1.348e+04 7.22e-05 4.45e-05 3.1e-03 0.0e+00 8.2e+01 4.45e-05
## 16 25 1.348e+04 1.85e-04 1.14e-04 8.2e-03 0.0e+00 2.1e+02 1.14e-04
## 17 26 1.347e+04 4.75e-04 2.90e-04 2.2e-02 0.0e+00 5.6e+02 2.90e-04
## 18 27 1.345e+04 1.27e-03 7.56e-04 6.6e-02 0.0e+00 1.5e+03 7.56e-04
## 19 29 1.339e+04 4.81e-03 2.40e-03 3.1e-01 0.0e+00 5.2e+03 2.40e-03
## 20 31 1.334e+04 3.65e-03 2.81e-03 2.3e-01 1.8e+00 2.1e+03 3.38e-02
## 21 33 1.332e+04 1.55e-03 1.14e-03 6.2e-02 2.0e+00 4.1e+02 1.62e+00
## 22 35 1.324e+04 5.86e-03 3.95e-03 1.5e-01 2.0e+00 8.3e+02 6.55e+00
## 23 36 1.320e+04 2.82e-03 1.44e-02 5.5e-01 2.0e+00 1.7e+03 4.48e+01
## 24 38 1.313e+04 5.25e-03 2.56e-02 1.4e-01 2.0e+00 1.7e+02 6.88e+00
## 25 40 1.310e+04 2.65e-03 1.66e-03 2.0e-01 2.0e+00 1.7e+02 8.13e+00
## 26 48 1.308e+04 1.57e-03 2.73e-03 4.2e-04 2.7e+00 2.8e-01 2.01e+00
## 27 49 1.308e+04 1.45e-04 2.80e-04 4.0e-04 2.0e+00 2.8e-01 3.20e+00
## 28 50 1.308e+04 3.67e-05 3.23e-05 4.2e-04 2.0e+00 2.8e-01 3.17e+00
## 29 51 1.308e+04 9.69e-07 1.00e-06 4.3e-04 2.0e+00 2.8e-01 3.16e+00
## 30 57 1.307e+04 2.76e-04 4.45e-04 7.7e-01 2.0e+00 2.9e+02 3.16e+00
## 31 59 1.307e+04 2.91e-06 3.05e-06 6.3e-02 1.8e+00 5.1e+00 7.81e-06
## 32 61 1.307e+04 3.05e-06 3.43e-06 3.7e-01 7.3e-01 2.0e+01 5.17e-06
## 33 62 1.307e+04 5.93e-07 6.10e-07 6.7e-01 0.0e+00 1.4e+01 6.10e-07
## 34 63 1.307e+04 9.13e-10 9.31e-10 6.5e-02 0.0e+00 4.8e-01 9.31e-10
## 35 64 1.307e+04 3.57e-13 3.57e-13 1.1e-03 0.0e+00 8.7e-03 3.57e-13
##
## ***** RELATIVE FUNCTION CONVERGENCE *****
##
## FUNCTION 1.307164e+04 RELDX 1.115e-03
## FUNC. EVALS 64 GRAD. EVALS 36
## PRELDF 3.572e-13 NPRELDF 3.572e-13
##
## I FINAL X(I) D(I) G(I)
##
## 1 3.913179e+00 1.000e+00 7.630e-10
## 2 1.002753e+00 1.000e+00 2.932e-07## Warning in sqrt(pred$e): NaNs producedamazonarch1 <- summary(amazon.arch1)
amazonarch1##
## Call:
## garch(x = data_amazon.ts.train, order = c(0, 1))
##
## Model:
## GARCH(0,1)
##
## Residuals:
## Min 1Q Median 3Q Max
## 0.7794 0.9872 0.9985 1.0118 1.2665
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## a0 3.913 2916.842 0.001 0.999
## a1 1.003 1.020 0.983 0.326
##
## Diagnostic Tests:
## Jarque Bera Test
##
## data: Residuals
## X-squared = 28094, df = 2, p-value < 2.2e-16
##
##
## Box-Ljung test
##
## data: Squared.Residuals
## X-squared = 0.24086, df = 1, p-value = 0.6236#str(sbydarch)
plot(amazon.arch1) 
hist(amazonarch1$residuals)
qqnorm(amazonarch1$residuals)
qqline(amazonarch1$residuals, col = "red", lwd = 2)
Model GARCH
#GARCH(1,1)
garchSpec11 <- ugarchspec(
variance.model=list(model="sGARCH",
garchOrder=c(1,1)),
mean.model=list(armaOrder=c(0,2)))
garchFit11 <- ugarchfit(spec=garchSpec11, data=diff.1.amazon)
coef(garchFit11)## mu ma1 ma2 omega alpha1 beta1
## 0.12463600 -0.03035405 -0.05831443 0.03763845 0.02575735 0.97324263garchFit11##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,1)
## Mean Model : ARFIMA(0,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.124636 0.052939 2.3543 0.018556
## ma1 -0.030354 0.022738 -1.3349 0.181902
## ma2 -0.058314 0.023207 -2.5127 0.011979
## omega 0.037638 0.007578 4.9671 0.000001
## alpha1 0.025757 0.002732 9.4281 0.000000
## beta1 0.973243 0.002867 339.4052 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.124636 0.058579 2.1276 0.033366
## ma1 -0.030354 0.027120 -1.1193 0.263031
## ma2 -0.058314 0.024251 -2.4047 0.016188
## omega 0.037638 0.033996 1.1071 0.268230
## alpha1 0.025757 0.008963 2.8737 0.004056
## beta1 0.973243 0.010706 90.9036 0.000000
##
## LogLikelihood : -6544.866
##
## Information Criteria
## ------------------------------------
##
## Akaike 5.4184
## Bayes 5.4328
## Shibata 5.4184
## Hannan-Quinn 5.4236
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.0001553 0.9901
## Lag[2*(p+q)+(p+q)-1][5] 0.2181728 1.0000
## Lag[4*(p+q)+(p+q)-1][9] 0.9518012 0.9998
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.766 0.1839
## Lag[2*(p+q)+(p+q)-1][5] 2.279 0.5541
## Lag[4*(p+q)+(p+q)-1][9] 2.500 0.8377
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.4636 0.500 2.000 0.4959
## ARCH Lag[5] 0.5937 1.440 1.667 0.8557
## ARCH Lag[7] 0.6559 2.315 1.543 0.9622
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.667
## Individual Statistics:
## mu 0.36018
## ma1 0.02986
## ma2 0.07162
## omega 0.16405
## alpha1 0.08142
## beta1 0.25034
##
## 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 0.1930 0.84700
## Negative Sign Bias 0.5549 0.57903
## Positive Sign Bias 1.9471 0.05164 *
## Joint Effect 4.3432 0.22671
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 278.4 5.318e-48
## 2 30 305.4 6.866e-48
## 3 40 305.3 5.258e-43
## 4 50 325.2 2.036e-42
##
##
## Elapsed time : 0.103076res<-garchFit11@fit$residuals
res.ts<-ts(res)
plot.ts(res.ts)
#GARCH(1,2)
garchSpec12 <- ugarchspec(
variance.model=list(model="sGARCH",
garchOrder=c(1,2)),
mean.model=list(armaOrder=c(0,2)))
garchFit12 <- ugarchfit(spec=garchSpec12, data=diff.1.amazon)
coef(garchFit12)## mu ma1 ma2 omega alpha1 beta1
## 0.11124578 -0.03056320 -0.05340995 0.06020831 0.04846366 0.03072131
## beta2
## 0.91981503garchFit12##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,2)
## Mean Model : ARFIMA(0,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.111246 0.051908 2.1431 0.032104
## ma1 -0.030563 0.023591 -1.2955 0.195138
## ma2 -0.053410 0.021149 -2.5254 0.011556
## omega 0.060208 0.012132 4.9629 0.000001
## alpha1 0.048464 0.004370 11.0893 0.000000
## beta1 0.030721 0.004594 6.6873 0.000000
## beta2 0.919815 0.004724 194.7209 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.111246 0.058198 1.9115 0.055940
## ma1 -0.030563 0.027373 -1.1165 0.264189
## ma2 -0.053410 0.022868 -2.3356 0.019514
## omega 0.060208 0.059284 1.0156 0.309826
## alpha1 0.048464 0.012727 3.8081 0.000140
## beta1 0.030721 0.008440 3.6398 0.000273
## beta2 0.919815 0.011589 79.3729 0.000000
##
## LogLikelihood : -6532.755
##
## Information Criteria
## ------------------------------------
##
## Akaike 5.4092
## Bayes 5.4260
## Shibata 5.4092
## Hannan-Quinn 5.4153
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01923 0.8897
## Lag[2*(p+q)+(p+q)-1][5] 0.16928 1.0000
## Lag[4*(p+q)+(p+q)-1][9] 0.90962 0.9999
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.5603 0.4541
## Lag[2*(p+q)+(p+q)-1][8] 1.2984 0.9490
## Lag[4*(p+q)+(p+q)-1][14] 1.5814 0.9968
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.3338 0.500 2.000 0.5635
## ARCH Lag[6] 0.3546 1.461 1.711 0.9314
## ARCH Lag[8] 0.3795 2.368 1.583 0.9900
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 3.3333
## Individual Statistics:
## mu 0.32710
## ma1 0.03703
## ma2 0.09091
## omega 0.15564
## alpha1 0.07438
## beta1 0.24861
## beta2 0.23574
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.69 1.9 2.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.1040 0.9172
## Negative Sign Bias 0.3401 0.7338
## Positive Sign Bias 1.4091 0.1589
## Joint Effect 2.2906 0.5143
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 266.4 1.419e-45
## 2 30 282.2 2.571e-43
## 3 40 293.1 1.097e-40
## 4 50 302.5 3.262e-38
##
##
## Elapsed time : 0.135596res2<-garchFit12@fit$residuals
res2.ts<-ts(res2)
plot.ts(res2.ts)
#GARCH(1,3)
garchSpec13 <- ugarchspec(
variance.model=list(model="sGARCH",
garchOrder=c(1,3)),
mean.model=list(armaOrder=c(0,2)))
garchFit13 <- ugarchfit(spec=garchSpec13, data=diff.1.amazon)
coef(garchFit13)## mu ma1 ma2 omega alpha1
## 1.223706e-01 9.014122e-03 -6.434255e-02 1.123435e-01 9.469583e-02
## beta1 beta2 beta3
## 3.769533e-08 3.825771e-02 8.660464e-01garchFit13##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,3)
## Mean Model : ARFIMA(0,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.122371 0.051302 2.385305 0.017065
## ma1 0.009014 0.024056 0.374719 0.707869
## ma2 -0.064343 0.019955 -3.224372 0.001262
## omega 0.112344 0.025785 4.356981 0.000013
## alpha1 0.094696 0.010768 8.794304 0.000000
## beta1 0.000000 0.008004 0.000005 0.999996
## beta2 0.038258 0.006945 5.508304 0.000000
## beta3 0.866046 0.014162 61.152209 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.122371 0.057711 2.120411 0.033971
## ma1 0.009014 0.033655 0.267840 0.788823
## ma2 -0.064343 0.020050 -3.209166 0.001331
## omega 0.112344 0.120427 0.932876 0.350884
## alpha1 0.094696 0.034323 2.758997 0.005798
## beta1 0.000000 0.039482 0.000001 0.999999
## beta2 0.038258 0.021520 1.777776 0.075441
## beta3 0.866046 0.043094 20.096578 0.000000
##
## LogLikelihood : -6502.891
##
## Information Criteria
## ------------------------------------
##
## Akaike 5.3854
## Bayes 5.4045
## Shibata 5.3853
## Hannan-Quinn 5.3923
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.954 0.08567
## Lag[2*(p+q)+(p+q)-1][5] 3.443 0.23016
## Lag[4*(p+q)+(p+q)-1][9] 4.299 0.61973
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.05194 0.8197
## Lag[2*(p+q)+(p+q)-1][11] 1.08365 0.9953
## Lag[4*(p+q)+(p+q)-1][19] 1.53700 0.9999
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.7949 0.500 2.000 0.3726
## ARCH Lag[7] 0.8648 1.473 1.746 0.7954
## ARCH Lag[9] 0.8837 2.402 1.619 0.9464
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 5.1071
## Individual Statistics:
## mu 0.27741
## ma1 0.08201
## ma2 0.08932
## omega 0.22958
## alpha1 0.11516
## beta1 0.26917
## beta2 0.17574
## beta3 0.19232
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.89 2.11 2.59
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.35998 0.7189
## Negative Sign Bias 0.07121 0.9432
## Positive Sign Bias 1.18966 0.2343
## Joint Effect 1.46857 0.6895
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 223.9 5.593e-37
## 2 30 235.5 3.228e-34
## 3 40 256.4 8.749e-34
## 4 50 265.0 2.083e-31
##
##
## Elapsed time : 0.2232869res3<-garchFit13@fit$residuals
res3.ts<-ts(res3)
plot.ts(res3.ts)
#GARCH(1,4)
garchSpec14 <- ugarchspec(
variance.model=list(model="sGARCH",
garchOrder=c(1,4)),
mean.model=list(armaOrder=c(0,2)))
garchFit14 <- ugarchfit(spec=garchSpec14, data=diff.1.amazon)
coef(garchFit14)## mu ma1 ma2 omega alpha1
## 1.222193e-01 -2.159528e-02 -6.418984e-02 1.350320e-01 1.005402e-01
## beta1 beta2 beta3 beta4
## 1.274961e-07 9.578452e-08 2.430906e-01 6.553690e-01garchFit14##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,4)
## Mean Model : ARFIMA(0,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.122219 0.052412 2.331892 0.019706
## ma1 -0.021595 0.024697 -0.874417 0.381891
## ma2 -0.064190 0.020259 -3.168425 0.001533
## omega 0.135032 0.025679 5.258375 0.000000
## alpha1 0.100540 0.012356 8.136652 0.000000
## beta1 0.000000 0.057452 0.000002 0.999998
## beta2 0.000000 0.062993 0.000002 0.999999
## beta3 0.243091 0.028039 8.669674 0.000000
## beta4 0.655369 0.075548 8.674904 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.122219 0.058670 2.08317 0.037236
## ma1 -0.021595 0.031432 -0.68706 0.492047
## ma2 -0.064190 0.026842 -2.39143 0.016783
## omega 0.135032 0.114369 1.18067 0.237732
## alpha1 0.100540 0.037656 2.66995 0.007586
## beta1 0.000000 0.326060 0.00000 1.000000
## beta2 0.000000 0.235368 0.00000 1.000000
## beta3 0.243091 0.230900 1.05280 0.292434
## beta4 0.655369 0.326154 2.00938 0.044496
##
## LogLikelihood : -6508.459
##
## Information Criteria
## ------------------------------------
##
## Akaike 5.3908
## Bayes 5.4123
## Shibata 5.3908
## Hannan-Quinn 5.3986
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2859 0.5929
## Lag[2*(p+q)+(p+q)-1][5] 0.7807 1.0000
## Lag[4*(p+q)+(p+q)-1][9] 1.4086 0.9980
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01318 0.9086
## Lag[2*(p+q)+(p+q)-1][14] 0.51250 1.0000
## Lag[4*(p+q)+(p+q)-1][24] 1.20951 1.0000
## d.o.f=5
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[6] 0.004247 0.500 2.000 0.9480
## ARCH Lag[8] 0.089316 1.480 1.774 0.9911
## ARCH Lag[10] 0.256136 2.424 1.650 0.9968
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 4.3228
## Individual Statistics:
## mu 0.33943
## ma1 0.05264
## ma2 0.09556
## omega 0.11841
## alpha1 0.08382
## beta1 0.31212
## beta2 0.29457
## beta3 0.27117
## beta4 0.29175
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.1 2.32 2.82
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.3032 0.7618
## Negative Sign Bias 0.1710 0.8642
## Positive Sign Bias 0.9553 0.3395
## Joint Effect 0.9902 0.8036
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 273.7 4.751e-47
## 2 30 298.4 1.683e-46
## 3 40 297.2 1.794e-41
## 4 50 309.2 1.908e-39
##
##
## Elapsed time : 0.126461res4<-garchFit14@fit$residuals
res4.ts<-ts(res4)
plot.ts(res4.ts)
#GARCH(2,1)
garchSpec21 <- ugarchspec(
variance.model=list(model="sGARCH",
garchOrder=c(2,1)),
mean.model=list(armaOrder=c(0,2)))
garchFit21 <- ugarchfit(spec=garchSpec21, data=diff.1.amazon)
coef(garchFit21)## mu ma1 ma2 omega alpha1
## 1.246391e-01 -3.035390e-02 -5.831529e-02 3.763826e-02 2.575720e-02
## alpha2 beta1
## 8.787294e-08 9.732427e-01garchFit21##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(2,1)
## Mean Model : ARFIMA(0,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.124639 0.052982 2.35246 0.018650
## ma1 -0.030354 0.022738 -1.33492 0.181903
## ma2 -0.058315 0.023212 -2.51229 0.011995
## omega 0.037638 0.007674 4.90476 0.000001
## alpha1 0.025757 0.008359 3.08130 0.002061
## alpha2 0.000000 0.008878 0.00001 0.999992
## beta1 0.973243 0.002991 325.39038 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.124639 0.059048 2.110816 0.034788
## ma1 -0.030354 0.027119 -1.119303 0.263011
## ma2 -0.058315 0.024183 -2.411432 0.015890
## omega 0.037638 0.033753 1.115093 0.264810
## alpha1 0.025757 0.018030 1.428546 0.153135
## alpha2 0.000000 0.019006 0.000005 0.999996
## beta1 0.973243 0.011050 88.073168 0.000000
##
## LogLikelihood : -6544.866
##
## Information Criteria
## ------------------------------------
##
## Akaike 5.4192
## Bayes 5.4360
## Shibata 5.4192
## Hannan-Quinn 5.4253
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.0001551 0.9901
## Lag[2*(p+q)+(p+q)-1][5] 0.2181961 1.0000
## Lag[4*(p+q)+(p+q)-1][9] 0.9518260 0.9998
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.766 0.1839
## Lag[2*(p+q)+(p+q)-1][8] 2.461 0.7827
## Lag[4*(p+q)+(p+q)-1][14] 2.700 0.9701
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.003034 0.500 2.000 0.9561
## ARCH Lag[6] 0.212764 1.461 1.711 0.9658
## ARCH Lag[8] 0.261205 2.368 1.583 0.9957
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 3.4695
## Individual Statistics:
## mu 0.36022
## ma1 0.02986
## ma2 0.07162
## omega 0.16405
## alpha1 0.08142
## alpha2 0.08324
## beta1 0.25034
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.69 1.9 2.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.1930 0.84700
## Negative Sign Bias 0.5549 0.57903
## Positive Sign Bias 1.9471 0.05164 *
## Joint Effect 4.3433 0.22670
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 278.4 5.318e-48
## 2 30 305.4 6.866e-48
## 3 40 305.3 5.258e-43
## 4 50 325.2 2.036e-42
##
##
## Elapsed time : 0.1099808res21<-garchFit21@fit$residuals
res21.ts<-ts(res21)
plot.ts(res21.ts)
# UJI DIAGNOSTIK GARCH(1,2)
amazon.garch12 <- garch(data_amazon.ts.train,c(1,2)) #ordo ARCH(1)##
## ***** ESTIMATION WITH ANALYTICAL GRADIENT *****
##
##
## I INITIAL X(I) D(I)
##
## 1 1.186014e+04 1.000e+00
## 2 5.000000e-02 1.000e+00
## 3 5.000000e-02 1.000e+00
## 4 5.000000e-02 1.000e+00
##
## IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF
## 0 1 1.424e+04
## 1 2 1.374e+04 3.50e-02 6.99e-01 3.0e-05 1.0e+04 1.0e+00 3.48e+03
## 2 4 1.369e+04 3.68e-03 3.50e-03 1.9e-06 6.6e+00 5.0e-02 2.64e+01
## 3 6 1.360e+04 6.52e-03 6.46e-03 3.8e-06 2.4e+00 1.0e-01 7.73e-01
## 4 8 1.359e+04 1.18e-03 1.18e-03 7.5e-07 2.8e+01 2.0e-02 4.82e-01
## 5 10 1.358e+04 2.32e-04 2.32e-04 1.5e-07 1.4e+02 4.0e-03 3.04e-01
## 6 13 1.356e+04 1.80e-03 1.80e-03 1.2e-06 5.5e+00 3.2e-02 2.72e-01
## 7 17 1.356e+04 3.50e-06 3.50e-06 2.4e-09 8.6e+03 6.4e-05 2.24e-01
## 8 19 1.356e+04 7.00e-06 7.00e-06 4.8e-09 1.1e+03 1.3e-04 1.88e-01
## 9 21 1.356e+04 1.40e-06 1.40e-06 9.5e-10 2.2e+04 2.6e-05 1.88e-01
## 10 23 1.356e+04 2.80e-06 2.80e-06 1.9e-09 2.7e+03 5.1e-05 1.88e-01
## 11 25 1.356e+04 5.60e-06 5.60e-06 3.8e-09 1.4e+03 1.0e-04 1.88e-01
## 12 27 1.356e+04 1.12e-06 1.12e-06 7.6e-10 2.7e+04 2.0e-05 1.88e-01
## 13 29 1.356e+04 2.24e-07 2.24e-07 1.5e-10 1.4e+05 4.1e-06 1.87e-01
## 14 31 1.356e+04 4.48e-08 4.48e-08 3.1e-11 6.8e+05 8.2e-07 1.87e-01
## 15 33 1.356e+04 8.96e-08 8.96e-08 6.1e-11 8.6e+04 1.6e-06 1.87e-01
## 16 35 1.356e+04 1.79e-08 1.79e-08 1.2e-11 1.7e+06 3.3e-07 1.87e-01
## 17 37 1.356e+04 3.58e-08 3.58e-08 2.4e-11 2.1e+05 6.6e-07 1.87e-01
## 18 39 1.356e+04 7.17e-09 7.17e-09 4.9e-12 4.3e+06 1.3e-07 1.87e-01
## 19 41 1.356e+04 1.43e-09 1.43e-09 9.8e-13 2.1e+07 2.6e-08 1.87e-01
## 20 43 1.356e+04 2.87e-09 2.87e-09 2.0e-12 2.7e+06 5.2e-08 1.87e-01
## 21 46 1.356e+04 5.73e-11 5.73e-11 3.9e-14 1.9e+00 1.0e-09 -2.17e-02
## 22 48 1.356e+04 1.15e-10 1.15e-10 7.8e-14 6.7e+07 2.1e-09 1.87e-01
## 23 50 1.356e+04 2.29e-11 2.29e-11 1.6e-14 1.9e+00 4.2e-10 -2.17e-02
## 24 53 1.356e+04 1.84e-10 1.84e-10 1.2e-13 4.2e+07 3.4e-09 1.87e-01
## 25 56 1.356e+04 -7.37e+05 3.67e-12 2.5e-15 1.9e+00 6.7e-11 -2.17e-02
##
## ***** FALSE CONVERGENCE *****
##
## FUNCTION 1.355994e+04 RELDX 2.499e-15
## FUNC. EVALS 56 GRAD. EVALS 25
## PRELDF 3.670e-12 NPRELDF -2.174e-02
##
## I FINAL X(I) D(I) G(I)
##
## 1 1.186014e+04 1.000e+00 2.664e-02
## 2 6.894395e-01 1.000e+00 2.461e+02
## 3 6.869600e-01 1.000e+00 2.458e+02
## 4 5.355173e-11 1.000e+00 6.549e+02## Warning in sqrt(pred$e): NaNs producedamazongarch12 <- summary(amazon.garch12)
amazongarch12##
## Call:
## garch(x = data_amazon.ts.train, order = c(1, 2))
##
## Model:
## GARCH(1,2)
##
## Residuals:
## Min 1Q Median 3Q Max
## 0.2265 0.5347 0.7324 0.8044 0.9466
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## a0 1.186e+04 1.374e+04 0.863 0.388
## a1 6.894e-01 3.940e+00 0.175 0.861
## a2 6.870e-01 4.234e+00 0.162 0.871
## b1 5.355e-11 1.147e+00 0.000 1.000
##
## Diagnostic Tests:
## Jarque Bera Test
##
## data: Residuals
## X-squared = 295.38, df = 2, p-value < 2.2e-16
##
##
## Box-Ljung test
##
## data: Squared.Residuals
## X-squared = 2379.2, df = 1, p-value < 2.2e-16#str(sbydarch)
plot(amazon.garch12) 
Peramalan
Peramalan dengan Data Train
## ramalan dari data train
model <-Arima(data_amazon.ts.train,order=c(0,1,2))
ramalan_model<-forecast(model,h=600)
plot(ramalan_model)
Plot ramalan dengan Data Test
f.arima<-predict(model, n.ahead=600)
for.arima<-cbind(datatest=data_amazon.ts.test,f.arima$pred,f.arima$se^2)
f.garch<-ugarchforecast(garchFit12,n.ahead=600)
plot.ts(for.arima)
Perbandingan hasil ramalan dengan data test
ramalan <- f.arima$pred
hasil_perbandingan<- as.data.frame(cbind(data_amazon.ts.test,ramalan))
hasil_perbandingan## data_amazon.ts.test ramalan
## 1 531.52 529.6449
## 2 535.22 529.4593
## 3 535.02 529.4593
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## 599 1186.10 529.4593
## 600 1169.47 529.4593Model GARCH(1,2)
# GARCH(1,2)
m.12 = garch(diff.1.amazon,order=c(1,2),trace =FALSE)
summary(m.12)##
## Call:
## garch(x = diff.1.amazon, order = c(1, 2), trace = FALSE)
##
## Model:
## GARCH(1,2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.399135 -0.350427 0.003428 0.414105 13.482314
##
## Coefficient(s):
## Estimate Std. Error t value Pr(>|t|)
## a0 1.662e+01 2.571e+00 6.465 1.01e-10 ***
## a1 1.901e-01 8.690e-03 21.875 < 2e-16 ***
## a2 4.208e-02 3.785e-02 1.112 0.266
## b1 2.222e-14 1.528e-01 0.000 1.000
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Diagnostic Tests:
## Jarque Bera Test
##
## data: Residuals
## X-squared = 92703, df = 2, p-value < 2.2e-16
##
##
## Box-Ljung test
##
## data: Squared.Residuals
## X-squared = 0.028166, df = 1, p-value = 0.8667MODEL ARIMA(0,1,2)-GARCH(1,2)
#ARIMA(0,1,2)+GARCH(1,2)
model12<-ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1,2)),
mean.model = list(armaOrder = c(0, 2), include.mean = TRUE),
distribution.model = "norm")
m.12<-ugarchfit(spec=model12,data=diff.1.amazon, out.sample = 100)
plot(m.12,which="all")##
## please wait...calculating quantiles...
m.12##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,2)
## Mean Model : ARFIMA(0,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.077176 0.050081 1.54103 0.123309
## ma1 -0.019215 0.023719 -0.81008 0.417893
## ma2 -0.046058 0.022024 -2.09129 0.036502
## omega 0.082927 0.019639 4.22263 0.000024
## alpha1 0.070842 0.009396 7.53955 0.000000
## beta1 0.005729 0.005247 1.09177 0.274936
## beta2 0.922430 0.008598 107.28352 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.077176 0.061354 1.25787 0.208438
## ma1 -0.019215 0.028534 -0.67339 0.500696
## ma2 -0.046058 0.026594 -1.73192 0.083289
## omega 0.082927 0.091669 0.90464 0.365658
## alpha1 0.070842 0.033202 2.13367 0.032870
## beta1 0.005729 0.013489 0.42468 0.671070
## beta2 0.922430 0.028667 32.17686 0.000000
##
## LogLikelihood : -6127.746
##
## Information Criteria
## ------------------------------------
##
## Akaike 5.2931
## Bayes 5.3105
## Shibata 5.2931
## Hannan-Quinn 5.2995
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1577 0.6913
## Lag[2*(p+q)+(p+q)-1][5] 0.5828 1.0000
## Lag[4*(p+q)+(p+q)-1][9] 1.8179 0.9909
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3557 0.5509
## Lag[2*(p+q)+(p+q)-1][8] 0.9663 0.9763
## Lag[4*(p+q)+(p+q)-1][14] 1.2813 0.9988
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.02383 0.500 2.000 0.8773
## ARCH Lag[6] 0.10765 1.461 1.711 0.9869
## ARCH Lag[8] 0.11675 2.368 1.583 0.9993
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.6873
## Individual Statistics:
## mu 0.12930
## ma1 0.04957
## ma2 0.13203
## omega 0.20428
## alpha1 0.12314
## beta1 0.29664
## beta2 0.22204
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.69 1.9 2.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.9323 0.35130
## Negative Sign Bias 0.2416 0.80908
## Positive Sign Bias 2.2075 0.02738 **
## Joint Effect 4.9937 0.17226
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 212.5 1.107e-34
## 2 30 218.7 5.345e-31
## 3 40 230.9 4.398e-29
## 4 50 254.4 1.566e-29
##
##
## Elapsed time : 0.1278448diperoleh mean model yaitu ARIMA(0,1,2) dan varian model yaitu GARCH(1,2) terbaik untuk digunakan dalam peralaman, terlihat pada uji dignostik model pada plot QQ-norm terlihat bahwa sebaran residual mengikuti garis lurus sehingga dapat disimpulkan bahwa residual menyebar normal, lalu untuk uji autokorelasi dapat dilihat plot ACF squared residual telah terlihat bahwa setiap lag berada dibawah batas, sehingga dapat dikatakan bahwa tidak ada autokorelasi antar residual, diperkuat dengan nilai p-value pada uji L-jung Box yang lebih besar dari alpha=0.05.
Peramalan dengan Model ARIMA(0,1,2)-GARCH(1,2)
forc = ugarchforecast(m.12, data = diff.1.amazon, n.ahead = 10, n.roll =10)
print(forc)##
## *------------------------------------*
## * GARCH Model Forecast *
## *------------------------------------*
## Model: sGARCH
## Horizon: 10
## Roll Steps: 10
## Out of Sample: 10
##
## 0-roll forecast [T0=1976-05-07 07:00:00]:
## Series Sigma
## T+1 -0.09997 4.771
## T+2 0.23595 7.638
## T+3 0.07718 5.055
## T+4 0.07718 7.473
## T+5 0.07718 5.285
## T+6 0.07718 7.331
## T+7 0.07718 5.473
## T+8 0.07718 7.207
## T+9 0.07718 5.630
## T+10 0.07718 7.101plot(forc, which= "all")
pada hasil ramalan untuk data saham amazon untuk ke 10 waktu kedepan dapat dilihat pada plot diatas menunjukkan bahwa hasil ramalan bernilai sama sehingga membentuk garis lurus.
Kesimpulan
karena dengan jika menggunakan model ARCH lag hingga 5 masih signifikan, lalu, dicobakan pada beberapa model GARCH dan dibandingkan nilai-nilai seperti AIC dan signifikansi parameter, maka akan digunakan model GARCH(1,2) yang memiliki nilai AIC kecil dan parameter yang hampir semua signifikan. Sehingga diperoleh model Mean yaitu ARIMA(0,1,2) dan model Varian yaitu GARCH(1,2).Dengan persamaan sebagai berikut :
Mean Model ARIMA(0,1,2)
\(Y_t=0.0771+e_t-0.0192 e_{t-1}-0.0460e_{t-2}\)
Varian Model
GARCH(1,2)
\(\sigma^2_t=0.0829+0.0708\epsilon^2_{t-1} +0.0057\sigma^2_{t-1}+ 0.9224 \sigma^2_{t-2}\)