Phân tích mối quan hệ giữa cổ phiếu Microsoft (MSFT) và cổ phiếu Intel (INTC).

“09:28:05, 10 - 08 - 2024”
***

library(xlsx)
h <- read.xlsx("F:/Các mô hình ngẫu nhiên/cmhnn3.xlsx", sheetIndex=1, header=T)

0.1 Mô tả thống kê

library(stargazer)

## 
## Please cite as:

##  Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.

##  R package version 5.2.3. https://CRAN.R-project.org/package=stargazer

library(corrplot)

## Warning: package 'corrplot' was built under R version 4.3.3

## corrplot 0.92 loaded

library(lmtest)

## Warning: package 'lmtest' was built under R version 4.3.3

## Loading required package: zoo

## Warning: package 'zoo' was built under R version 4.3.3

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

library(tseries)

## Warning: package 'tseries' was built under R version 4.3.3

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

library(forecast)

## Warning: package 'forecast' was built under R version 4.3.3

library(moments)
e <- h[c(2:3409),c(4,5)]
stargazer(e,type= "text",title = "thống kê mô tả")

## 
## thống kê mô tả
## ==========================================
## Statistic   N   Mean  St. Dev.  Min   Max 
## ------------------------------------------
## MSFT2     3,408 1.001  0.016   0.853 1.142
## INTC2     3,408 1.000  0.020   0.820 1.195
## ------------------------------------------

corrplot.mixed(cor(e), lower ="number", upper="circle",tl.col='black' ) # biểu đồ hệ số tương quan

cor(e)

##           MSFT2     INTC2
## MSFT2 1.0000000 0.5544902
## INTC2 0.5544902 1.0000000

0.1.1 Biến động chuỗi lợi suất

library(stats)
MSFT2 <- e$MSFT2
INTC2 <- e$INTC2
plot.ts(MSFT2)

plot.ts(INTC2)

0.2 Kiểm định

# Kiểm định ADF
adf.test(e$MSFT2)

## Warning in adf.test(e$MSFT2): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  e$MSFT2
## Dickey-Fuller = -15.455, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary

adf.test(e$INTC2)

## Warning in adf.test(e$INTC2): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  e$INTC2
## Dickey-Fuller = -15.633, Lag order = 15, p-value = 0.01
## alternative hypothesis: stationary

# kiểm định J-B
jarque.bera.test(e$MSFT2)

## 
##  Jarque Bera Test
## 
## data:  e$MSFT2
## X-squared = 8650.2, df = 2, p-value < 2.2e-16

jarque.bera.test(e$INTC2)

## 
##  Jarque Bera Test
## 
## data:  e$INTC2
## X-squared = 16084, df = 2, p-value < 2.2e-16

# kiểm định ljung-box cho chuỗi tương quan bậc 2
library(stats)
Box.test(e$MSFT2, lag=2,type="Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  e$MSFT2
## X-squared = 45.522, df = 2, p-value = 1.303e-10

Box.test(e$INTC2,lag=2, type="Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  e$INTC2
## X-squared = 44.574, df = 2, p-value = 2.093e-10

# Kiểm định arch-lm

library(fGarch)

## Warning: package 'fGarch' was built under R version 4.3.3

## 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")

library(rugarch)

## Warning: package 'rugarch' was built under R version 4.3.3

## Loading required package: parallel

## 
## Attaching package: 'rugarch'

## The following object is masked from 'package:stats':
## 
##     sigma

arch.spec <- ugarchspec(variance.model=list(model="sGARCH"))
arch.MSFT2 <- ugarchfit(spec=arch.spec,data=e$MSFT2)
residuals <- residuals(arch.MSFT2)

n <- length(residuals)

x <- 1:n
# Tạo mô hình tuyến tính
arch_lm_model <- lm(residuals^2 ~ x + lag(residuals^2, 1))
# Kiểm định hiệu ứng ARCH-LM
arch <- bptest(arch_lm_model)
# Hiển thị kết quả
arch

## 
##  studentized Breusch-Pagan test
## 
## data:  arch_lm_model
## BP = 444, df = 2, p-value < 2.2e-16

arch.spec <- ugarchspec(variance.model=list(model="sGARCH"))
arch.INTC2 <- ugarchfit(spec=arch.spec,data=e$INTC2)
residuals1 <- residuals(arch.INTC2)

n <- length(residuals1)

x <- 1:n
# Tạo mô hình tuyến tính
arch_lm_model1 <- lm(residuals1^2 ~ x + lag(residuals1^2, 1))
# Kiểm định hiệu ứng ARCH-LM
arch1 <- bptest(arch_lm_model1)
# Hiển thị kết quả
arch1

## 
##  studentized Breusch-Pagan test
## 
## data:  arch_lm_model1
## BP = 272.46, df = 2, p-value < 2.2e-16

• Biểu đồ ma trận tương quan.

f <- h[c(2:3409),]
m <- f[,c(4,5)]
g <- h[,c(2,3)]
library(PerformanceAnalytics)

## Warning: package 'PerformanceAnalytics' was built under R version 4.3.3

## Loading required package: xts

## Warning: package 'xts' was built under R version 4.3.3

## 
## Attaching package: 'PerformanceAnalytics'

## The following objects are masked from 'package:fGarch':
## 
##     ES, VaR

## The following objects are masked from 'package:moments':
## 
##     kurtosis, skewness

## The following object is masked from 'package:graphics':
## 
##     legend

j <- chart.Correlation(g)

## Warning in par(usr): argument 1 does not name a graphical parameter

n <- chart.Correlation(m)

## Warning in par(usr): argument 1 does not name a graphical parameter

n

## NULL

MSFT2 <- diff(f$MSFT2)
INTC2 <- diff(f$INTC2)
library(rugarch)
library(lmtest)
library(stats)
library(tseries)
library(fGarch)

0.3 Mô hình ARIMA

# Mô hình ARIMA
autoarfima(MSFT2, ar.max=2, ma.max=2, criterion="AIC", method= "full")$fit

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(2,0,2)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error    t value Pr(>|t|)
## mu     0.000000    0.000000     63.227        0
## ar1   -1.021338    0.006352   -160.784        0
## ar2   -0.136656    0.007439    -18.370        0
## ma1   -0.102299    0.000004 -24669.192        0
## ma2   -0.900337    0.000049 -18431.534        0
## sigma  0.016175    0.000185     87.302        0
## 
## Robust Standard Errors:
##        Estimate  Std. Error    t value Pr(>|t|)
## mu     0.000000    0.000000     7.2658 0.000000
## ar1   -1.021338    0.050391   -20.2681 0.000000
## ar2   -0.136656    0.039574    -3.4532 0.000554
## ma1   -0.102299    0.000020 -5238.7949 0.000000
## ma2   -0.900337    0.000213 -4226.7476 0.000000
## sigma  0.016175    0.000975    16.5815 0.000000
## 
## LogLikelihood : 9208.091 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -5.4019
## Bayes        -5.3911
## Shibata      -5.4019
## Hannan-Quinn -5.3980
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic   p-value
## Lag[1]                      0.2049 6.508e-01
## Lag[2*(p+q)+(p+q)-1][11]   18.3085 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19]   32.3548 3.184e-10
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                      355.6       0
## Lag[2*(p+q)+(p+q)-1][2]     444.0       0
## Lag[4*(p+q)+(p+q)-1][5]     578.4       0
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF P-Value
## ARCH Lag[2]      413.3   2       0
## ARCH Lag[5]      447.3   5       0
## ARCH Lag[10]     486.2  10       0
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  4.3434
## Individual Statistics:             
## mu    0.03637
## ar1   0.01998
## ar2   0.14457
## ma1   0.07407
## ma2   0.06284
## sigma 1.64729
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          1.49 1.68 2.12
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.20365

autoarfima(INTC2, ar.max=2, ma.max=2, criterion="AIC", method = "full")$fit

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(2,0,2)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error    t value Pr(>|t|)
## ar1   -0.845848     6.0e-06 -140672.76        0
## ar2   -0.088881     1.3e-05   -7040.65        0
## ma1   -0.264613     1.1e-05  -23157.28        0
## ma2   -0.740294     2.1e-05  -35607.42        0
## sigma  0.019386     4.2e-05     465.38        0
## 
## Robust Standard Errors:
##        Estimate  Std. Error   t value Pr(>|t|)
## ar1   -0.845848    0.000020 -41977.51        0
## ar2   -0.088881    0.000013  -6776.51        0
## ma1   -0.264613    0.000022 -12075.92        0
## ma2   -0.740294    0.000023 -32423.81        0
## sigma  0.019386    0.000115    168.67        0
## 
## LogLikelihood : 8596.117 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -5.0432
## Bayes        -5.0342
## Shibata      -5.0432
## Hannan-Quinn -5.0400
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                      0.8369  0.3603
## Lag[2*(p+q)+(p+q)-1][11]   27.3571  0.0000
## Lag[4*(p+q)+(p+q)-1][19]   45.5977  0.0000
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                      405.5       0
## Lag[2*(p+q)+(p+q)-1][2]     463.1       0
## Lag[4*(p+q)+(p+q)-1][5]     549.8       0
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF P-Value
## ARCH Lag[2]      421.6   2       0
## ARCH Lag[5]      447.1   5       0
## ARCH Lag[10]     468.9  10       0
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  14.4453
## Individual Statistics:             
## ar1   0.02253
## ar2   0.02252
## ma1   0.02229
## ma2   0.02480
## sigma 6.10544
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          1.28 1.47 1.88
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.2571669

0.4 Mô hình GJR-GARCH

0.4.1 Các dạng mô hình GJR_GARCH

• Các dạng mô hình GJR-GARCH cho MSFT2.

# Mô hình GJR-GARCH cho MSFT2
MSFT.garch11n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
MSFT.garch11n.fit <- ugarchfit(spec = MSFT.garch11n.spec, data = MSFT2)
MSFT.garch11t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
MSFT.garch11t.fit <- ugarchfit(spec = MSFT.garch11t.spec, data = MSFT2)
MSFT.garch11st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
MSFT.garch11st.fit <- ugarchfit(spec = MSFT.garch11st.spec, data = MSFT2)
MSFT.garch11g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
MSFT.garch11g.fit <- ugarchfit(spec = MSFT.garch11g.spec, data = MSFT2)

MSFT.garch11sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
MSFT.garch11sg.fit <- ugarchfit(spec = MSFT.garch11sg.spec, data = MSFT2)

MSFT.garch12n.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(1,2)), mean.model=list(armaOrder=c(2,2),include.mean= TRUE), distribution.model="norm")
MSFT.garch12n.fit <- ugarchfit(spec=MSFT.garch12n.spec, data =MSFT2)

MSFT.garch12t.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(1,2)), mean.model= list(armaOrder=c(2,2), include.mean= TRUE), distribution.model= "std")
MSFT.garch12t.fit <- ugarchfit(spec=MSFT.garch12t.spec, data=MSFT2)

MSFT.garch12st.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(1,2)), mean.model=list(armaOrder=c(2,2), include.mean=TRUE), distribution.model= "sstd")
MSFT.garch12st.fit <- ugarchfit(spec=MSFT.garch12st.spec, data=MSFT2)


MSFT.garch12g.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(1,2)), mean.model= list(armaOrder=c(2,2), include.mean= TRUE), distribution.model="ged")
MSFT.garch12g.fit <- ugarchfit(spec=MSFT.garch12g.spec, data= MSFT2)

MSFT.garch12sg.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(1,2)), mean.model=list(armaOrder=c(2,2), include.mean=TRUE), distribution.model="sged")
MSFT.garch12sg.fit <- ugarchfit(spec=MSFT.garch12sg.spec, data=MSFT2)

MSFT.garch21n.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,1)), mean.model=list(armaOrder=c(2,2),include.mean= TRUE), distribution.model="norm")
MSFT.garch21n.fit <- ugarchfit(spec=MSFT.garch21n.spec, data =MSFT2)

MSFT.garch21t.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,1)), mean.model= list(armaOrder=c(2,2), include.mean= TRUE), distribution.model= "std")
MSFT.garch21t.fit <- ugarchfit(spec=MSFT.garch21t.spec, data=MSFT2)

MSFT.garch21st.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,1)), mean.model=list(armaOrder=c(2,2), include.mean=TRUE), distribution.model= "sstd")
MSFT.garch21st.fit <- ugarchfit(spec=MSFT.garch21st.spec, data=MSFT2)

MSFT.garch21g.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,1)), mean.model= list(armaOrder=c(2,2), include.mean= TRUE), distribution.model="ged")
MSFT.garch21g.fit <- ugarchfit(spec=MSFT.garch21g.spec, data= MSFT2)

MSFT.garch21sg.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,1)), mean.model=list(armaOrder=c(2,2), include.mean=TRUE), distribution.model="sged")
MSFT.garch21sg.fit <- ugarchfit(spec=MSFT.garch21sg.spec, data=MSFT2)

MSFT.garch22n.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,2)), mean.model=list(armaOrder=c(2,2),include.mean= TRUE), distribution.model="norm")
MSFT.garch22n.fit <- ugarchfit(spec=MSFT.garch22n.spec, data =MSFT2)

MSFT.garch22t.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,2)), mean.model= list(armaOrder=c(2,2), include.mean= TRUE), distribution.model= "std")
MSFT.garch22t.fit <- ugarchfit(spec=MSFT.garch22t.spec, data=MSFT2)

MSFT.garch22st.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,2)), mean.model=list(armaOrder=c(2,2), include.mean=TRUE), distribution.model= "sstd")
MSFT.garch22st.fit <- ugarchfit(spec=MSFT.garch22st.spec, data=MSFT2)

MSFT.garch22g.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,2)), mean.model= list(armaOrder=c(2,2), include.mean= TRUE), distribution.model="ged")
MSFT.garch22g.fit <- ugarchfit(spec=MSFT.garch22g.spec, data= MSFT2)

MSFT.garch22sg.spec <- ugarchspec(variance.model=list(model="gjrGARCH", garchOrder=c(2,2)), mean.model=list(armaOrder=c(2,2), include.mean=TRUE), distribution.model="sged")
MSFT.garch22sg.fit <- ugarchfit(spec=MSFT.garch22sg.spec, data=MSFT2)

• Các dạng mô hình GJR_GARCH cho chuỗi INTC2.

INTC.garch11n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
INTC.garch11n.fit <- ugarchfit(spec = INTC.garch11n.spec, data = INTC2)
INTC.garch11t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
INTC.garch11t.fit <- ugarchfit(spec =INTC.garch11t.spec, data = INTC2)
INTC.garch11st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
INTC.garch11st.fit <- ugarchfit(spec = INTC.garch11st.spec, data = INTC2)
INTC.garch11g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
INTC.garch11g.fit <- ugarchfit(spec = INTC.garch11g.spec, data = INTC2)
INTC.garch11sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
INTC.garch11sg.fit <- ugarchfit(spec = INTC.garch11sg.spec, data = INTC2)

INTC.garch12n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
INTC.garch12n.fit <- ugarchfit(spec = INTC.garch12n.spec, data = INTC2)

INTC.garch12t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
INTC.garch12t.fit <- ugarchfit(spec =INTC.garch12t.spec, data = INTC2)

INTC.garch12st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
INTC.garch12st.fit <- ugarchfit(spec = INTC.garch12st.spec, data = INTC2)

INTC.garch12g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
INTC.garch12g.fit <- ugarchfit(spec = INTC.garch12g.spec, data = INTC2)

INTC.garch12sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
INTC.garch12sg.fit <- ugarchfit(spec = INTC.garch12sg.spec, data = INTC2)

INTC.garch21n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
INTC.garch21n.fit <- ugarchfit(spec = INTC.garch21n.spec, data = INTC2)

INTC.garch21t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
INTC.garch21t.fit <- ugarchfit(spec =INTC.garch21t.spec, data = INTC2)


INTC.garch21st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
INTC.garch21st.fit <- ugarchfit(spec = INTC.garch21st.spec, data = INTC2)

INTC.garch21g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
INTC.garch21g.fit <- ugarchfit(spec = INTC.garch21g.spec, data = INTC2)

INTC.garch21sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
INTC.garch21sg.fit <- ugarchfit(spec = INTC.garch21sg.spec, data = INTC2)

INTC.garch22n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
INTC.garch22n.fit <- ugarchfit(spec = INTC.garch22n.spec, data = INTC2)

INTC.garch22t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
INTC.garch22t.fit <- ugarchfit(spec =INTC.garch22t.spec, data = INTC2)

INTC.garch22st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
INTC.garch22st.fit <- ugarchfit(spec = INTC.garch22st.spec, data = INTC2)

INTC.garch22g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
INTC.garch22g.fit <- ugarchfit(spec = INTC.garch22g.spec, data = INTC2)

INTC.garch22sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
INTC.garch22sg.fit <- ugarchfit(spec = INTC.garch22sg.spec, data = INTC2)

0.4.2 Lựa chọn mô hình

• Lựa chọn mô hình cho MSFT

safe_infocriteria <- function(model) {tryCatch(infocriteria(model),error = function(e) return(rep(NA, 4)))}


# Lựa chọn mô hình cho MSFT
MSFT.model.list <- list(garch11n = MSFT.garch11n.fit, garch11t = MSFT.garch11t.fit, garch11st = MSFT.garch11st.fit, 
garch11g = MSFT.garch11g.fit, garch11sg = MSFT.garch11sg.fit, garch12n=MSFT.garch12n.fit, garch12t = MSFT.garch12t.fit, garch12st= MSFT.garch12st.fit, garch12g=MSFT.garch12g.fit, garch12sg= MSFT.garch12sg.fit, garch21n = MSFT.garch21n.fit, garch21t=MSFT.garch21t.fit, garch21st=MSFT.garch21st.fit, garch21g=MSFT.garch21g.fit, garch21sg=MSFT.garch21sg.fit, garch22n=MSFT.garch22n.fit, garch22t= MSFT.garch22t.fit, garch22st=MSFT.garch22st.fit, garch22g=MSFT.garch22g.fit, garch22sg=MSFT.garch22sg.fit)

MSFT.info.mat <- sapply(MSFT.model.list, safe_infocriteria)

## Warning in log(log(nObs)): NaNs produced

## Warning in log(log(nObs)): NaNs produced

## Warning in log(log(nObs)): NaNs produced

rownames(MSFT.info.mat) <- rownames(infocriteria(MSFT.garch11n.fit))

MSFT.info.mat

##               garch11n  garch11t garch11st  garch11g garch11sg  garch12n
## Akaike       -5.563748 -5.686385        NA -5.669903 -5.669175 -5.563828
## Bayes        -5.547546 -5.668382        NA -5.651900 -5.649372 -5.545825
## Shibata      -5.563762 -5.686402        NA -5.669920 -5.669196 -5.563845
## Hannan-Quinn -5.557958 -5.679951        NA -5.663469 -5.662098 -5.557394
##              garch12t garch12st garch12g garch12sg  garch21n  garch21t
## Akaike             NA -5.685469       NA -5.669404 -5.566571 -5.685680
## Bayes              NA -5.663865       NA -5.647800 -5.546768 -5.664077
## Shibata            NA -5.685494       NA -5.669428 -5.566592 -5.685705
## Hannan-Quinn       NA -5.677748       NA -5.661683 -5.559494 -5.677959
##              garch21st  garch21g garch21sg  garch22n  garch22t garch22st
## Akaike       -5.685097 -5.668388 -5.669196 -5.566033 -5.685085 -5.684474
## Bayes        -5.661693 -5.646785 -5.645792 -5.544430 -5.661681 -5.659270
## Shibata      -5.685126 -5.668413 -5.669225 -5.566058 -5.685114 -5.684508
## Hannan-Quinn -5.676733 -5.660668 -5.660832 -5.558312 -5.676721 -5.675467
##               garch22g garch22sg
## Akaike       -5.668920 -5.668659
## Bayes        -5.645516 -5.643455
## Shibata      -5.668949 -5.668693
## Hannan-Quinn -5.660556 -5.659652

MSFT.garch11t.fit

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(2,0,2)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.000001    0.000000      9.8870 0.000000
## ar1    -0.818893    0.017327    -47.2599 0.000000
## ar2    -0.050848    0.014898     -3.4130 0.000642
## ma1    -0.231509    0.000043  -5421.4160 0.000000
## ma2    -0.768805    0.000022 -34614.8879 0.000000
## omega   0.000008    0.000003      3.0123 0.002593
## alpha1  0.024102    0.001758     13.7101 0.000000
## beta1   0.885537    0.005176    171.0992 0.000000
## gamma1  0.132893    0.019150      6.9396 0.000000
## shape   4.789510    0.122497     39.0991 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.000001    0.000000  2.2545e+00 0.024163
## ar1    -0.818893    0.017865 -4.5838e+01 0.000000
## ar2    -0.050848    0.018078 -2.8126e+00 0.004914
## ma1    -0.231509    0.000032 -7.3100e+03 0.000000
## ma2    -0.768805    0.000045 -1.7137e+04 0.000000
## omega   0.000008    0.000009  8.8204e-01 0.377753
## alpha1  0.024102    0.008020  3.0054e+00 0.002652
## beta1   0.885537    0.031510  2.8103e+01 0.000000
## gamma1  0.132893    0.076509  1.7370e+00 0.082393
## shape   4.789510    1.302904  3.6760e+00 0.000237
## 
## LogLikelihood : 9696.757 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -5.6864
## Bayes        -5.6684
## Shibata      -5.6864
## Hannan-Quinn -5.6800
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic   p-value
## Lag[1]                      0.2971 0.5856788
## Lag[2*(p+q)+(p+q)-1][11]    8.1186 0.0006846
## Lag[4*(p+q)+(p+q)-1][19]   12.2845 0.1655722
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                    0.03131  0.8596
## Lag[2*(p+q)+(p+q)-1][5]   0.90685  0.8804
## Lag[4*(p+q)+(p+q)-1][9]   2.16413  0.8845
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]    0.8366 0.500 2.000  0.3604
## ARCH Lag[5]    1.8868 1.440 1.667  0.4968
## ARCH Lag[7]    2.3865 2.315 1.543  0.6359
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  183.4231
## Individual Statistics:               
## mu     67.29780
## ar1     0.13555
## ar2     0.08513
## ma1     0.10667
## ma2     0.11560
## omega   3.06186
## alpha1  0.47558
## beta1   0.52699
## gamma1  0.66604
## shape   1.13453
## 
## 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           0.3296 0.7418    
## Negative Sign Bias  0.2154 0.8294    
## Positive Sign Bias  0.4766 0.6337    
## Joint Effect        0.3437 0.9516    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     30.95     0.040873
## 2    30     49.67     0.009789
## 3    40     55.01     0.046018
## 4    50     70.80     0.022454
## 
## 
## Elapsed time : 1.367071

• Lựa chọn mô hình cho INTC

INTC.model.list <- list(garch11n = INTC.garch11n.fit, garch11t = INTC.garch11t.fit, garch11st = INTC.garch11st.fit, garch11g = INTC.garch11g.fit, garch11sg = INTC.garch11sg.fit,garch12n = INTC.garch12n.fit, garch12t = INTC.garch12t.fit, garch12st = INTC.garch12st.fit, garch12g = INTC.garch12g.fit, garch12sg = INTC.garch12sg.fit, garch21n = INTC.garch21n.fit, garch21t = INTC.garch21t.fit, garch21st = INTC.garch21st.fit, garch21g = INTC.garch21g.fit, garch21sg = INTC.garch21sg.fit, garch22n = INTC.garch22n.fit, garch22t = INTC.garch22t.fit, garch22st = INTC.garch22st.fit, garch22g = INTC.garch22g.fit, garch22sg = INTC.garch22sg.fit )

INTC.info.mat <- sapply(INTC.model.list, safe_infocriteria)

## Warning in log(log(nObs)): NaNs produced

## Warning in log(log(nObs)): NaNs produced

rownames(INTC.info.mat) <-rownames(infocriteria(INTC.garch11n.fit))

INTC.info.mat

##               garch11n garch11t garch11st  garch11g garch11sg  garch12n
## Akaike       -5.195382       NA        NA -5.343292 -5.340263 -5.197554
## Bayes        -5.179179       NA        NA -5.325289 -5.320459 -5.179551
## Shibata      -5.195396       NA        NA -5.343309 -5.340283 -5.197571
## Hannan-Quinn -5.189591       NA        NA -5.336859 -5.333185 -5.191120
##               garch12t garch12st  garch12g garch12sg  garch21n  garch21t
## Akaike       -5.369988 -5.369173 -5.342374 -5.342555 -5.201582 -5.369752
## Bayes        -5.350185 -5.347570 -5.322571 -5.320952 -5.181779 -5.348148
## Shibata      -5.370009 -5.369198 -5.342395 -5.342580 -5.201603 -5.369776
## Hannan-Quinn -5.362911 -5.361453 -5.335297 -5.334835 -5.194505 -5.362031
##              garch21st  garch21g garch21sg  garch22n  garch22t garch22st
## Akaike       -5.369368 -5.342739 -5.342541 -5.199918 -5.368063 -5.367605
## Bayes        -5.345964 -5.321135 -5.319137 -5.178315 -5.344660 -5.342400
## Shibata      -5.369397 -5.342763 -5.342570 -5.199943 -5.368092 -5.367638
## Hannan-Quinn -5.361004 -5.335018 -5.334177 -5.192198 -5.359700 -5.358597
##               garch22g garch22sg
## Akaike       -5.341548 -5.341463
## Bayes        -5.318144 -5.316259
## Shibata      -5.341576 -5.341497
## Hannan-Quinn -5.333184 -5.332456

0.4.3 Tham số ước lượng mô hình biên phù hợp nhất

MSFT.garch11t.fit

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(2,0,2)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.000001    0.000000      9.8870 0.000000
## ar1    -0.818893    0.017327    -47.2599 0.000000
## ar2    -0.050848    0.014898     -3.4130 0.000642
## ma1    -0.231509    0.000043  -5421.4160 0.000000
## ma2    -0.768805    0.000022 -34614.8879 0.000000
## omega   0.000008    0.000003      3.0123 0.002593
## alpha1  0.024102    0.001758     13.7101 0.000000
## beta1   0.885537    0.005176    171.0992 0.000000
## gamma1  0.132893    0.019150      6.9396 0.000000
## shape   4.789510    0.122497     39.0991 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.000001    0.000000  2.2545e+00 0.024163
## ar1    -0.818893    0.017865 -4.5838e+01 0.000000
## ar2    -0.050848    0.018078 -2.8126e+00 0.004914
## ma1    -0.231509    0.000032 -7.3100e+03 0.000000
## ma2    -0.768805    0.000045 -1.7137e+04 0.000000
## omega   0.000008    0.000009  8.8204e-01 0.377753
## alpha1  0.024102    0.008020  3.0054e+00 0.002652
## beta1   0.885537    0.031510  2.8103e+01 0.000000
## gamma1  0.132893    0.076509  1.7370e+00 0.082393
## shape   4.789510    1.302904  3.6760e+00 0.000237
## 
## LogLikelihood : 9696.757 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -5.6864
## Bayes        -5.6684
## Shibata      -5.6864
## Hannan-Quinn -5.6800
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic   p-value
## Lag[1]                      0.2971 0.5856788
## Lag[2*(p+q)+(p+q)-1][11]    8.1186 0.0006846
## Lag[4*(p+q)+(p+q)-1][19]   12.2845 0.1655722
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                    0.03131  0.8596
## Lag[2*(p+q)+(p+q)-1][5]   0.90685  0.8804
## Lag[4*(p+q)+(p+q)-1][9]   2.16413  0.8845
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]    0.8366 0.500 2.000  0.3604
## ARCH Lag[5]    1.8868 1.440 1.667  0.4968
## ARCH Lag[7]    2.3865 2.315 1.543  0.6359
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  183.4231
## Individual Statistics:               
## mu     67.29780
## ar1     0.13555
## ar2     0.08513
## ma1     0.10667
## ma2     0.11560
## omega   3.06186
## alpha1  0.47558
## beta1   0.52699
## gamma1  0.66604
## shape   1.13453
## 
## 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           0.3296 0.7418    
## Negative Sign Bias  0.2154 0.8294    
## Positive Sign Bias  0.4766 0.6337    
## Joint Effect        0.3437 0.9516    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     30.95     0.040873
## 2    30     49.67     0.009789
## 3    40     55.01     0.046018
## 4    50     70.80     0.022454
## 
## 
## Elapsed time : 1.367071

INTC.garch12t.fit

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,2)
## Mean Model   : ARFIMA(2,0,2)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.000000    0.000000 -3.3097e+00 0.000934
## ar1    -0.812940    0.014539 -5.5913e+01 0.000000
## ar2    -0.003265    0.012843 -2.5420e-01 0.799341
## ma1    -0.200464    0.000025 -8.0014e+03 0.000000
## ma2    -0.801609    0.000025 -3.2454e+04 0.000000
## omega   0.000005    0.000001  3.6603e+00 0.000252
## alpha1  0.063283    0.014551  4.3490e+00 0.000014
## beta1   0.581051    0.013767  4.2205e+01 0.000000
## beta2   0.344721    0.012772  2.6989e+01 0.000000
## gamma1  0.005552    0.021024  2.6409e-01 0.791709
## shape   3.924135    0.247646  1.5846e+01 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.000000    0.000001 -5.1105e-01  0.60931
## ar1    -0.812940    0.027381 -2.9690e+01  0.00000
## ar2    -0.003265    0.017564 -1.8588e-01  0.85254
## ma1    -0.200464    0.000059 -3.4099e+03  0.00000
## ma2    -0.801609    0.000121 -6.6131e+03  0.00000
## omega   0.000005    0.000003  1.4877e+00  0.13684
## alpha1  0.063283    0.108512  5.8319e-01  0.55977
## beta1   0.581051    0.011185  5.1950e+01  0.00000
## beta2   0.344721    0.010282  3.3526e+01  0.00000
## gamma1  0.005552    0.162007  3.4271e-02  0.97266
## shape   3.924135    0.361396  1.0858e+01  0.00000
## 
## LogLikelihood : 9158.775 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -5.3700
## Bayes        -5.3502
## Shibata      -5.3700
## Hannan-Quinn -5.3629
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                      0.2149 0.64299
## Lag[2*(p+q)+(p+q)-1][11]    7.2209 0.02652
## Lag[4*(p+q)+(p+q)-1][19]   16.0375 0.01299
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                     0.02078  0.8854
## Lag[2*(p+q)+(p+q)-1][8]    1.18841  0.9593
## Lag[4*(p+q)+(p+q)-1][14]   2.57887  0.9750
## d.o.f=3
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[4]    0.4877 0.500 2.000  0.4850
## ARCH Lag[6]    0.7336 1.461 1.711  0.8250
## ARCH Lag[8]    2.1742 2.368 1.583  0.7063
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  13.063
## Individual Statistics:              
## mu     0.14723
## ar1    0.03030
## ar2    0.03589
## ma1    0.03996
## ma2    0.03876
## omega  1.66128
## alpha1 0.26644
## beta1  0.33400
## beta2  0.33509
## gamma1 0.16202
## shape  0.25961
## 
## 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           0.3525 0.7245    
## Negative Sign Bias  1.0564 0.2909    
## Positive Sign Bias  0.8756 0.3813    
## Joint Effect        2.0423 0.5637    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     24.56       0.1754
## 2    30     27.96       0.5200
## 3    40     43.34       0.2913
## 4    50     50.66       0.4078
## 
## 
## Elapsed time : 1.093254

0.4.4 kiểm định sự phù hợp của mô hình biên

MSFT.res <- residuals(MSFT.garch11t.fit)/sigma(MSFT.garch11t.fit)
fitdist(distribution="std",MSFT.res, control=list())$pars

##           mu        sigma        shape 
## 0.0008340824 1.0003331582 4.7853035512

u <- pdist(distribution="std",q=MSFT.res,mu=0.0008340824, sigma=1.0003331582, shape=4.7853035512)


INTC.res <- residuals(INTC.garch12t.fit)/sigma(INTC.garch12t.fit)
fitdist(distribution="sstd",INTC.res, control=list())$pars

##         mu      sigma       skew      shape 
## -0.0189951  0.9905165  0.9715729  4.0837104

v <- pdist(distribution="sstd", INTC.res, mu=-0.0189951, sigma= 0.9905165, skew= 0.9715729, shape= 4.0837104 )

# Kiểm định Anderson-Darling

library(goftest)
ad.test(u,"punif")

## 
##  Anderson-Darling test of goodness-of-fit
##  Null hypothesis: uniform distribution
##  Parameters assumed to be fixed
## 
## data:  u
## An = 0.68315, p-value = 0.5731

ad.test(v,"punif")

## 
##  Anderson-Darling test of goodness-of-fit
##  Null hypothesis: uniform distribution
##  Parameters assumed to be fixed
## 
## data:  v
## An = 0.25327, p-value = 0.9686

# Kiểm định Cramer-von Mises

cvm.test(u,"punif")

## 
##  Cramer-von Mises test of goodness-of-fit
##  Null hypothesis: uniform distribution
##  Parameters assumed to be fixed
## 
## data:  u
## omega2 = 0.10406, p-value = 0.5654

cvm.test(v, "punif")

## 
##  Cramer-von Mises test of goodness-of-fit
##  Null hypothesis: uniform distribution
##  Parameters assumed to be fixed
## 
## data:  v
## omega2 = 0.030317, p-value = 0.9751

# Kiểm định ks-test

ks.test(u,"punif")

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  u
## D = 0.015542, p-value = 0.3829
## alternative hypothesis: two-sided

ks.test(v, "punif")

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  v
## D = 0.008252, p-value = 0.9745
## alternative hypothesis: two-sided

0.4.5 Ước lượng tham số mô hình copula

library(VineCopula)

## Warning: package 'VineCopula' was built under R version 4.3.3

cop <-BiCopSelect(u,v,familyset=1:9, selectioncrit="AIC", indeptest=FALSE,level=0.05)
summary(cop)

## Family
## ------ 
## No:    2
## Name:  t
## 
## Parameter(s)
## ------------
## par:  0.54
## par2: 5.66
## Dependence measures
## -------------------
## Kendall's tau:    0.36 (empirical = 0.37, p value < 0.01)
## Upper TD:         0.2 
## Lower TD:         0.2 
## 
## Fit statistics
## --------------
## logLik:  593.71 
## AIC:    -1183.42 
## BIC:    -1171.15

Stu <- BiCopEst(u,v,family=9, method="mle", se=T, max.df=10)
summary(Stu)

## Family
## ------ 
## No:    9
## Name:  BB7
## 
## Parameter(s)
## ------------
## par:  1.38  (SE = 0.03)
## par2: 0.6  (SE = 0.04)
## Dependence measures
## -------------------
## Kendall's tau:    0.34 (empirical = 0.37, p value < 0.01)
## Upper TD:         0.35 
## Lower TD:         0.32 
## 
## Fit statistics
## --------------
## logLik:  551.07 
## AIC:    -1098.14 
## BIC:    -1085.88

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