CMHNN
Lam Tam Nhu
2024-08-09
library(PerformanceAnalytics)## Warning: package 'PerformanceAnalytics' was built under R version 4.4.1## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric##
## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':
##
## legendlibrary(readxl)## Warning: package 'readxl' was built under R version 4.4.1library(PerformanceAnalytics)
library(readxl)
data <- read_xlsx("D:/CMHNN/VNI_SET.xlsx")
lgvni<- diff(log(data$VNI), lag = 1)
lgset<- diff(log(data$SET), lag = 1)
mhnn <- data.frame(VNI= lgvni, SET= lgset)
tn <- data[,c(2:3)]
head(data,10)## # A tibble: 10 × 3
## Date VNI SET
## <dttm> <dbl> <dbl>
## 1 2018-01-03 00:00:00 1006. 1779.
## 2 2018-01-04 00:00:00 1020. 1791.
## 3 2018-01-05 00:00:00 1013. 1795.
## 4 2018-01-08 00:00:00 1023. 1793.
## 5 2018-01-09 00:00:00 1034. 1795.
## 6 2018-01-10 00:00:00 1038. 1795.
## 7 2018-01-11 00:00:00 1048. 1803.
## 8 2018-01-12 00:00:00 1050. 1810.
## 9 2018-01-15 00:00:00 1063. 1823.
## 10 2018-01-16 00:00:00 1063. 1822.summary(mhnn)## VNI SET
## Min. :-0.069076 Min. :-1.143e-01
## 1st Qu.:-0.004635 1st Qu.:-4.671e-03
## Median : 0.001110 Median : 9.755e-05
## Mean : 0.000167 Mean :-1.744e-04
## 3rd Qu.: 0.006744 3rd Qu.: 4.570e-03
## Max. : 0.062002 Max. : 7.653e-02library(psych)## Warning: package 'psych' was built under R version 4.4.1detailed <- describe(mhnn)
print(detailed)## vars n mean sd median trimmed mad min max range skew kurtosis se
## VNI 1 1463 0 0.01 0 0 0.01 -0.07 0.06 0.13 -0.87 3.74 0
## SET 2 1463 0 0.01 0 0 0.01 -0.11 0.08 0.19 -1.82 24.77 0plot.ts(tn$VNI)
plot.ts(tn$SET)
# Vẽ đồ thị chuỗi thời gian cho VN-Index
plot.ts(mhnn$VNI, main="VN-Index Time Series", ylab="VN-Index", xlab="Time", col="blue")
# Vẽ đồ thị chuỗi thời gian cho SET Index
plot.ts(mhnn$SET, main="SET Index Time Series", ylab="SET Index", xlab="Time", col="red")
Kiểm định phân phối chuẩn bằng QQ_lot
library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.4.1##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
##
## %+%, alphaggplot(data.frame(price = mhnn$VNI), aes(sample = price)) +
geom_qq() +
geom_qq_line()
library(ggplot2)
ggplot(data.frame(price = mhnn$SET), aes(sample = price)) +
geom_qq() +
geom_qq_line()
TƯƠNG QUAN
###TƯƠNG QUAN
res <- cor(mhnn)
round(res, 2)## VNI SET
## VNI 1.00 0.31
## SET 0.31 1.00library(corrplot)## Warning: package 'corrplot' was built under R version 4.4.1## corrplot 0.92 loadedres <- cor(mhnn)
rounded_res <- round(res, 2)
round(res, 2)## VNI SET
## VNI 1.00 0.31
## SET 0.31 1.00corrplot(rounded_res, method = "color")
library(corrplot)
corrplot(res, type = "upper", order = "hclust",
tl.col = "black", tl.srt = 45)
chart.Correlation(mhnn, histogram=TRUE, pch=19)## Warning in par(usr): argument 1 does not name a graphical parameter
library(ggplot2)
library(ggcorrplot)## Warning: package 'ggcorrplot' was built under R version 4.4.1df <- dplyr::select_if(mhnn, is.numeric)
r <- cor(df, use="complete.obs")
ggcorrplot(r)
Thực hành các kiểm định
library(tseries)## Warning: package 'tseries' was built under R version 4.4.1## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoomhnn <- data.frame(VNI= lgvni, SET= lgset)Kiểm định phân phối chuẩn: Jarque-Bera
# Kiểm định
Var1 <- mhnn$VNI
Var2 <- mhnn$SET
# Kiểm định phân phối chuẩn cho ORS
result1 <- jarque.bera.test(Var1)
print(result1)##
## Jarque Bera Test
##
## data: Var1
## X-squared = 1042, df = 2, p-value < 2.2e-16result2 <- jarque.bera.test(Var2)
print(result2)##
## Jarque Bera Test
##
## data: Var2
## X-squared = 38337, df = 2, p-value < 2.2e-16Kiểm định tính dừng: Augmented Dickey–Fuller
adf.test(Var1)## Warning in adf.test(Var1): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: Var1
## Dickey-Fuller = -11.716, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationaryadf.test(Var2)## Warning in adf.test(Var2): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: Var2
## Dickey-Fuller = -9.2563, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationaryKiểm định tương quan chuỗi: Ljung-Box
library(stats)
result11 <- Box.test(Var1, lag = 10, type = "Ljung-Box")
print(result11)##
## Box-Ljung test
##
## data: Var1
## X-squared = 20.897, df = 10, p-value = 0.02182result22 <- Box.test(Var2, lag = 10, type = "Ljung-Box")
print(result22)##
## Box-Ljung test
##
## data: Var2
## X-squared = 82.36, df = 10, p-value = 1.729e-132.4 Tính dừng
library(forecast)## Warning: package 'forecast' was built under R version 4.4.1modeld <- auto.arima(mhnn$VNI)
modeld## Series: mhnn$VNI
## ARIMA(1,0,0) with zero mean
##
## Coefficients:
## ar1
## 0.0615
## s.e. 0.0261
##
## sigma^2 = 0.0001687: log likelihood = 4279.57
## AIC=-8555.15 AICc=-8555.14 BIC=-8544.57modeld1 <- auto.arima(mhnn$SET)
modeld1## Series: mhnn$SET
## ARIMA(3,0,1) with zero mean
##
## Coefficients:
## ar1 ar2 ar3 ma1
## -0.7289 0.0103 0.1295 0.6976
## s.e. 0.0739 0.0323 0.0270 0.0711
##
## sigma^2 = 0.000102: log likelihood = 4648.98
## AIC=-9287.96 AICc=-9287.92 BIC=-9261.52library(lmtest)## Warning: package 'lmtest' was built under R version 4.4.1library(fGarch)## Warning: package 'fGarch' was built under R version 4.4.1## NOTE: Packages 'fBasics', 'timeDate', and 'timeSeries' are no longer
## attached to the search() path when 'fGarch' is attached.
##
## If needed attach them yourself in your R script by e.g.,
## require("timeSeries")##
## Attaching package: 'fGarch'## The following objects are masked from 'package:PerformanceAnalytics':
##
## ES, VaRlibrary(rugarch)## Warning: package 'rugarch' was built under R version 4.4.1## Loading required package: parallel##
## Attaching package: 'rugarch'## The following object is masked from 'package:stats':
##
## sigmalibrary(readxl)Kiểm định ARCH - LM
# Kiểm định hiệu ứng ARCH - LM cho chỉ số chứng khoán
arch_spec <- ugarchspec(variance.model = list(model = "sGARCH"))
arch_VNI <- ugarchfit(spec = arch_spec, data = mhnn$VNI)
residuals <- residuals(arch_VNI)
n <- length(residuals)
x <- 1:n
# Tạo mô hình tuyến tính
arch_lm_model <- lm(residuals^2 ~ x)
# Kiểm định hiệu ứng ARCH-LM
aTSA::arch.test(arima(mhnn$VNI,order = c(1,0,0)))## ARCH heteroscedasticity test for residuals
## alternative: heteroscedastic
##
## Portmanteau-Q test:
## order PQ p.value
## [1,] 4 166 0
## [2,] 8 283 0
## [3,] 12 389 0
## [4,] 16 410 0
## [5,] 20 432 0
## [6,] 24 434 0
## Lagrange-Multiplier test:
## order LM p.value
## [1,] 4 1103 0
## [2,] 8 466 0
## [3,] 12 285 0
## [4,] 16 208 0
## [5,] 20 162 0
## [6,] 24 132 0
# Kiểm định hiệu ứng ARCH - LM cho chỉ số chứng khoán
arch_spec <- ugarchspec(variance.model = list(model = "sGARCH"))
arch_SET <- ugarchfit(spec = arch_spec, data = mhnn$SET)
residuals <- residuals(arch_SET)
n <- length(residuals)
x <- 1:n
# Tạo mô hình tuyến tính
arch_lm_model <- lm(residuals^2 ~ x)
# Kiểm định hiệu ứng ARCH-LM
aTSA::arch.test(arima(mhnn$SET,order = c(3,0,1)))## ARCH heteroscedasticity test for residuals
## alternative: heteroscedastic
##
## Portmanteau-Q test:
## order PQ p.value
## [1,] 4 236 0
## [2,] 8 550 0
## [3,] 12 841 0
## [4,] 16 953 0
## [5,] 20 1005 0
## [6,] 24 1011 0
## Lagrange-Multiplier test:
## order LM p.value
## [1,] 4 1810 0.00e+00
## [2,] 8 488 0.00e+00
## [3,] 12 263 0.00e+00
## [4,] 16 156 0.00e+00
## [5,] 20 123 0.00e+00
## [6,] 24 100 1.34e-11
MÔ HÌNH GARCH
library(rugarch)
VNIts<- ts(mhnn$VNI)
head(VNIts)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] 0.013903513 -0.006986842 0.010071073 0.010367423 0.004392599
## [6] 0.009644034library(rugarch)
SETts<- ts(mhnn$SET)
head(SETts)## Time Series:
## Start = 1
## End = 6
## Frequency = 1
## [1] 0.006998110 0.002470397 -0.001471466 0.001337785 -0.000161554
## [6] 0.004380559library(lmtest)
VNIspec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,1)), mean.model = list(armaOrder = c(1,0), include.mean =TRUE), distribution.model = 'norm')
print(VNIspec)##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : gjrGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(1,0,0)
## Include Mean : TRUE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSElibrary(lmtest)
SETspec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,1)), mean.model = list(armaOrder = c(3,1), include.mean =TRUE), distribution.model = 'norm')
print(SETspec)##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : gjrGARCH(1,1)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(3,0,1)
## Include Mean : TRUE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSEVNIfit <- ugarchfit(spec = VNIspec, VNIts)
print(VNIfit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(1,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000252 0.000303 0.83019 0.406430
## ar1 0.086104 0.029697 2.89943 0.003738
## omega 0.000007 0.000000 48.96693 0.000000
## alpha1 0.018647 0.005305 3.51485 0.000440
## beta1 0.870058 0.008651 100.57113 0.000000
## gamma1 0.116479 0.019269 6.04506 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000252 0.000328 0.76895 0.441926
## ar1 0.086104 0.026966 3.19300 0.001408
## omega 0.000007 0.000000 35.95992 0.000000
## alpha1 0.018647 0.006331 2.94520 0.003228
## beta1 0.870058 0.012251 71.02161 0.000000
## gamma1 0.116479 0.026882 4.33295 0.000015
##
## LogLikelihood : 4440.556
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.0623
## Bayes -6.0406
## Shibata -6.0623
## Hannan-Quinn -6.0542
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2085 0.6479
## Lag[2*(p+q)+(p+q)-1][2] 0.9098 0.7926
## Lag[4*(p+q)+(p+q)-1][5] 2.5128 0.5627
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.02992 0.8627
## Lag[2*(p+q)+(p+q)-1][5] 0.30420 0.9833
## Lag[4*(p+q)+(p+q)-1][9] 0.79687 0.9932
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.4371 0.500 2.000 0.5085
## ARCH Lag[5] 0.4632 1.440 1.667 0.8944
## ARCH Lag[7] 0.7994 2.315 1.543 0.9438
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 18.1224
## Individual Statistics:
## mu 0.30267
## ar1 0.07353
## omega 4.12741
## alpha1 0.06405
## beta1 0.07956
## gamma1 0.05009
##
## 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 1.47638 0.14006
## Negative Sign Bias 0.01921 0.98468
## Positive Sign Bias 1.08656 0.27741
## Joint Effect 8.99863 0.02931 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 126.7 6.181e-18
## 2 30 148.4 5.674e-18
## 3 40 154.7 1.045e-15
## 4 50 173.0 9.778e-16
##
##
## Elapsed time : 0.422405SETfit <- ugarchfit(spec = SETspec, SETts)
print(SETfit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(3,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000405 0.000225 -1.80315 0.071365
## ar1 0.336868 0.507070 0.66434 0.506471
## ar2 -0.044120 0.041027 -1.07538 0.282205
## ar3 0.056252 0.028652 1.96326 0.049616
## ma1 -0.279802 0.506412 -0.55252 0.580593
## omega 0.000002 0.000002 1.42861 0.153116
## alpha1 0.033046 0.011458 2.88408 0.003926
## beta1 0.886825 0.015331 57.84589 0.000000
## gamma1 0.105600 0.022895 4.61241 0.000004
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000405 0.000347 -1.16666 0.243348
## ar1 0.336868 0.484206 0.69571 0.486609
## ar2 -0.044120 0.043981 -1.00316 0.315785
## ar3 0.056252 0.030389 1.85108 0.064159
## ma1 -0.279802 0.483556 -0.57864 0.562835
## omega 0.000002 0.000009 0.24023 0.810151
## alpha1 0.033046 0.019678 1.67940 0.093075
## beta1 0.886825 0.062999 14.07685 0.000000
## gamma1 0.105600 0.059648 1.77038 0.076663
##
## LogLikelihood : 4962.008
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.7710
## Bayes -6.7385
## Shibata -6.7711
## Hannan-Quinn -6.7589
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01214 0.9123
## Lag[2*(p+q)+(p+q)-1][11] 2.47550 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 6.39433 0.9519
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2694 0.6037
## Lag[2*(p+q)+(p+q)-1][5] 3.5700 0.3128
## Lag[4*(p+q)+(p+q)-1][9] 5.0851 0.4170
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 3.238 0.500 2.000 0.07193
## ARCH Lag[5] 4.590 1.440 1.667 0.12769
## ARCH Lag[7] 5.059 2.315 1.543 0.21862
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 5.2762
## Individual Statistics:
## mu 0.05887
## ar1 0.02582
## ar2 0.12448
## ar3 0.12543
## ma1 0.02926
## omega 1.01517
## alpha1 0.25936
## beta1 0.17479
## gamma1 0.13743
##
## 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 1.415340 0.1572
## Negative Sign Bias 0.923612 0.3558
## Positive Sign Bias 0.006387 0.9949
## Joint Effect 2.717958 0.4372
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 46.41 0.0004342
## 2 30 55.19 0.0023550
## 3 40 58.18 0.0247185
## 4 50 71.07 0.0213044
##
##
## Elapsed time : 0.7732229VNIst.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(1, 0), include.mean = TRUE), distribution.model = "std")
VNIst1<- ugarchfit(VNIst.spec,VNIts)
print(VNIst1)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(1,0,0)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001140 0.000238 4.7835 0.000002
## ar1 0.046067 0.026757 1.7217 0.085125
## omega 0.000012 0.000000 25.7491 0.000000
## alpha1 0.032933 0.012698 2.5935 0.009500
## beta1 0.787379 0.021618 36.4229 0.000000
## gamma1 0.229134 0.046661 4.9106 0.000001
## shape 3.626860 0.300767 12.0587 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001140 0.000253 4.4993 0.000007
## ar1 0.046067 0.026457 1.7412 0.081649
## omega 0.000012 0.000001 22.2505 0.000000
## alpha1 0.032933 0.013286 2.4787 0.013185
## beta1 0.787379 0.019570 40.2334 0.000000
## gamma1 0.229134 0.047193 4.8553 0.000001
## shape 3.626860 0.282615 12.8332 0.000000
##
## LogLikelihood : 4544.987
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.2037
## Bayes -6.1784
## Shibata -6.2037
## Hannan-Quinn -6.1942
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.6946 0.4046
## Lag[2*(p+q)+(p+q)-1][2] 1.0433 0.7137
## Lag[4*(p+q)+(p+q)-1][5] 2.1192 0.6768
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8956 0.3440
## Lag[2*(p+q)+(p+q)-1][5] 2.2542 0.5597
## Lag[4*(p+q)+(p+q)-1][9] 2.8306 0.7866
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 1.494 0.500 2.000 0.2216
## ARCH Lag[5] 1.702 1.440 1.667 0.5409
## ARCH Lag[7] 1.772 2.315 1.543 0.7654
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 41.6054
## Individual Statistics:
## mu 0.33652
## ar1 0.09476
## omega 9.34867
## alpha1 0.10291
## beta1 0.13361
## gamma1 0.14912
## shape 0.15740
##
## 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 1.806 0.07107 *
## Negative Sign Bias 1.455 0.14590
## Positive Sign Bias 1.068 0.28591
## Joint Effect 8.979 0.02957 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 46.43 0.0004303
## 2 30 62.49 0.0002998
## 3 40 79.45 0.0001396
## 4 50 74.01 0.0120097
##
##
## Elapsed time : 0.522985SETst.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(3, 1), include.mean = TRUE), distribution.model = "std")
SETst1<- ugarchfit(SETst.spec,SETts)
print(SETst1)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(3,0,1)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000175 0.000198 -0.88491 0.376207
## ar1 0.685259 0.499775 1.37114 0.170333
## ar2 -0.031393 0.035460 -0.88533 0.375979
## ar3 0.026914 0.027023 0.99599 0.319256
## ma1 -0.656143 0.500050 -1.31216 0.189468
## omega 0.000003 0.000002 1.74803 0.080458
## alpha1 0.016974 0.002695 6.29866 0.000000
## beta1 0.879854 0.013564 64.86481 0.000000
## gamma1 0.120370 0.027196 4.42598 0.000010
## shape 6.060553 0.920224 6.58595 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000175 0.000250 -0.69856 0.484824
## ar1 0.685259 0.473157 1.44827 0.147541
## ar2 -0.031393 0.036953 -0.84955 0.395572
## ar3 0.026914 0.029229 0.92082 0.357143
## ma1 -0.656143 0.470650 -1.39412 0.163281
## omega 0.000003 0.000006 0.52348 0.600637
## alpha1 0.016974 0.040391 0.42024 0.674309
## beta1 0.879854 0.024743 35.55953 0.000000
## gamma1 0.120370 0.031239 3.85322 0.000117
## shape 6.060553 1.134862 5.34034 0.000000
##
## LogLikelihood : 5004.842
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.8282
## Bayes -6.7921
## Shibata -6.8283
## Hannan-Quinn -6.8147
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8101 0.3681
## Lag[2*(p+q)+(p+q)-1][11] 3.1753 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 7.6590 0.8389
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1153 0.7341
## Lag[2*(p+q)+(p+q)-1][5] 4.0068 0.2532
## Lag[4*(p+q)+(p+q)-1][9] 5.4779 0.3627
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 4.890 0.500 2.000 0.02702
## ARCH Lag[5] 5.582 1.440 1.667 0.07528
## ARCH Lag[7] 5.818 2.315 1.543 0.15392
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 3.699
## Individual Statistics:
## mu 0.13103
## ar1 0.01392
## ar2 0.06351
## ar3 0.05764
## ma1 0.01245
## omega 0.34273
## alpha1 0.28199
## beta1 0.13556
## gamma1 0.07166
## shape 0.11804
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.29 2.54 3.05
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.9229 0.05468 *
## Negative Sign Bias 1.1452 0.25233
## Positive Sign Bias 0.7663 0.44364
## Joint Effect 3.8728 0.27553
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 11.96 0.8875
## 2 30 24.96 0.6802
## 3 40 39.15 0.4633
## 4 50 43.73 0.6859
##
##
## Elapsed time : 0.926527# Phân phối Student đối xứng (sstd)
VNIst1.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(1, 0), include.mean = TRUE), distribution.model = "sstd")
VNIst2<- ugarchfit(VNIst1.spec,VNIts)
print(VNIst2)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(1,0,0)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000415 0.000274 1.5120 0.130533
## ar1 0.037114 0.026856 1.3820 0.166983
## omega 0.000011 0.000000 27.1406 0.000000
## alpha1 0.035126 0.010451 3.3609 0.000777
## beta1 0.803315 0.018895 42.5151 0.000000
## gamma1 0.198526 0.039760 4.9930 0.000001
## skew 0.827937 0.031138 26.5892 0.000000
## shape 3.988498 0.365313 10.9180 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000415 0.000296 1.4001 0.161491
## ar1 0.037114 0.027624 1.3435 0.179103
## omega 0.000011 0.000000 22.9989 0.000000
## alpha1 0.035126 0.011134 3.1549 0.001605
## beta1 0.803315 0.016473 48.7644 0.000000
## gamma1 0.198526 0.039086 5.0792 0.000000
## skew 0.827937 0.032375 25.5731 0.000000
## shape 3.988498 0.333050 11.9757 0.000000
##
## LogLikelihood : 4558.381
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.2206
## Bayes -6.1917
## Shibata -6.2207
## Hannan-Quinn -6.2098
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.733 0.1881
## Lag[2*(p+q)+(p+q)-1][2] 2.306 0.1282
## Lag[4*(p+q)+(p+q)-1][5] 3.797 0.2595
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.924 0.3364
## Lag[2*(p+q)+(p+q)-1][5] 2.181 0.5763
## Lag[4*(p+q)+(p+q)-1][9] 2.747 0.7999
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 1.358 0.500 2.000 0.2439
## ARCH Lag[5] 1.563 1.440 1.667 0.5760
## ARCH Lag[7] 1.640 2.315 1.543 0.7929
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 44.9897
## Individual Statistics:
## mu 0.30100
## ar1 0.10822
## omega 8.95396
## alpha1 0.08742
## beta1 0.13009
## gamma1 0.11666
## skew 0.10455
## shape 0.12495
##
## 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 2.118 0.03431 **
## Negative Sign Bias 1.507 0.13211
## Positive Sign Bias 1.099 0.27190
## Joint Effect 10.896 0.01230 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 25.63 0.14095
## 2 30 33.29 0.26626
## 3 40 54.29 0.05267
## 4 50 68.82 0.03235
##
##
## Elapsed time : 0.700639# Phân phối Student đối xứng (sstd)
SETst1.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(3, 1), include.mean = TRUE), distribution.model = "sstd")
SETst2<- ugarchfit(SETst1.spec,SETts)
print(SETst2)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(3,0,1)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000367 0.000199 -1.843790 0.065214
## ar1 -0.671124 6.103944 -0.109949 0.912450
## ar2 0.001369 0.176363 0.007765 0.993805
## ar3 -0.003866 0.123622 -0.031272 0.975053
## ma1 0.694709 6.113176 0.113641 0.909522
## omega 0.000003 0.000003 0.868946 0.384877
## alpha1 0.019700 0.006767 2.911124 0.003601
## beta1 0.885346 0.019234 46.030202 0.000000
## gamma1 0.115252 0.016854 6.838177 0.000000
## skew 0.887947 0.029821 29.776104 0.000000
## shape 6.160223 0.844457 7.294890 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000367 0.000726 -0.505393 0.613283
## ar1 -0.671124 105.096698 -0.006386 0.994905
## ar2 0.001369 2.759656 0.000496 0.999604
## ar3 -0.003866 2.063729 -0.001873 0.998505
## ma1 0.694709 104.981792 0.006617 0.994720
## omega 0.000003 0.000040 0.070824 0.943538
## alpha1 0.019700 0.211336 0.093218 0.925730
## beta1 0.885346 0.219591 4.031799 0.000055
## gamma1 0.115252 0.217437 0.530050 0.596077
## skew 0.887947 0.133987 6.627126 0.000000
## shape 6.160223 7.034863 0.875671 0.381209
##
## LogLikelihood : 5009.701
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.8335
## Bayes -6.7937
## Shibata -6.8336
## Hannan-Quinn -6.8187
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.217 0.2699
## Lag[2*(p+q)+(p+q)-1][11] 4.923 0.9693
## Lag[4*(p+q)+(p+q)-1][19] 9.287 0.5895
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1112 0.7388
## Lag[2*(p+q)+(p+q)-1][5] 4.1067 0.2410
## Lag[4*(p+q)+(p+q)-1][9] 5.6219 0.3440
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 4.859 0.500 2.000 0.02750
## ARCH Lag[5] 5.753 1.440 1.667 0.06864
## ARCH Lag[7] 5.982 2.315 1.543 0.14244
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 8.306
## Individual Statistics:
## mu 0.11242
## ar1 0.13356
## ar2 0.20844
## ar3 0.18670
## ma1 0.13653
## omega 0.95232
## alpha1 0.27469
## beta1 0.12895
## gamma1 0.05733
## skew 0.20088
## shape 0.11776
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.49 2.75 3.27
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.4311 0.1526
## Negative Sign Bias 0.9525 0.3410
## Positive Sign Bias 0.4005 0.6888
## Joint Effect 2.2922 0.5140
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 8.018 0.9865
## 2 30 22.830 0.7842
## 3 40 37.834 0.5230
## 4 50 38.880 0.8494
##
##
## Elapsed time : 0.9870639# Phân phối Generalized Error Distribution(ged)
VNIged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(1, 0), include.mean = TRUE), distribution.model = "ged")
VNIged1 <- ugarchfit(VNIged.spec,VNIts)
print(VNIged1)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(1,0,0)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001051 0.000151 6.9514 0.000000
## ar1 0.018679 0.006934 2.6937 0.007065
## omega 0.000010 0.000000 29.0025 0.000000
## alpha1 0.024589 0.010087 2.4378 0.014778
## beta1 0.819167 0.016797 48.7683 0.000000
## gamma1 0.161187 0.034503 4.6716 0.000003
## shape 1.057066 0.046426 22.7690 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001051 0.000116 9.0888 0.000000
## ar1 0.018679 0.001965 9.5069 0.000000
## omega 0.000010 0.000000 28.8227 0.000000
## alpha1 0.024589 0.009896 2.4846 0.012968
## beta1 0.819167 0.016212 50.5293 0.000000
## gamma1 0.161187 0.032306 4.9894 0.000001
## shape 1.057066 0.048672 21.7180 0.000000
##
## LogLikelihood : 4539.418
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.1961
## Bayes -6.1708
## Shibata -6.1961
## Hannan-Quinn -6.1866
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.871 0.09016
## Lag[2*(p+q)+(p+q)-1][2] 3.372 0.01652
## Lag[4*(p+q)+(p+q)-1][5] 4.623 0.14259
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4747 0.4908
## Lag[2*(p+q)+(p+q)-1][5] 1.2729 0.7954
## Lag[4*(p+q)+(p+q)-1][9] 1.7238 0.9353
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.9987 0.500 2.000 0.3176
## ARCH Lag[5] 1.0692 1.440 1.667 0.7125
## ARCH Lag[7] 1.1605 2.315 1.543 0.8861
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 31.7617
## Individual Statistics:
## mu 0.28257
## ar1 0.07815
## omega 8.00581
## alpha1 0.09393
## beta1 0.10647
## gamma1 0.10902
## shape 0.14927
##
## 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 2.0324 0.04230 **
## Negative Sign Bias 1.0389 0.29903
## Positive Sign Bias 0.8566 0.39182
## Joint Effect 9.6021 0.02227 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 52.15 6.289e-05
## 2 30 69.62 3.412e-05
## 3 40 76.17 3.410e-04
## 4 50 90.14 3.116e-04
##
##
## Elapsed time : 0.877182# Phân phối Generalized Error Distribution(ged)
SETged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(3, 1), include.mean = TRUE), distribution.model = "ged")
SETged1 <- ugarchfit(SETged.spec,SETts)
print(SETged1)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(3,0,1)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000161 0.000238 -0.67458 0.499941
## ar1 0.632954 0.046720 13.54789 0.000000
## ar2 -0.035128 0.028415 -1.23625 0.216367
## ar3 0.041614 0.026958 1.54367 0.122669
## ma1 -0.601097 0.046907 -12.81476 0.000000
## omega 0.000003 0.000004 0.73474 0.462499
## alpha1 0.022981 0.016704 1.37580 0.168883
## beta1 0.885013 0.025537 34.65578 0.000000
## gamma1 0.110244 0.029128 3.78478 0.000154
## shape 1.336464 0.065976 20.25693 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000161 0.000636 -0.25269 0.80051
## ar1 0.632954 0.020803 30.42603 0.00000
## ar2 -0.035128 0.036860 -0.95300 0.34059
## ar3 0.041614 0.032842 1.26708 0.20513
## ma1 -0.601097 0.019533 -30.77355 0.00000
## omega 0.000003 0.000025 0.10330 0.91772
## alpha1 0.022981 0.077743 0.29561 0.76753
## beta1 0.885013 0.150563 5.87803 0.00000
## gamma1 0.110244 0.100213 1.10009 0.27129
## shape 1.336464 0.115417 11.57941 0.00000
##
## LogLikelihood : 4997.957
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.8188
## Bayes -6.7827
## Shibata -6.8189
## Hannan-Quinn -6.8053
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.5816 0.4457
## Lag[2*(p+q)+(p+q)-1][11] 2.6839 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 6.9771 0.9103
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2207 0.6385
## Lag[2*(p+q)+(p+q)-1][5] 3.6614 0.2994
## Lag[4*(p+q)+(p+q)-1][9] 5.0403 0.4235
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 3.985 0.500 2.000 0.0459
## ARCH Lag[5] 4.868 1.440 1.667 0.1102
## ARCH Lag[7] 5.173 2.315 1.543 0.2076
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 6.6556
## Individual Statistics:
## mu 0.10617
## ar1 0.01361
## ar2 0.06078
## ar3 0.08375
## ma1 0.01608
## omega 1.03989
## alpha1 0.28096
## beta1 0.16457
## gamma1 0.10405
## shape 0.27251
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.29 2.54 3.05
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.8627 0.06271 *
## Negative Sign Bias 1.1234 0.26144
## Positive Sign Bias 0.4944 0.62113
## Joint Effect 3.8018 0.28367
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 17.75 0.5391
## 2 30 28.00 0.5180
## 3 40 40.95 0.3849
## 4 50 52.76 0.3310
##
##
## Elapsed time : 1.211175# Phân phối Generalized Error Distribution đối xứng ("sged")
VNIged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(1, 0), include.mean = TRUE), distribution.model = "sged")
VNIged2 <- ugarchfit(VNIged.spec,VNIts)
print(VNIged2)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(1,0,0)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000267 0.000153 1.7434 0.081271
## ar1 0.030277 0.014082 2.1500 0.031554
## omega 0.000009 0.000000 29.1984 0.000000
## alpha1 0.026147 0.007947 3.2900 0.001002
## beta1 0.835662 0.014246 58.6588 0.000000
## gamma1 0.141116 0.027927 5.0530 0.000000
## skew 0.861255 0.018085 47.6219 0.000000
## shape 1.128199 0.051426 21.9381 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000267 0.000106 2.5252 0.011562
## ar1 0.030277 0.008258 3.6665 0.000246
## omega 0.000009 0.000000 28.6082 0.000000
## alpha1 0.026147 0.007780 3.3609 0.000777
## beta1 0.835662 0.013202 63.2990 0.000000
## gamma1 0.141116 0.024650 5.7248 0.000000
## skew 0.861255 0.014480 59.4771 0.000000
## shape 1.128199 0.053745 20.9918 0.000000
##
## LogLikelihood : 4552.441
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.2125
## Bayes -6.1836
## Shibata -6.2126
## Hannan-Quinn -6.2017
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.293 0.12994
## Lag[2*(p+q)+(p+q)-1][2] 3.021 0.03372
## Lag[4*(p+q)+(p+q)-1][5] 4.706 0.13374
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4637 0.4959
## Lag[2*(p+q)+(p+q)-1][5] 1.1589 0.8228
## Lag[4*(p+q)+(p+q)-1][9] 1.6429 0.9431
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.8753 0.500 2.000 0.3495
## ARCH Lag[5] 0.9507 1.440 1.667 0.7476
## ARCH Lag[7] 1.1036 2.315 1.543 0.8961
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 31.4178
## Individual Statistics:
## mu 0.43513
## ar1 0.16953
## omega 7.35901
## alpha1 0.09656
## beta1 0.13479
## gamma1 0.10740
## skew 0.18930
## shape 0.09610
##
## 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 1.8720 0.06141 *
## Negative Sign Bias 0.8735 0.38252
## Positive Sign Bias 1.1173 0.26405
## Joint Effect 9.8380 0.01999 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 33.01 0.02399
## 2 30 41.61 0.06080
## 3 40 52.22 0.07663
## 4 50 59.80 0.13882
##
##
## Elapsed time : 1.358645# Phân phối Generalized Error Distribution đối xứng ("sged")
SETged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(3, 1), include.mean = TRUE), distribution.model = "sged")
SETged2 <- ugarchfit(SETged.spec,SETts)
print(SETged2)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(3,0,1)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000442 0.000219 -2.0200 0.043387
## ar1 0.730901 0.083556 8.7474 0.000000
## ar2 -0.036319 0.038940 -0.9327 0.350975
## ar3 0.031610 0.025469 1.2411 0.214563
## ma1 -0.706433 0.084591 -8.3511 0.000000
## omega 0.000002 0.000002 1.1393 0.254594
## alpha1 0.023779 0.012901 1.8431 0.065308
## beta1 0.891736 0.020190 44.1678 0.000000
## gamma1 0.107800 0.028110 3.8350 0.000126
## skew 0.885676 0.030756 28.7972 0.000000
## shape 1.341635 0.067806 19.7863 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000442 0.000269 -1.64165 0.100663
## ar1 0.730901 0.025139 29.07416 0.000000
## ar2 -0.036319 0.051445 -0.70598 0.480200
## ar3 0.031610 0.027645 1.14342 0.252863
## ma1 -0.706433 0.029538 -23.91579 0.000000
## omega 0.000002 0.000009 0.25692 0.797244
## alpha1 0.023779 0.019141 1.24229 0.214131
## beta1 0.891736 0.067430 13.22468 0.000000
## gamma1 0.107800 0.059813 1.80230 0.071498
## skew 0.885676 0.054138 16.35967 0.000000
## shape 1.341635 0.115644 11.60141 0.000000
##
## LogLikelihood : 5005.038
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.8271
## Bayes -6.7874
## Shibata -6.8272
## Hannan-Quinn -6.8123
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.031 0.3098
## Lag[2*(p+q)+(p+q)-1][11] 3.746 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 7.865 0.8126
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1818 0.6698
## Lag[2*(p+q)+(p+q)-1][5] 3.8077 0.2791
## Lag[4*(p+q)+(p+q)-1][9] 5.2684 0.3911
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 4.093 0.500 2.000 0.04305
## ARCH Lag[5] 5.218 1.440 1.667 0.09147
## ARCH Lag[7] 5.508 2.315 1.543 0.17796
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 13.518
## Individual Statistics:
## mu 0.07961
## ar1 0.01948
## ar2 0.08448
## ar3 0.08279
## ma1 0.01687
## omega 2.34711
## alpha1 0.26567
## beta1 0.14846
## gamma1 0.07456
## skew 0.11620
## shape 0.30944
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.49 2.75 3.27
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.5480 0.1218
## Negative Sign Bias 0.9976 0.3186
## Positive Sign Bias 0.2315 0.8170
## Joint Effect 2.8686 0.4123
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 12.42 0.8669
## 2 30 23.73 0.7420
## 3 40 37.78 0.5255
## 4 50 54.40 0.2766
##
##
## Elapsed time : 2.221092# Tạo danh sách bao gồm các phân phối và ước lượng của VNI
VNI_list <- list(
garchn= VNIfit,
garcht= VNIst1,
garchst = VNIst2,
garchg = VNIged1,
garchsg = VNIged2
)
# Tính toán các thông tin
VNI_info_mat <- sapply(VNI_list, infocriteria)
rownames(VNI_info_mat) <- rownames(infocriteria(VNIfit))
print(VNI_info_mat)## garchn garcht garchst garchg garchsg
## Akaike -6.062277 -6.203674 -6.220616 -6.196060 -6.212496
## Bayes -6.040589 -6.178371 -6.191699 -6.170758 -6.183579
## Shibata -6.062311 -6.203719 -6.220675 -6.196106 -6.212555
## Hannan-Quinn -6.054188 -6.194236 -6.209830 -6.186622 -6.201710# Tạo danh sách bao gồm các phân phối và ước lượng của SET
SET_list <- list(
garchn= SETfit,
garcht= SETst1,
garchst = SETst2,
garchg = SETged1,
garchsg = SETged2
)
# Tính toán các thông tin
SET_info_mat <- sapply(SET_list, infocriteria)
rownames(SET_info_mat) <- rownames(infocriteria(SETfit))
print(SET_info_mat)## garchn garcht garchst garchg garchsg
## Akaike -6.771029 -6.828219 -6.833494 -6.818806 -6.827120
## Bayes -6.738497 -6.792073 -6.793733 -6.782660 -6.787359
## Shibata -6.771104 -6.828312 -6.833606 -6.818899 -6.827232
## Hannan-Quinn -6.758895 -6.814736 -6.818663 -6.805323 -6.812289TRÍCH XUẤT PHẦN DƯ
VNI.res <- residuals(VNIst2)/sigma(VNIst2)
fitdist(distribution = "sstd", VNI.res, control = list())## $pars
## mu sigma skew shape
## -0.006437266 1.006945123 0.824410534 3.948967168
##
## $convergence
## [1] 0
##
## $values
## [1] 2119.625 1932.710 1932.710
##
## $lagrange
## [1] 0
##
## $hessian
## [,1] [,2] [,3] [,4]
## [1,] 2273.49325 547.6364 -768.82877 29.84075
## [2,] 547.63641 1787.5356 202.94989 143.32332
## [3,] -768.82877 202.9499 1331.03255 29.73594
## [4,] 29.84075 143.3233 29.73594 16.92159
##
## $ineqx0
## NULL
##
## $nfuneval
## [1] 102
##
## $outer.iter
## [1] 2
##
## $elapsed
## Time difference of 0.06486893 secs
##
## $vscale
## [1] 1 1 1 1 1SET.res <- residuals(SETst2)/sigma(SETst2)
fitdist(distribution = "sstd", SET.res, control = list())## $pars
## mu sigma skew shape
## 0.01229265 0.99197059 0.89326609 6.29073256
##
## $convergence
## [1] 0
##
## $values
## [1] 2152.401 2018.255 2018.255
##
## $lagrange
## [1] 0
##
## $hessian
## [,1] [,2] [,3] [,4]
## [1,] 1764.533578 240.03987 -430.255685 4.157051
## [2,] 240.039866 2026.88230 192.464738 32.880268
## [3,] -430.255685 192.46474 1170.249007 5.290859
## [4,] 4.157051 32.88027 5.290859 1.622396
##
## $ineqx0
## NULL
##
## $nfuneval
## [1] 121
##
## $outer.iter
## [1] 2
##
## $elapsed
## Time difference of 0.09074092 secs
##
## $vscale
## [1] 1 1 1 1 1s = pdist("sstd",VNI.res, mu = -0.006437266, sigma = 1.006945123, skew = 0.824410534, shape = 3.948967168 )
head(s,10)## [1] 0.90330343 0.20177741 0.84679514 0.85149378 0.63230860 0.86345748
## [7] 0.51465155 0.94049905 0.38860692 0.01035891s1 = pdist("sstd",SET.res, mu = 0.01229265, sigma = 0.99197059, skew = 0.89326609, shape = 6.29073256 )
head(s1,10)## [1] 0.7862829 0.6022263 0.4235651 0.5563165 0.4794785 0.7154878 0.7024680
## [8] 0.8329672 0.4592902 0.7256200Kiểm định cho biến VNI
# Kiểm định Anderson_Darling
library(nortest)
ad.test(s)##
## Anderson-Darling normality test
##
## data: s
## A = 14.928, p-value < 2.2e-16# Kiểm định Cramer-von Mises
cvm.test(s)## Warning in cvm.test(s): p-value is smaller than 7.37e-10, cannot be computed
## more accurately##
## Cramer-von Mises normality test
##
## data: s
## W = 1.8967, p-value = 7.37e-10# Kiểm định Kolmogorov-Smirnov
ks.test(s, y = "punif")##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: s
## D = 0.026582, p-value = 0.2525
## alternative hypothesis: two-sidedKiểm định cho biến SET
# Kiểm định Anderson_Darling
library(nortest)
ad.test(s1)##
## Anderson-Darling normality test
##
## data: s1
## A = 15.907, p-value < 2.2e-16# Kiểm định Cramer-von Mises
cvm.test(s1)## Warning in cvm.test(s1): p-value is smaller than 7.37e-10, cannot be computed
## more accurately##
## Cramer-von Mises normality test
##
## data: s1
## W = 2.1103, p-value = 7.37e-10# Kiểm định Kolmogorov-Smirnov
ks.test(s1, y = "punif")##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: s1
## D = 0.010965, p-value = 0.9946
## alternative hypothesis: two-sidedMÔ HÌNH COPULA
library(VineCopula)## Warning: package 'VineCopula' was built under R version 4.4.1library(copula)## Warning: package 'copula' was built under R version 4.4.1##
## Attaching package: 'copula'## The following object is masked from 'package:VineCopula':
##
## pobslibrary(scatterplot3d)
#Chuyển đôi dữ liệu phân phối đều
u <- pobs(s)
head(u,10)## [1] 0.90163934 0.19262295 0.83811475 0.84153005 0.64344262 0.85519126
## [7] 0.53415301 0.94535519 0.38251366 0.01434426k <- pobs(s1)
head(k,10)## [1] 0.7875683 0.6010929 0.4187158 0.5587432 0.4808743 0.7178962 0.7103825
## [8] 0.8306011 0.4590164 0.7260929BiCopSelect(s,s1, familyset= c(1:10), selectioncrit="AIC",indeptest = FALSE, level = 0.05)## Bivariate copula: Survival Gumbel (par = 1.16, tau = 0.14)#Biểu đồ phân tán:
gumbel.cop <- gumbelCopula(param = 1.16, dim = 2)
plot(mhnn, xlab = "u", ylab = "k")
persp(gumbel.cop, dCopula, xlab = "u", ylab = "k", zlab = "Mật độ",
main = "Đồ thị mật độ của copula Gumbel")
contour(gumbel.cop, dCopula, xlab = "u", ylab = "k",
main = "Đồ thị contour của copula Gumbel")
gumbel.cop1 <- gumbelCopula(param = 1.16, dim = 2)
set.seed(123)
data12 <- rCopula(1463, gumbel.cop1)
scatterplot3d(data12[,1], data12[,2], pch = 16, color = "blue",
type = "h", highlight.3d = TRUE,
xlab = "u", ylab = "k", zlab = "Probability")## Warning in scatterplot3d(data12[, 1], data12[, 2], pch = 16, color = "blue", :
## color is ignored when highlight.3d = TRUE
library(copula)
# Thiết lập Joe copula với tham số par = 1.16
theta <- 1.16
gumbel_cop <- gumbelCopula(param = theta)
# Kiểm tra Kendall's tau của Joe copula
tau <- tau(gumbel_cop)
print(tau)## [1] 0.137931e <- cbind(u,k)
fit <- fitCopula(gumbelCopula(), data = e, method = "ml")
# Maximum Likelihood Estimation (MLE)
theta <- coef(fit)
print(theta)## alpha
## 1.123401# Tạo thêm dữ liệu từ Gumbel copula
set.seed(654)
e <- rCopula(1463, gumbel_cop)
x <- qnorm(e[,1])
y <- qnorm(e[,2])
# Vẽ biểu đồ hộp và râu
boxplot(x, y,
col = c("lightblue", "pink"),
names = c("VNI", "SET"),
main = "Box Plot")
plot(data12[, 1], data12[, 2], pch = 16, col = "blue",
main = "Scatter Plot of Gumbel Copula Data",
xlab = "VNI", ylab = "SET")
# Tạo dữ liệu giả định
set.seed(123)
data <- data.frame(u = u, k = k)
# Vẽ đồ thị phân tán
ggplot(data, aes(x = u, y = k)) +
geom_point(size = 1, alpha = 0.5) +
labs(x = "VNI", y = "SET", title = "Đồ thị phân tán của VNI và SET") +
theme_classic()
# Load necessary libraries
library(copula)
library(MASS)## Warning: package 'MASS' was built under R version 4.4.1library(scatterplot3d)
# Define the parameter for the Gumbel copula
theta <- 1.16
# Create the Joe copula object
gumbel_copula <- gumbelCopula(param = theta)
# Perform Kernel Density Estimation
kde2d_result <- kde2d(e[,1], e[,2], n = 50)
# Convert kde2d result to a format suitable for scatterplot3d
x <- kde2d_result$x
y <- kde2d_result$y
z <- kde2d_result$z
# Create a grid of points for scatterplot3d
grid <- expand.grid(x = x, y = y)
# Flatten z for scatterplot3d
z_flat <- as.vector(z)
# Plot the density using scatterplot3d
scatterplot3d(grid$x, grid$y, z_flat, type = "h", angle = 30,
main = "Density Plot of Gumbel Copula",
xlab = "VNI",
ylab = "SET",
zlab = "Bivariate Distribution",
pch = 20, color = "yellow")
# Load necessary libraries
library(copula)
library(MASS)
# Define the parameter for the Joe copula
theta <- 1.16
# Create the Joe copula object
gumbel_copula <- gumbelCopula(param = theta)
# Perform Kernel Density Estimation
kde2d_result <- kde2d(e[,1], e[,2], n = 1000)
# Extract the results
x <- kde2d_result$x
y <- kde2d_result$y
z <- kde2d_result$z
# Plot the PDF using persp
persp(x, y, z, phi = 30, theta = 50, col = "blue",
xlab = "VNI", ylab = "SET", zlab = "Density",
main = "PDF of Gumbel Copula")
# Plot the contour plot
contour(x, y, z, xlab = "VNI", ylab = "SET",
main = "Contour Plot of Gumbel Copula")