TIỂU LUẬN MÔ HÌNH NGẪU NHIÊN

library(xlsx)
library(moments)
library(tidyverse)

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library(corrplot)

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library(tseries)

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library(FinTS)

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library(ggplot2)
library(rugarch)

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library(kableExtra)

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library(nortest)
library(goftest)

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library(VineCopula)

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library(copula)

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library(png)
library(grid)
library(rgl)

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library(VC2copula)

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dl<- read.xlsx("D:/mhnn/TLMHNN_PHAN NGUYEN QUYNH HUONG.xlsx", sheetIndex = 1, header=T)

THỐNG KÊ MÔ TẢ

# mô tả thống kê VNI
tkmtvni<-dl %>% summarise(Min = min(VNI),
            Max = max(VNI),
            Mean = mean(VNI),
            StDev = sd(VNI),
            Skewness = skewness(VNI),
    Kurtosis = kurtosis(VNI))
tkmtvni

##         Min      Max     Mean      StDev   Skewness Kurtosis
## 1 0.9332556 1.049801 1.000171 0.01295708 -0.8365168 6.474186

# mô tả thống kê SP500 
tkmtsp500<-dl %>% summarise(Min = min(SP500),
            Max = max(SP500),
            Mean = mean(SP500),
            StDev = sd(SP500),
            Skewness = skewness(SP500),
            Kurtosis = kurtosis(SP500))

HỆ SỐ TƯƠNG QUAN

 #Hệ sô tương quan pearson 
cor_pea<- cor(dl[, c("SP500", "VNI")], method = "pearson")
cor_pea

##            SP500        VNI
## SP500  1.0000000 -0.1081054
## VNI   -0.1081054  1.0000000

corrplot(cor_pea, method = "color")

# Hệ sô tương quan spearman
cor_spe<-cor(dl[, c("SP500", "VNI")], method = "spearman")
cor_spe

##             SP500         VNI
## SP500  1.00000000 -0.02876506
## VNI   -0.02876506  1.00000000

corrplot(cor_spe, method = "color")

# Hệ sô tương quan kendall
cor_ken<-cor(dl[, c("SP500", "VNI")], method = "kendall")
cor_ken

##             SP500         VNI
## SP500  1.00000000 -0.01925444
## VNI   -0.01925444  1.00000000

corrplot(cor_ken, method = "color")

# ĐỘ BIẾN ĐỘNG CỦA VNI VÀ S&P500

#độ biến động VNI 
library(ggplot2)
ggplot(dl, aes(x = DATE, y= VNI))+
  geom_line()+
  labs(title = "VNI",x = "Ngày", y="Độ biến động")+
  theme(plot.title = element_text(hjust = 0.5))

#ĐỘ BIẾN ĐỘNG SP500
ggplot(dl, aes(x = DATE, y= SP500))+
  geom_line()+
  labs(title = "SP500",x = "Ngày", y="Độ biến động")+
  theme(plot.title = element_text(hjust = 0.5))

KIỂM ĐỊNH TÍNH DỪNG, PP CHUẨN, Ljung-Box, Box-Pierce

#kiemdinh VNI
adf.test(dl$VNI)

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

## 
##  Augmented Dickey-Fuller Test
## 
## data:  dl$VNI
## Dickey-Fuller = -11.404, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationary

jarque.bera.test(dl$VNI)

## 
##  Jarque Bera Test
## 
## data:  dl$VNI
## X-squared = 902.05, df = 2, p-value < 2.2e-16

Box.test(dl$VNI, lag = 2, type = "Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  dl$VNI
## X-squared = 6.4215, df = 2, p-value = 0.04033

Box.test(dl$VNI, lag = 2, type = "Box-Pierce")

## 
##  Box-Pierce test
## 
## data:  dl$VNI
## X-squared = 6.4064, df = 2, p-value = 0.04063

ArchTest(dl$VNI,lags=2)

## 
##  ARCH LM-test; Null hypothesis: no ARCH effects
## 
## data:  dl$VNI
## Chi-squared = 5.8171, df = 2, p-value = 0.05455

#Kiemdinh SP500
adf.test(dl$SP500)

## Warning in adf.test(dl$SP500): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  dl$SP500
## Dickey-Fuller = -10.167, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationary

jarque.bera.test(dl$SP500)

## 
##  Jarque Bera Test
## 
## data:  dl$SP500
## X-squared = 47179, df = 2, p-value < 2.2e-16

Box.test(dl$SP500, lag = 2, type = "Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  dl$SP500
## X-squared = 17.71, df = 2, p-value = 0.0001427

Box.test(dl$SP500, lag = 2, type = "Box-Pierce")

## 
##  Box-Pierce test
## 
## data:  dl$SP500
## X-squared = 17.665, df = 2, p-value = 0.0001459

ArchTest(dl$SP500,lags=2)

## 
##  ARCH LM-test; Null hypothesis: no ARCH effects
## 
## data:  dl$SP500
## Chi-squared = 20.873, df = 2, p-value = 2.934e-05

ARMA PHÙ HỢP

#ARMA phù hợp VNI
library(rugarch)
autoarfima(dl$VNI,ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")$fit

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(1,0,1)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error   t value Pr(>|t|)
## mu     1.000175    0.000389 2572.1252 0.000000
## ar1    0.675615    0.208862    3.2347 0.001217
## ma1   -0.627524    0.220386   -2.8474 0.004408
## sigma  0.012925    0.000240   53.9630 0.000000
## 
## Robust Standard Errors:
##        Estimate  Std. Error   t value Pr(>|t|)
## mu     1.000175    0.000385 2595.1167 0.000000
## ar1    0.675615    0.226990    2.9764 0.002916
## ma1   -0.627524    0.234055   -2.6811 0.007338
## sigma  0.012925    0.000684   18.9037 0.000000
## 
## LogLikelihood : 4265.557 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -5.8538
## Bayes        -5.8393
## Shibata      -5.8538
## Hannan-Quinn -5.8484
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                  0.0007509  0.9781
## Lag[2*(p+q)+(p+q)-1][5] 0.7958154  1.0000
## Lag[4*(p+q)+(p+q)-1][9] 2.1240024  0.9787
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic   p-value
## Lag[1]                      53.77 2.248e-13
## Lag[2*(p+q)+(p+q)-1][2]     83.41 0.000e+00
## Lag[4*(p+q)+(p+q)-1][5]    149.41 0.000e+00
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF P-Value
## ARCH Lag[2]      94.53   2       0
## ARCH Lag[5]     128.32   5       0
## ARCH Lag[10]    174.91  10       0
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  0.6137
## Individual Statistics:             
## mu    0.07134
## ar1   0.10347
## ma1   0.10280
## sigma 0.34530
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          1.07 1.24 1.6
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.04631495

#ARMA phù hợp SP500
autoarfima(dl$SP500, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")$fit

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(2,0,2)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error   t value Pr(>|t|)
## mu     0.999754    0.000864 1156.5520 0.000000
## ar1    0.000000          NA        NA       NA
## ar2   -0.358874    0.132623   -2.7060 0.006810
## ma1   -0.071841    0.023787   -3.0202 0.002526
## ma2    0.460710    0.123703    3.7243 0.000196
## sigma  0.032273    0.000598   53.9630 0.000000
## 
## Robust Standard Errors:
##        Estimate  Std. Error   t value Pr(>|t|)
## mu     0.999754    0.000865 1156.1541 0.000000
## ar1    0.000000          NA        NA       NA
## ar2   -0.358874    0.186808   -1.9211 0.054721
## ma1   -0.071841    0.045952   -1.5634 0.117966
## ma2    0.460710    0.143299    3.2150 0.001304
## sigma  0.032273    0.002252   14.3311 0.000000
## 
## LogLikelihood : 2933.249 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -4.0223
## Bayes        -4.0042
## Shibata      -4.0223
## Hannan-Quinn -4.0156
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic   p-value
## Lag[1]                      0.1941 0.6594877
## Lag[2*(p+q)+(p+q)-1][11]    8.3596 0.0002115
## Lag[4*(p+q)+(p+q)-1][19]   18.4654 0.0016426
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic   p-value
## Lag[1]                      16.83 4.079e-05
## Lag[2*(p+q)+(p+q)-1][2]     51.60 2.365e-14
## Lag[4*(p+q)+(p+q)-1][5]    106.68 0.000e+00
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF P-Value
## ARCH Lag[2]      79.63   2       0
## ARCH Lag[5]     138.35   5       0
## ARCH Lag[10]    148.66  10       0
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  1.2246
## Individual Statistics:             
## mu    0.23268
## ar2   0.22898
## ma1   0.07026
## ma2   0.24044
## sigma 0.71308
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          1.28 1.47 1.88
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.04935789

GARCH

#GARCH(1,1)_VNI
vni.garch11n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "norm")
vni.garch11n.fit <- ugarchfit(spec = vni.garch11n.spec, data = dl[,2])
show(vni.garch11n.fit )

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(1,0,1)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.000111    0.000672 1487.5039 0.000000
## ar1     0.665137    0.235883    2.8198 0.004806
## ma1    -0.592563    0.232215   -2.5518 0.010717
## omega   0.000009    0.000000   59.7726 0.000000
## alpha1  0.019597    0.007329    2.6738 0.007501
## beta1   0.847365    0.010845   78.1370 0.000000
## gamma1  0.143301    0.025344    5.6542 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error  t value Pr(>|t|)
## mu      1.000111    0.001582 632.3517 0.000000
## ar1     0.665137    0.464942   1.4306 0.152550
## ma1    -0.592563    0.428318  -1.3835 0.166522
## omega   0.000009    0.000000  36.5158 0.000000
## alpha1  0.019597    0.011324   1.7305 0.083540
## beta1   0.847365    0.023408  36.1997 0.000000
## gamma1  0.143301    0.039278   3.6484 0.000264
## 
## LogLikelihood : 4424.805 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -6.0684
## Bayes        -6.0430
## Shibata      -6.0685
## Hannan-Quinn -6.0589
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.2200  0.6391
## Lag[2*(p+q)+(p+q)-1][5]    0.2908  1.0000
## Lag[4*(p+q)+(p+q)-1][9]    0.7027  1.0000
## d.o.f=2
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.0272  0.8690
## Lag[2*(p+q)+(p+q)-1][5]    0.3809  0.9744
## Lag[4*(p+q)+(p+q)-1][9]    1.1996  0.9764
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]    0.4864 0.500 2.000  0.4855
## ARCH Lag[5]    0.6060 1.440 1.667  0.8520
## ARCH Lag[7]    0.8389 2.315 1.543  0.9383
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  28.5762
## Individual Statistics:              
## mu     0.17643
## ar1    0.18842
## ma1    0.18887
## omega  5.25357
## alpha1 0.09718
## beta1  0.08105
## gamma1 0.05971
## 
## 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           0.3841 0.7010    
## Negative Sign Bias  0.3324 0.7396    
## Positive Sign Bias  1.2250 0.2208    
## Joint Effect        4.2623 0.2345    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     111.0    5.324e-15
## 2    30     134.2    1.811e-15
## 3    40     153.6    1.575e-15
## 4    50     162.9    3.795e-14
## 
## 
## Elapsed time : 0.5587609

vni.garch11t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "std") 
vni.garch11t.fit <- ugarchfit(spec = vni.garch11t.spec, data = dl[, 2])
show(vni.garch11t.fit)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(1,0,1)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error  t value Pr(>|t|)
## mu      1.001005    0.001278 783.3167 0.000000
## ar1     0.719397    0.327646   2.1957 0.028117
## ma1    -0.664103    0.311647  -2.1309 0.033093
## omega   0.000013    0.000001  25.5935 0.000000
## alpha1  0.022415    0.046562   0.4814 0.630233
## beta1   0.759282    0.023167  32.7736 0.000000
## gamma1  0.289742    0.087077   3.3274 0.000877
## shape   3.901376    0.452746   8.6171 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error    t value Pr(>|t|)
## mu      1.001005    0.006841 146.314595 0.000000
## ar1     0.719397    1.510334   0.476316 0.633849
## ma1    -0.664103    1.351009  -0.491561 0.623030
## omega   0.000013    0.000001  12.506058 0.000000
## alpha1  0.022415    0.236158   0.094914 0.924383
## beta1   0.759282    0.022827  33.262912 0.000000
## gamma1  0.289742    0.370594   0.781831 0.434314
## shape   3.901376    1.597491   2.442189 0.014598
## 
## LogLikelihood : 4522.391 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -6.2011
## Bayes        -6.1721
## Shibata      -6.2011
## Hannan-Quinn -6.1903
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                    0.02966  0.8633
## Lag[2*(p+q)+(p+q)-1][5]   0.16886  1.0000
## Lag[4*(p+q)+(p+q)-1][9]   0.49349  1.0000
## d.o.f=2
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                      1.036  0.3088
## Lag[2*(p+q)+(p+q)-1][5]     2.117  0.5910
## Lag[4*(p+q)+(p+q)-1][9]     3.054  0.7501
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]     1.166 0.500 2.000  0.2801
## ARCH Lag[5]     1.422 1.440 1.667  0.6129
## ARCH Lag[7]     1.503 2.315 1.543  0.8207
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  41.7646
## Individual Statistics:             
## mu     0.2333
## ar1    0.2087
## ma1    0.1965
## omega  9.0004
## alpha1 0.2084
## beta1  0.2111
## gamma1 0.1748
## shape  0.2109
## 
## 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           0.3019 0.76274    
## Negative Sign Bias  0.8814 0.37823    
## Positive Sign Bias  1.7846 0.07453   *
## Joint Effect        4.0660 0.25443    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     35.84    0.0110412
## 2    30     54.38    0.0029211
## 3    40     73.95    0.0006136
## 4    50     83.77    0.0014496
## 
## 
## Elapsed time : 0.7100089

vni.garch11st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "sstd") 
vni.garch11st.fit <- ugarchfit(spec = vni.garch11st.spec, data = dl[, 2])
show(vni.garch11st.fit)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(1,0,1)
## Distribution : sstd 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.000264    0.000279 3582.3203 0.000000
## ar1     0.930879    0.048835   19.0616 0.000000
## ma1    -0.900299    0.062192  -14.4760 0.000000
## omega   0.000011    0.000000   24.4197 0.000000
## alpha1  0.025853    0.012891    2.0055 0.044912
## beta1   0.792915    0.019233   41.2274 0.000000
## gamma1  0.243466    0.048216    5.0494 0.000000
## skew    0.836503    0.028443   29.4098 0.000000
## shape   4.288637    0.436064    9.8349 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.000264    0.000365 2737.4034 0.000000
## ar1     0.930879    0.060099   15.4892 0.000000
## ma1    -0.900299    0.074218  -12.1305 0.000000
## omega   0.000011    0.000001   18.1466 0.000000
## alpha1  0.025853    0.014215    1.8186 0.068966
## beta1   0.792915    0.017740   44.6973 0.000000
## gamma1  0.243466    0.049432    4.9252 0.000001
## skew    0.836503    0.030467   27.4560 0.000000
## shape   4.288637    0.418969   10.2362 0.000000
## 
## LogLikelihood : 4534.214 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -6.2160
## Bayes        -6.1833
## Shibata      -6.2160
## Hannan-Quinn -6.2038
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                      1.292  0.2557
## Lag[2*(p+q)+(p+q)-1][5]     1.634  0.9945
## Lag[4*(p+q)+(p+q)-1][9]     2.177  0.9758
## d.o.f=2
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.8592  0.3540
## Lag[2*(p+q)+(p+q)-1][5]    1.9570  0.6286
## Lag[4*(p+q)+(p+q)-1][9]    3.0046  0.7582
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]     1.197 0.500 2.000  0.2739
## ARCH Lag[5]     1.496 1.440 1.667  0.5933
## ARCH Lag[7]     1.586 2.315 1.543  0.8040
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  43.2216
## Individual Statistics:              
## mu     0.18228
## ar1    0.18077
## ma1    0.19057
## omega  9.47558
## alpha1 0.16663
## beta1  0.17405
## gamma1 0.11933
## skew   0.09849
## shape  0.15482
## 
## 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           0.5779 0.5634    
## Negative Sign Bias  1.0718 0.2840    
## Positive Sign Bias  1.4164 0.1569    
## Joint Effect        4.3477 0.2263    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     35.70    0.0114765
## 2    30     49.03    0.0114712
## 3    40     62.57    0.0096871
## 4    50     86.38    0.0007833
## 
## 
## Elapsed time : 9.016754

vni.garch11g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "ged") 
vni.garch11g.fit <- ugarchfit(spec = vni.garch11g.spec, data = dl[, 2])
show(vni.garch11g.fit)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(1,0,1)
## Distribution : ged 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.001025    0.000715 1400.1793 0.000000
## ar1     0.909700    0.015946   57.0478 0.000000
## ma1    -0.883610    0.020378  -43.3607 0.000000
## omega   0.000011    0.000000   31.7820 0.000000
## alpha1  0.023010    0.014979    1.5361 0.124513
## beta1   0.794615    0.019142   41.5109 0.000000
## gamma1  0.203300    0.044047    4.6155 0.000004
## shape   1.072843    0.049190   21.8101 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.001025    0.002138 468.20394 0.000000
## ar1     0.909700    0.028486  31.93468 0.000000
## ma1    -0.883610    0.044115 -20.02949 0.000000
## omega   0.000011    0.000000  25.92415 0.000000
## alpha1  0.023010    0.023329   0.98633 0.323970
## beta1   0.794615    0.024818  32.01779 0.000000
## gamma1  0.203300    0.047195   4.30766 0.000016
## shape   1.072843    0.067527  15.88769 0.000000
## 
## LogLikelihood : 4517.522 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -6.1944
## Bayes        -6.1654
## Shibata      -6.1945
## Hannan-Quinn -6.1836
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                      1.171  0.2793
## Lag[2*(p+q)+(p+q)-1][5]     1.520  0.9976
## Lag[4*(p+q)+(p+q)-1][9]     2.022  0.9836
## d.o.f=2
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.5708  0.4500
## Lag[2*(p+q)+(p+q)-1][5]    1.3184  0.7844
## Lag[4*(p+q)+(p+q)-1][9]    2.2034  0.8794
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]    0.9098 0.500 2.000  0.3402
## ARCH Lag[5]    1.0762 1.440 1.667  0.7104
## ARCH Lag[7]    1.1677 2.315 1.543  0.8848
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  37.8862
## Individual Statistics:             
## mu     0.2094
## ar1    0.1819
## ma1    0.2070
## omega  9.4917
## alpha1 0.1882
## beta1  0.1437
## gamma1 0.1369
## shape  0.1316
## 
## 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           0.1435 0.8859    
## Negative Sign Bias  0.4160 0.6775    
## Positive Sign Bias  1.6272 0.1039    
## Joint Effect        3.3146 0.3456    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     49.30    1.659e-04
## 2    30     63.78    2.045e-04
## 3    40     70.54    1.468e-03
## 4    50    113.02    5.715e-07
## 
## 
## Elapsed time : 1.099863

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

#GARCH(1,2)_VNI
vni.garch12n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "norm")
vni.garch12n.fit <- ugarchfit(spec = vni.garch12n.spec, data = dl[,2])

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

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,2)
## Mean Model   : ARFIMA(1,0,1)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.000994    0.001551 645.38452 0.000000
## ar1     0.714380    0.401676   1.77850 0.075322
## ma1    -0.658274    0.379472  -1.73471 0.082792
## omega   0.000014    0.000001  26.13715 0.000000
## alpha1  0.022502    0.087835   0.25619 0.797808
## beta1   0.619948    0.145308   4.26645 0.000020
## beta2   0.120112    0.132297   0.90790 0.363934
## gamma1  0.315382    0.119164   2.64663 0.008130
## shape   3.924783    0.407975   9.62015 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.000994    0.011038 90.685899 0.000000
## ar1     0.714380    2.577869  0.277120 0.781688
## ma1    -0.658274    2.340261 -0.281282 0.778494
## omega   0.000014    0.000004  3.189466 0.001425
## alpha1  0.022502    0.608593  0.036974 0.970506
## beta1   0.619948    0.217627  2.848670 0.004390
## beta2   0.120112    0.195018  0.615899 0.537961
## gamma1  0.315382    0.731983  0.430860 0.666570
## shape   3.924783    1.290143  3.042131 0.002349
## 
## LogLikelihood : 4522.849 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -6.2003
## Bayes        -6.1677
## Shibata      -6.2004
## Hannan-Quinn -6.1882
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                    0.02483  0.8748
## Lag[2*(p+q)+(p+q)-1][5]   0.16530  1.0000
## Lag[4*(p+q)+(p+q)-1][9]   0.48293  1.0000
## d.o.f=2
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                       1.297  0.2547
## Lag[2*(p+q)+(p+q)-1][8]      2.766  0.7283
## Lag[4*(p+q)+(p+q)-1][14]     5.888  0.6538
## d.o.f=3
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[4]    0.2477 0.500 2.000  0.6187
## ARCH Lag[6]    0.3187 1.461 1.711  0.9405
## ARCH Lag[8]    1.4749 2.368 1.583  0.8443
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  40.177
## Individual Statistics:             
## mu     0.2387
## ar1    0.2067
## ma1    0.1955
## omega  5.3938
## alpha1 0.2016
## beta1  0.1989
## beta2  0.2089
## gamma1 0.1709
## shape  0.2124
## 
## 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           0.3345 0.73808    
## Negative Sign Bias  0.9959 0.31946    
## Positive Sign Bias  1.7746 0.07618   *
## Joint Effect        4.1810 0.24257    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     37.21    0.0074593
## 2    30     63.45    0.0002256
## 3    40     73.78    0.0006406
## 4    50     88.23    0.0005000
## 
## 
## Elapsed time : 0.799232

 vni.garch12st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch12st.fit <- ugarchfit(spec = vni.garch12st.spec, data = dl[, 2])
 
 vni.garch12g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "ged") 
 vni.garch12g.fit <- ugarchfit(spec = vni.garch12g.spec, data = dl[, 2])
 
 vni.garch12sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "sged")
 vni.garch12sg.fit <- ugarchfit(spec = vni.garch12sg.spec, data = dl[, 2])
 
 #GARCH(2.1)_VNI
 vni.garch21n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.mode
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "norm")
vni.garch21n.fit <- ugarchfit(spec = vni.garch21n.spec, data = dl[,2])

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

 vni.garch21st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch21st.fit <- ugarchfit(spec = vni.garch21st.spec, data = dl[, 2])
 
vni.garch21g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "ged") 
 vni.garch21g.fit <- ugarchfit(spec = vni.garch21g.spec, data = dl[, 2])
 
 vni.garch21sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "sged") 
 vni.garch21sg.fit <- ugarchfit(spec = vni.garch21sg.spec, data = dl[, 2])
 
 #GARCH(2,2)_VNI
vni.garch22n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "norm")
 vni.garch22n.fit <- ugarchfit(spec = vni.garch22n.spec, data = dl[,2])
 vni.garch22t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "std") 
vni.garch22t.fit <- ugarchfit(spec = vni.garch22t.spec, data = dl[, 2])
 
 vni.garch22st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch22st.fit <- ugarchfit(spec = vni.garch22st.spec, data = dl[, 2])
 
 vni.garch22g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "ged") 
vni.garch22g.fit <- ugarchfit(spec = vni.garch22g.spec, data = dl[, 2])

 vni.garch22sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(1, 1), include.mean = TRUE), distribution.model = "sged") 
 vni.garch22sg.fit <- ugarchfit(spec = vni.garch22sg.spec, data = dl[, 2])

# Các dạng MH GJR-GARCH cho chuỗi sp500
## GJR-GARCH(11)SP500
sp500.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")
sp500.garch11n.fit <- ugarchfit(spec = sp500.garch11n.spec, data = dl[,3])

sp500.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") 
 sp500.garch11t.fit <- ugarchfit(spec =sp500.garch11t.spec, data = dl[, 3])
 
 sp500.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") 
sp500.garch11st.fit <- ugarchfit(spec = sp500.garch11st.spec, data = dl[, 3])
 
 sp500.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") 
 sp500.garch11g.fit <- ugarchfit(spec =sp500.garch11g.spec, data = dl[, 3])

 sp500.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") 
 sp500.garch11sg.fit <- ugarchfit(spec = sp500.garch11sg.spec, data = dl[, 3])
## GJR-GARCH(12)sp500
 sp500.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")
 sp500.garch12n.fit <- ugarchfit(spec = sp500.garch12n.spec, data = dl[,3])
 
sp500.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") 
sp500.garch12t.fit <- ugarchfit(spec = sp500.garch12t.spec, data = dl[, 3])
 
sp500.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") 
sp500.garch12st.fit <- ugarchfit(spec = sp500.garch12st.spec, data = dl[, 3])
 
sp500.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") 
sp500.garch12g.fit <- ugarchfit(spec = sp500.garch12g.spec, data = dl[, 3])
 

sp500.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") 
sp500.garch12sg.fit <- ugarchfit(spec = sp500.garch12sg.spec, data = dl[, 3])
## GJR-GARCH(21)sp500
sp500.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")
sp500.garch21n.fit <- ugarchfit(spec = sp500.garch21n.spec, data = dl[, 3])

sp500.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") 
sp500.garch21t.fit <- ugarchfit(spec = sp500.garch21t.spec, data = dl[, 3])

sp500.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") 
sp500.garch21st.fit <- ugarchfit(spec = sp500.garch21st.spec, data = dl[, 3])

sp500.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") 
sp500.garch21g.fit <- ugarchfit(spec =sp500.garch21g.spec, data = dl[, 3])

sp500.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") 
sp500.garch21sg.fit <- ugarchfit(spec = sp500.garch21sg.spec, data = dl[, 3])
## GJR-GARCH(22)SP500
sp500.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")
sp500.garch22n.fit <- ugarchfit(spec = sp500.garch22n.spec, data = dl[, 3])

sp500.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") 
sp500.garch22t.fit <- ugarchfit(spec = sp500.garch22t.spec, data = dl[, 3])

sp500.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") 
sp500.garch22st.fit <- ugarchfit(spec = sp500.garch22st.spec, data = dl[, 3])

sp500.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") 
sp500.garch22g.fit <- ugarchfit(spec = sp500.garch22g.spec, data = dl[, 3])

sp500.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") 
sp500.garch22sg.fit <- ugarchfit(spec =sp500.garch22sg.spec, data = dl[, 3])

LỰA CHỌN MÔ HÌNH BIÊN PHÙ HỢP

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

vni.info.mat <- sapply(vni.model.list, infocriteria)
rownames(vni.info.mat) <- rownames(infocriteria(vni.garch11n.fit))
 vni.info.mat

##               garch11n  garch11t garch11st  garch11g garch11sg  garch12n
## Akaike       -6.068413 -6.201087 -6.215953 -6.194398 -6.211257 -6.068398
## Bayes        -6.043012 -6.172057 -6.183295 -6.165368 -6.178598 -6.039368
## Shibata      -6.068459 -6.201147 -6.216029 -6.194458 -6.211332 -6.068458
## Hannan-Quinn -6.058936 -6.190256 -6.203769 -6.183567 -6.199072 -6.057567
##               garch12t garch12st  garch12g garch12sg  garch21n  garch21t
## Akaike       -6.200342 -6.215487 -6.193576 -6.210640 -6.073841 -6.201058
## Bayes        -6.167683 -6.179200 -6.160917 -6.174352 -6.041182 -6.164770
## Shibata      -6.200418 -6.215581 -6.193651 -6.210733 -6.073917 -6.201151
## Hannan-Quinn -6.188157 -6.201949 -6.181391 -6.197101 -6.061656 -6.187519
##              garch21st  garch21g garch21sg  garch22n  garch22t garch22st
## Akaike       -6.215822 -6.194634 -6.211688 -6.072468 -6.199684 -6.214448
## Bayes        -6.175905 -6.158347 -6.171772 -6.036180 -6.159768 -6.170903
## Shibata      -6.215935 -6.194727 -6.211801 -6.072561 -6.199797 -6.214582
## Hannan-Quinn -6.200929 -6.181095 -6.196796 -6.058929 -6.184792 -6.198202
##               garch22g garch22sg
## Akaike       -6.193260 -6.210314
## Bayes        -6.153344 -6.166769
## Shibata      -6.193373 -6.210449
## Hannan-Quinn -6.178368 -6.194068

 vni.inds <- which(vni.info.mat == min(vni.info.mat), arr.ind=TRUE)
model.vni <- colnames(vni.info.mat)[vni.inds[,2]]
 model.vni

## [1] "garch11st"

# Lựa chọn mô hình biên phù hợp nhất cho chuỗi sp500
sp500.model.list <- list(garch11n = sp500.garch11n.fit, garch11t = sp500.garch11t.fit, garch11st = 
sp500.garch11st.fit, garch11g = sp500.garch11g.fit, garch11sg = sp500.garch11sg.fit,
garch12n = sp500.garch12n.fit, garch12t = sp500.garch12t.fit, garch12st = sp500.garch12st.fit, 
garch12g = sp500.garch12g.fit, garch12sg = sp500.garch12sg.fit,
garch21n = sp500.garch21n.fit, garch21t = sp500.garch21t.fit, garch21st = sp500.garch21st.fit, 
garch21g = sp500.garch21g.fit, garch21sg = sp500.garch21sg.fit,
garch22n = sp500.garch22n.fit, garch22t =sp500.garch22t.fit, garch22st = sp500.garch22st.fit, 
garch22g = sp500.garch22g.fit, garch22sg = sp500.garch22sg.fit)
 sp500.info.mat <- sapply(sp500.model.list, infocriteria) 
 rownames(sp500.info.mat) <- rownames(infocriteria(sp500.garch11n.fit))
 sp500.info.mat

##               garch11n  garch11t garch11st  garch11g garch11sg  garch12n
## Akaike       -4.531249 -4.685160 -4.750474 -4.649937 -4.731633 -4.531520
## Bayes        -4.498590 -4.648873 -4.710558 -4.613649 -4.691717 -4.495233
## Shibata      -4.531325 -4.685253 -4.750587 -4.650030 -4.731746 -4.531614
## Hannan-Quinn -4.519064 -4.671621 -4.735582 -4.636398 -4.716740 -4.517982
##               garch12t garch12st  garch12g garch12sg  garch21n  garch21t
## Akaike       -4.683226 -4.749101 -4.648563 -4.728687 -4.533647 -4.686150
## Bayes        -4.643310 -4.705556 -4.608647 -4.685142 -4.493731 -4.642605
## Shibata      -4.683339 -4.749235 -4.648676 -4.728822 -4.533760 -4.686284
## Hannan-Quinn -4.668334 -4.732854 -4.633671 -4.712441 -4.518755 -4.669904
##              garch21st  garch21g garch21sg  garch22n  garch22t garch22st
## Akaike       -4.751333 -4.650871 -4.732770 -4.536538 -4.685296 -4.749960
## Bayes        -4.704160 -4.607327 -4.685596 -4.492993 -4.638123 -4.699157
## Shibata      -4.751491 -4.651006 -4.732927 -4.536672 -4.685454 -4.750142
## Hannan-Quinn -4.733733 -4.634625 -4.715170 -4.520291 -4.667696 -4.731006
##               garch22g garch22sg
## Akaike       -4.649655 -4.731396
## Bayes        -4.602482 -4.680594
## Shibata      -4.649813 -4.731579
## Hannan-Quinn -4.632055 -4.712442

sp500.inds <- which(sp500.info.mat == min(sp500.info.mat), arr.ind = TRUE)
 model.sp500 <- colnames(sp500.info.mat)[sp500.inds[,2]]
 model.sp500

## [1] "garch21st"

#ƯỚC LƯỢNG MÔ HÌNH BIẾN

### THAM SỐ ƯỚC LƯỢNG MÔ HÌNH BIÊN PHÙ HỢP NHẤT:
extract_garch_results <- function(fit) {
  coef <- coef(fit)
  se <- fit@fit$se.coef
  pvalues <- 2 * (1 - pnorm(abs(fit@fit$tval))) # tính giá trị p từ giá trị t
  results <- cbind(coef, se, pvalues)
  colnames(results) <- c("Estimate", "Std. Error", "Pr(>|z|)")
  return(results)
}
library(kableExtra)
fit1 <- extract_garch_results(vni.garch11st.fit)
kable(as.data.frame(fit1), 
  caption = "Bảng 5: Kết quả mô hình ARMA(1,1)-GJR-Garch(1,1)-Skewed Student của biến VNI", 
  format = 'pandoc') %>% kable_styling(
            bootstrap_options = c("striped", "hover", "condensed"), 
            full_width = F)

## Warning in kable_styling(., bootstrap_options = c("striped", "hover",
## "condensed"), : Please specify format in kable. kableExtra can customize either
## HTML or LaTeX outputs. See https://haozhu233.github.io/kableExtra/ for details.

Bảng 5: Kết quả mô hình ARMA(1,1)-GJR-Garch(1,1)-Skewed Student của biến VNI

	Estimate	Std. Error	Pr(>|z|)
mu	1.0002636	0.0002792	0.0000000
ar1	0.9308793	0.0488353	0.0000000
ma1	-0.9002987	0.0621923	0.0000000
omega	0.0000105	0.0000004	0.0000000
alpha1	0.0258526	0.0128910	0.0449120
beta1	0.7929153	0.0192327	0.0000000
gamma1	0.2434658	0.0482163	0.0000004
skew	0.8365026	0.0284430	0.0000000
shape	4.2886371	0.4360637	0.0000000

extract_garch_results <- function(fit) {
  coef <- coef(fit)
  se <- fit@fit$se.coef
  pvalues <- 2 * (1 - pnorm(abs(fit@fit$tval))) # tính giá trị p từ giá trị t
  results <- cbind(coef, se, pvalues)
  colnames(results) <- c("Estimate", "Std. Error", "Pr(>|z|)")
  return(results)
}

fit1 <- extract_garch_results(sp500.garch21st.fit)
kable(as.data.frame(fit1), 
  caption = "Bảng 5: Kết quả mô hình ARMA(2,2)-GJR-Garch(2,1)-Skewed Student của biến VNI", 
  format = 'pandoc') %>% kable_styling(
            bootstrap_options = c("striped", "hover", "condensed"), 
            full_width = F)

## Warning in kable_styling(., bootstrap_options = c("striped", "hover",
## "condensed"), : Please specify format in kable. kableExtra can customize either
## HTML or LaTeX outputs. See https://haozhu233.github.io/kableExtra/ for details.

Bảng 5: Kết quả mô hình ARMA(2,2)-GJR-Garch(2,1)-Skewed Student của biến VNI

	Estimate	Std. Error	Pr(>|z|)
mu	0.9993791	0.0003429	0.0000000
ar1	0.3678745	0.0576473	0.0000000
ar2	0.5546145	0.0309664	0.0000000
ma1	-0.4093224	0.0582344	0.0000000
ma2	-0.5373071	0.0415071	0.0000000
omega	0.0000811	0.0000144	0.0000000
alpha1	0.1782402	0.0538989	0.0009432
alpha2	0.1437518	0.0652052	0.0274817
beta1	0.6761241	0.0394507	0.0000000
gamma1	0.0042258	0.0860512	0.9608331
gamma2	-0.2101218	0.0770761	0.0064076
skew	1.4546350	0.0520990	0.0000000
shape	4.8257809	0.5920977	0.0000000
# KIỂM ĐỊ	NH SỰ PHÙ HỢP	CỦA MÔ HÌNH	BIÊN

## Trích xuất chuỗi phần dư v của chuỗi lợi suất S&P500
sp500.res <- residuals(sp500.garch21st.fit)/sigma(sp500.garch21st.fit)
fitdist(distribution = "sstd", sp500.res, control = list())$pars

##          mu       sigma        skew       shape 
## 0.007560442 0.999048157 1.460140356 4.891704011

v <- pdist(distribution = "sstd", q = sp500.res, mu =0.007560442 , sigma = 0.999048157, skew = 1.460140356, shape = 4.891704011 )

## Trích xuất chuỗi phần dư u của chuỗi lợi suất VNI
vni.res <- residuals(vni.garch11st.fit)/sigma(vni.garch11st.fit)
fitdist(distribution = "sstd", vni.res, control = list())$pars

##           mu        sigma         skew        shape 
## -0.001894329  1.004416729  0.835631546  4.249451143

u = pdist(distribution ="sstd",vni.res, mu = -0.001894329   , sigma =1.004416729 , skew =0.835631546  , shape = 4.249451143  )

### Các kiểm định sự phù hợp của mô hình biên:
 # Kiem dinh Anderson-Darling
library(nortest)
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 = 0.80976, p-value = 0.474

 ad.test(v, "punif")

## 
##  Anderson-Darling test of goodness-of-fit
##  Null hypothesis: uniform distribution
##  Parameters assumed to be fixed
## 
## data:  v
## An = 0.17138, p-value = 0.9963

 cvm.test(u, "punif")

## 
##  Cramer-von Mises test of goodness-of-fit
##  Null hypothesis: uniform distribution
##  Parameters assumed to be fixed
## 
## data:  u
## omega2 = 0.15514, p-value = 0.3743

cvm.test(v, "punif")

## 
##  Cramer-von Mises test of goodness-of-fit
##  Null hypothesis: uniform distribution
##  Parameters assumed to be fixed
## 
## data:  v
## omega2 = 0.018096, p-value = 0.9984

# Kiem dinh ks-test
ks.test(u, "punif")

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  u
## D = 0.030072, p-value = 0.1436
## alternative hypothesis: two-sided

 ks.test(v, "punif")

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  v
## D = 0.010015, p-value = 0.9986
## alternative hypothesis: two-sided

#Ước lượng
library(VineCopula)
gau <- BiCopEst(u,v,family = 1, method = "mle", se = T, max.df = 10)
stu <- BiCopEst(u,v,family = 2, method = "mle", se = T, max.df = 10)
#Trình bày kết quả

est <- data.frame(mqh = c('VNI-SP500' ,'VNI-SP500'),
                    Copula = c('Gauss', 'Student'),
                    Thamso = c(gau$par, stu$par),
                  Thamso2 = c(gau$par2, stu$par2),
                   duoi = c(gau$taildep$lower,stu$taildep$lower))

kable(est, caption = "Bảng 8: Kết quả ước lượng Copula họ Elip", col.names = c("Chỉ số","Copula", "Par","Par2", "Phụ thuộc đuôi"), 
  format = 'pandoc') %>% kable_styling(
            bootstrap_options = c("striped", "hover", "condensed"), 
            full_width = F)

## Warning in kable_styling(., bootstrap_options = c("striped", "hover",
## "condensed"), : Please specify format in kable. kableExtra can customize either
## HTML or LaTeX outputs. See https://haozhu233.github.io/kableExtra/ for details.

Bảng 8: Kết quả ước lượng Copula họ Elip

Chỉ số	Copula	Par	Par2	Phụ thuộc đuôi
VNI-SP500	Gauss	-0.0773425	0	0.0000000
VNI-SP500	Student	-0.0610718	10	0.0047501

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

## Family
## ------ 
## No:    26
## Name:  Rotated Joe 90 degrees
## 
## Parameter(s)
## ------------
## par:  -1.07
## 
## Dependence measures
## -------------------
## Kendall's tau:    -0.04 (empirical = -0.03, p value = 0.05)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  10.52 
## AIC:    -19.03 
## BIC:    -13.75

 Stu <- BiCopEst(u, v, family = 36, method = "mle", se = T, max.df = 10)
summary(Stu)

## Family
## ------ 
## No:    36
## Name:  Rotated Joe 270 degrees
## 
## Parameter(s)
## ------------
## par:  -1.02  (SE = 0.01)
## 
## Dependence measures
## -------------------
## Kendall's tau:    -0.01 (empirical = -0.03, p value = 0.05)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  0.33 
## AIC:    1.34 
## BIC:    6.63

#Lựa chọn và ước lượng
opt_cop <- BiCopSelect(u,v,selectioncrit = "AIC",method = "mle")
est_opt_cop <- BiCopEst(u,v,family = opt_cop$family,method = "mle",max.df = 30)

#Trình bày kết quả
est_opt_cop_dt <- data.frame(mqh = c('VNI-Sp500'),
                    Copula = est_opt_cop$familyname,
                    Thamso = est_opt_cop$par,
                  Thamso2 = est_opt_cop$par2,
                   duoiduoi = est_opt_cop$taildep$lower,
                  duoitren = est_opt_cop$taildep$upper,
                  tau = est_opt_cop$tau,
                  aic = est_opt_cop$AIC,
                  bic = est_opt_cop$BIC)

kable(est_opt_cop_dt, 
  caption = "Bảng 9: Kết quả ước lượng mô hình Copula tối ưu", col.names = c("Chỉ số","Copula", "Par","Par2", "Đuôi dưới", "Đuôi trên","Hệ số Kendall", "AIC","BIC"), 
  format = 'pandoc') %>% kable_styling(
            bootstrap_options = c("striped", "hover", "condensed"), 
            full_width = F)

## Warning in kable_styling(., bootstrap_options = c("striped", "hover",
## "condensed"), : Please specify format in kable. kableExtra can customize either
## HTML or LaTeX outputs. See https://haozhu233.github.io/kableExtra/ for details.

Bảng 9: Kết quả ước lượng mô hình Copula tối ưu

Chỉ số	Copula	Par	Par2	Đuôi dưới	Đuôi trên	Hệ số Kendall	AIC	BIC
VNI-Sp500	Rotated Joe 90 degrees	-1.066832	0	0	0	-0.0371115	-19.03345	-13.75001
# VẼ ĐỒ THÌ	PDF

library(copula)
library(png)
library(grid)
library(rgl)
library(VineCopula) 
opt_cop <- BiCopSelect(u,v,selectioncrit = "AIC",method = "mle")
est_opt_cop <- BiCopEst(u,v,family = opt_cop$family,method = "mle",max.df = 30)

#Trình bày kết quả
est_opt_cop_dt <- data.frame(mqh = c('VNI-SP500'),
                    Copula = est_opt_cop$familyname,
                    Thamso = est_opt_cop$par,
                  Thamso2 = est_opt_cop$par2,
                   duoiduoi = est_opt_cop$taildep$lower,
                  duoitren = est_opt_cop$taildep$upper,
                  tau = est_opt_cop$tau,
                  aic = est_opt_cop$AIC,
                  bic = est_opt_cop$BIC)

kable(est_opt_cop_dt, 
  caption = "Bảng : Kết quả ước lượng mô hình Copula tối ưu", col.names = c("Chỉ số","Copula", "Par","Par2", "Đuôi dưới", "Đuôi trên","Hệ số Kendall", "AIC","BIC"), 
  format = 'html') %>% kable_styling(
            bootstrap_options = c("striped", "hover", "condensed"), 
            full_width = F)

Bảng : Kết quả ước lượng mô hình Copula tối ưu

Chỉ số	Copula	Par	Par2	Đuôi dưới	Đuôi trên	Hệ số Kendall	AIC	BIC
VNI-SP500	Rotated Joe 90 degrees	-1.066832	0	0	0	-0.0371115	-19.03345	-13.75001

library(VC2copula)
copula <- r270JoeBiCopula(param = est_opt_cop$par)
# Sử dụng hàm persp để vẽ đồ thị 3D
persp(copula, dCopula, xlab = "u", ylab = "v",
      main = "Đồ thị PDF của mô hình Rotated Joe 90 degrees", 
      col = "pink")

# VNI VÀ S&P500 TRONG 3 GIAI ĐOẠN

#Trích dữ liệu
library(xts)

## 
## ######################### Warning from 'xts' package ##########################
## #                                                                             #
## # The dplyr lag() function breaks how base R's lag() function is supposed to  #
## # work, which breaks lag(my_xts). Calls to lag(my_xts) that you type or       #
## # source() into this session won't work correctly.                            #
## #                                                                             #
## # Use stats::lag() to make sure you're not using dplyr::lag(), or you can add #
## # conflictRules('dplyr', exclude = 'lag') to your .Rprofile to stop           #
## # dplyr from breaking base R's lag() function.                                #
## #                                                                             #
## # Code in packages is not affected. It's protected by R's namespace mechanism #
## # Set `options(xts.warn_dplyr_breaks_lag = FALSE)` to suppress this warning.  #
## #                                                                             #
## ###############################################################################

## 
## Attaching package: 'xts'

## The following objects are masked from 'package:dplyr':
## 
##     first, last

library(xlsx)
a1<- read.xlsx("D:/mhnn/vni.xlsx", sheetIndex=1, header=T)
a2<- read.xlsx("D:/mhnn/sp500.xlsx", sheetIndex=1, header=T)
vni<- xts(a1[,-1], order.by = a1$DATE)

sp500<-xts(a2[,-1], order.by = a2$DATE)

dlt <- merge.xts(vni,sp500,join = 'inner')
truoccov<- dlt["2018-01-03/2019-12-31"]
cov<- dlt["2020-01-02/2021-12-31"]
saucov<- dlt["2022-01-04/2023-12-29"]

ARMA

#arma vni trước covid 
armavnitruoc<-autoarfima(truoccov$vni, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")$fit

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

armavnitruoc

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(2,0,0)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error   t value Pr(>|t|)
## mu     1.000101    0.000561 1783.5809 0.000000
## ar1    0.000000          NA        NA       NA
## ar2    0.133571    0.045103    2.9615 0.003062
## sigma  0.010684    0.000344   31.0806 0.000000
## 
## Robust Standard Errors:
##        Estimate  Std. Error   t value Pr(>|t|)
## mu     1.000101    0.000560 1784.8187 0.000000
## ar1    0.000000          NA        NA       NA
## ar2    0.133571    0.062105    2.1507 0.031497
## sigma  0.010684    0.000518   20.6146 0.000000
## 
## LogLikelihood : 1506.978 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -6.2277
## Bayes        -6.2017
## Shibata      -6.2277
## Hannan-Quinn -6.2175
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                      0.209  0.6475
## Lag[2*(p+q)+(p+q)-1][5]     1.744  0.9889
## Lag[4*(p+q)+(p+q)-1][9]     3.987  0.6941
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic   p-value
## Lag[1]                      18.63 1.583e-05
## Lag[2*(p+q)+(p+q)-1][2]     27.20 5.750e-08
## Lag[4*(p+q)+(p+q)-1][5]     43.86 3.642e-12
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF   P-Value
## ARCH Lag[2]      29.61   2 3.711e-07
## ARCH Lag[5]      37.43   5 4.908e-07
## ARCH Lag[10]     47.21  10 8.630e-07
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  5.2943
## Individual Statistics:             
## mu    0.07554
## ar2   0.10260
## sigma 4.72074
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          0.846 1.01 1.35
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.01867199

# arma vni trong covid

armavnitrong<-autoarfima(cov$vni, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")$fit

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

armavnitrong

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(2,0,2)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error    t value Pr(>|t|)
## mu     1.001286    0.000636  1575.0229 0.000000
## ar1   -0.063999    0.020774    -3.0808 0.002065
## ar2   -0.929639    0.003559  -261.2181 0.000000
## ma1    0.069458    0.006531    10.6345 0.000000
## ma2    0.994114    0.000019 51817.5202 0.000000
## sigma  0.013526    0.000429    31.5177 0.000000
## 
## Robust Standard Errors:
##        Estimate  Std. Error    t value Pr(>|t|)
## mu     1.001286    0.000687  1456.4430 0.000000
## ar1   -0.063999    0.020313    -3.1507 0.001629
## ar2   -0.929639    0.007299  -127.3658 0.000000
## ma1    0.069458    0.006544    10.6141 0.000000
## ma2    0.994114    0.000023 43296.5530 0.000000
## sigma  0.013526    0.001215    11.1355 0.000000
## 
## LogLikelihood : 1398.834 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -5.7436
## Bayes        -5.6919
## Shibata      -5.7439
## Hannan-Quinn -5.7233
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic   p-value
## Lag[1]                       1.717 1.901e-01
## Lag[2*(p+q)+(p+q)-1][11]    11.274 9.418e-13
## Lag[4*(p+q)+(p+q)-1][19]    19.662 5.389e-04
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic   p-value
## Lag[1]                      21.86 2.933e-06
## Lag[2*(p+q)+(p+q)-1][2]     30.45 8.074e-09
## Lag[4*(p+q)+(p+q)-1][5]     47.73 2.838e-13
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF   P-Value
## ARCH Lag[2]      31.92   2 1.174e-07
## ARCH Lag[5]      43.30   5 3.212e-08
## ARCH Lag[10]     62.56  10 1.187e-09
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  1.1756
## Individual Statistics:             
## mu    0.10942
## ar1   0.01744
## ar2   0.06746
## ma1   0.06375
## ma2   0.07320
## sigma 0.69665
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          1.49 1.68 2.12
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.05071211

# arma vni sau covid
armavnisau<-autoarfima(saucov$vni, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")$fit

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

armavnisau

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(0,0,1)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error   t value Pr(>|t|)
## mu     0.999511    0.000646 1546.2723  0.00000
## ma1    0.055539    0.048034    1.1563  0.24757
## sigma  0.013474    0.000435   30.9999  0.00000
## 
## Robust Standard Errors:
##        Estimate  Std. Error   t value Pr(>|t|)
## mu     0.999511    0.000637 1569.7906  0.00000
## ma1    0.055539    0.049075    1.1317  0.25775
## sigma  0.013474    0.000928   14.5203  0.00000
## 
## LogLikelihood : 1398.987 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -5.7685
## Bayes        -5.7426
## Shibata      -5.7686
## Hannan-Quinn -5.7584
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                   0.003832  0.9506
## Lag[2*(p+q)+(p+q)-1][2]  0.612223  0.9316
## Lag[4*(p+q)+(p+q)-1][5]  1.152468  0.9215
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic   p-value
## Lag[1]                      8.282 4.004e-03
## Lag[2*(p+q)+(p+q)-1][2]    11.857 6.180e-04
## Lag[4*(p+q)+(p+q)-1][5]    31.909 9.155e-09
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF   P-Value
## ARCH Lag[2]      13.58   2 1.123e-03
## ARCH Lag[5]      35.32   5 1.298e-06
## ARCH Lag[10]     47.38  10 8.046e-07
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  0.9941
## Individual Statistics:             
## mu    0.19239
## ma1   0.03409
## sigma 0.90587
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          0.846 1.01 1.35
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.01100612

# arma sp500 trước covid
armasp500truoc<-autoarfima(truoccov$sp500, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")$fit

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

armasp500truoc

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(2,0,2)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error  t value Pr(>|t|)
## mu     0.999218    0.001032 967.9819 0.000000
## ar1   -0.124133    0.039990  -3.1041 0.001909
## ar2   -0.619908    0.152804  -4.0569 0.000050
## ma1    0.000000          NA       NA       NA
## ma2    0.595930    0.160142   3.7212 0.000198
## sigma  0.024787    0.000798  31.0805 0.000000
## 
## Robust Standard Errors:
##        Estimate  Std. Error  t value Pr(>|t|)
## mu     0.999218    0.001034 966.1085 0.000000
## ar1   -0.124133    0.061917  -2.0048 0.044982
## ar2   -0.619908    0.141907  -4.3684 0.000013
## ma1    0.000000          NA       NA       NA
## ma2    0.595930    0.146334   4.0724 0.000047
## sigma  0.024787    0.001319  18.7885 0.000000
## 
## LogLikelihood : 1100.517 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -4.5363
## Bayes        -4.4930
## Shibata      -4.5365
## Hannan-Quinn -4.5193
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                     0.04199  0.8376
## Lag[2*(p+q)+(p+q)-1][11]   2.55172  1.0000
## Lag[4*(p+q)+(p+q)-1][19]   4.88224  0.9954
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic   p-value
## Lag[1]                      19.59 9.582e-06
## Lag[2*(p+q)+(p+q)-1][2]     34.81 5.855e-10
## Lag[4*(p+q)+(p+q)-1][5]     62.24 0.000e+00
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF   P-Value
## ARCH Lag[2]      41.41   2 1.021e-09
## ARCH Lag[5]      52.75   5 3.792e-10
## ARCH Lag[10]     66.21  10 2.373e-10
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  0.5344
## Individual Statistics:             
## mu    0.05408
## ar1   0.05007
## ar2   0.08869
## ma2   0.08351
## sigma 0.19840
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          1.28 1.47 1.88
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.05162501

# arma sp500 trong covid
armasp500trong<-autoarfima(cov$sp500, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")$fit

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

armasp500trong

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(2,0,2)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error  t value Pr(>|t|)
## mu     0.999052    0.001566 638.1659 0.000000
## ar1   -0.080077    0.042141  -1.9002 0.057405
## ar2   -0.594859    0.166990  -3.5623 0.000368
## ma1    0.000000          NA       NA       NA
## ma2    0.665224    0.164120   4.0533 0.000051
## sigma  0.034677    0.001113  31.1448 0.000000
## 
## Robust Standard Errors:
##        Estimate  Std. Error  t value Pr(>|t|)
## mu     0.999052    0.001568 637.0412 0.000000
## ar1   -0.080077    0.072115  -1.1104 0.266825
## ar2   -0.594859    0.227923  -2.6099 0.009057
## ma1    0.000000          NA       NA       NA
## ma2    0.665224    0.236606   2.8115 0.004931
## sigma  0.034677    0.002435  14.2430 0.000000
## 
## LogLikelihood : 942.2264 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -3.8649
## Bayes        -3.8217
## Shibata      -3.8651
## Hannan-Quinn -3.8479
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic   p-value
## Lag[1]                       0.457 4.990e-01
## Lag[2*(p+q)+(p+q)-1][11]    10.511 3.113e-10
## Lag[4*(p+q)+(p+q)-1][19]    20.072 3.631e-04
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic   p-value
## Lag[1]                      19.74 8.884e-06
## Lag[2*(p+q)+(p+q)-1][2]     27.59 4.531e-08
## Lag[4*(p+q)+(p+q)-1][5]    119.37 0.000e+00
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF   P-Value
## ARCH Lag[2]      29.24   2 4.476e-07
## ARCH Lag[5]     132.15   5 0.000e+00
## ARCH Lag[10]    163.47  10 0.000e+00
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  2.8091
## Individual Statistics:             
## mu    0.16322
## ar1   0.06762
## ar2   0.02967
## ma2   0.03045
## sigma 2.17161
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          1.28 1.47 1.88
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.05019999

# arma sp500 sau covid
armasp500sau<-autoarfima(saucov$sp500, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")$fit

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

## Warning in .makearfimafitmodel(f = .arfimaLLH, T = T, m = m, timer = timer, : 
## rugarch-->warning: failed to invert hessian

armasp500sau

## 
## *----------------------------------*
## *          ARFIMA Model Fit        *
## *----------------------------------*
## Mean Model   : ARFIMA(2,0,2)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##        Estimate  Std. Error  t value Pr(>|t|)
## mu     1.000875    0.000011  89308.7        0
## ar1    0.190450    0.000709    268.8        0
## ar2    0.789596    0.000079   9953.1        0
## ma1   -0.253558    0.000009 -27505.0        0
## ma2   -0.776267    0.000038 -20457.9        0
## sigma  0.024187    0.000015   1635.8        0
## 
## Robust Standard Errors:
##        Estimate  Std. Error    t value Pr(>|t|)
## mu     1.000875    0.000148  6779.3135 0.000000
## ar1    0.190450    0.027189     7.0046 0.000000
## ar2    0.789596    0.004428   178.3074 0.000000
## ma1   -0.253558    0.000222 -1140.8922 0.000000
## ma2   -0.776267    0.000729 -1064.8297 0.000000
## sigma  0.024187    0.007321     3.3038 0.000954
## 
## LogLikelihood : 1115.113 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -4.5831
## Bayes        -4.5313
## Shibata      -4.5834
## Hannan-Quinn -4.5627
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                      0.4171  0.5184
## Lag[2*(p+q)+(p+q)-1][11]    4.1792  0.9996
## Lag[4*(p+q)+(p+q)-1][19]    5.8131  0.9775
## 
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic   p-value
## Lag[1]                      29.68 5.097e-08
## Lag[2*(p+q)+(p+q)-1][2]     31.92 3.342e-09
## Lag[4*(p+q)+(p+q)-1][5]     35.41 9.341e-10
## 
## 
## ARCH LM Tests
## ------------------------------------
##              Statistic DoF   P-Value
## ARCH Lag[2]      30.03   2 3.017e-07
## ARCH Lag[5]      31.94   5 6.112e-06
## ARCH Lag[10]     36.47  10 7.000e-05
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  6.7085
## Individual Statistics:             
## mu    0.03340
## ar1   0.03481
## ar2   0.03307
## ma1   0.03218
## ma2   0.03202
## sigma 0.68601
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          1.49 1.68 2.12
## Individual Statistic:     0.35 0.47 0.75
## 
## 
## Elapsed time : 0.159718

GARCH VNI

#garch trước covid vni 
#(1,1)
vni.garch11n.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "norm")
vni.garch11n.fit1 <- ugarchfit(spec = vni.garch11n.spec1, data = truoccov[,1])


vni.garch11t.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "std") 
vni.garch11t.fit1 <- ugarchfit(spec = vni.garch11t.spec1, data = truoccov[, 1])


vni.garch11st.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "sstd") 
vni.garch11st.fit1 <- ugarchfit(spec = vni.garch11st.spec1, data = truoccov[, 1])


vni.garch11g.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "ged") 
vni.garch11g.fit1 <- ugarchfit(spec = vni.garch11g.spec1, data =truoccov[, 1])


vni.garch11sg.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "sged") 
vni.garch11sg.fit1 <- ugarchfit(spec = vni.garch11sg.spec1, data =truoccov[, 1])

##(1,2)
vni.garch12n.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "norm")
vni.garch12n.fit1 <- ugarchfit(spec = vni.garch12n.spec1, data = truoccov[,1])

 vni.garch12t.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "std") 
 vni.garch12t.fit1 <- ugarchfit(spec = vni.garch12t.spec1, data = truoccov[, 1])

 vni.garch12st.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch12st.fit1 <- ugarchfit(spec = vni.garch12st.spec1, data = truoccov[, 1])
 
 vni.garch12g.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "ged") 
 vni.garch12g.fit1 <- ugarchfit(spec = vni.garch12g.spec1, data = truoccov[, 1])
 
 vni.garch12sg.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "sged")
 vni.garch12sg.fit1 <- ugarchfit(spec = vni.garch12sg.spec1, data = truoccov[, 1])
 
 #(2.1)
 vni.garch21n.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.mode
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "norm")
vni.garch21n.fit1 <- ugarchfit(spec = vni.garch21n.spec1, data = truoccov[,1])

 vni.garch21t.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "std") 
vni.garch21t.fit1 <- ugarchfit(spec = vni.garch21t.spec1, data = truoccov[, 1])

 vni.garch21st.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch21st.fit1 <- ugarchfit(spec = vni.garch21st.spec1, data = truoccov[, 1])
 
vni.garch21g.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "ged") 
 vni.garch21g.fit1 <- ugarchfit(spec = vni.garch21g.spec1, data = truoccov[, 1])
 
 vni.garch21sg.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "sged") 
 vni.garch21sg.fit1 <- ugarchfit(spec = vni.garch21sg.spec1, data = truoccov[, 1])
 
 #(2,2)
vni.garch22n.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "norm")
 vni.garch22n.fit1 <- ugarchfit(spec = vni.garch22n.spec1, data = truoccov[, 1])
 vni.garch22t.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "std") 
vni.garch22t.fit1 <- ugarchfit(spec = vni.garch22t.spec1, data = truoccov[, 1])
 
 vni.garch22st.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch22st.fit1 <- ugarchfit(spec = vni.garch22st.spec1, data = truoccov[, 1])
 
 vni.garch22g.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "ged") 
vni.garch22g.fit1 <- ugarchfit(spec = vni.garch22g.spec1, data = truoccov[, 1])

 vni.garch22sg.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 0), include.mean = TRUE), distribution.model = "sged") 
 vni.garch22sg.fit1 <- ugarchfit(spec = vni.garch22sg.spec1, data = truoccov[, 1])

#garch trong covid vni 
#(1,1)
vni.garch11n.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
vni.garch11n.fit2 <- ugarchfit(spec = vni.garch11n.spec2, data = cov[,1])


vni.garch11t.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
vni.garch11t.fit2 <- ugarchfit(spec = vni.garch11t.spec2, data = cov[, 1])


vni.garch11st.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
vni.garch11st.fit2 <- ugarchfit(spec = vni.garch11st.spec2, data = cov[, 1])


vni.garch11g.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
vni.garch11g.fit2 <- ugarchfit(spec = vni.garch11g.spec2, data =cov[, 1])


vni.garch11sg.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
vni.garch11sg.fit2 <- ugarchfit(spec = vni.garch11sg.spec2, data =cov[, 1])

##(1,2)
vni.garch12n.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
vni.garch12n.fit2 <- ugarchfit(spec = vni.garch12n.spec2, data = cov[,1])

 vni.garch12t.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
 vni.garch12t.fit2 <- ugarchfit(spec = vni.garch12t.spec2, data = cov[, 1])

 vni.garch12st.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch12st.fit2 <- ugarchfit(spec = vni.garch12st.spec2, data = cov[, 1])
 
 vni.garch12g.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
 vni.garch12g.fit2 <- ugarchfit(spec = vni.garch12g.spec2, data = cov[, 1])
 
 vni.garch12sg.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
 vni.garch12sg.fit2 <- ugarchfit(spec = vni.garch12sg.spec2, data = cov[, 1])
 
 #(2.1)
 vni.garch21n.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.mode
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
vni.garch21n.fit2 <- ugarchfit(spec = vni.garch21n.spec2, data = cov[,1])

 vni.garch21t.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
vni.garch21t.fit2 <- ugarchfit(spec = vni.garch21t.spec2, data = cov[, 1])

 vni.garch21st.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch21st.fit2 <- ugarchfit(spec = vni.garch21st.spec2, data = cov[, 1])
 
vni.garch21g.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
 vni.garch21g.fit2 <- ugarchfit(spec = vni.garch21g.spec2, data = cov[, 1])
 
 vni.garch21sg.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
 vni.garch21sg.fit2 <- ugarchfit(spec = vni.garch21sg.spec2, data = cov[, 1])
 
 #(2,2)
vni.garch22n.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
 vni.garch22n.fit2 <- ugarchfit(spec = vni.garch22n.spec2, data = cov[,1])
 vni.garch22t.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
vni.garch22t.fit2 <- ugarchfit(spec = vni.garch22t.spec2, data = cov[, 1])
 
 vni.garch22st.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch22st.fit2 <- ugarchfit(spec = vni.garch22st.spec2, data = cov[, 1])
 
 vni.garch22g.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
vni.garch22g.fit2 <- ugarchfit(spec = vni.garch22g.spec2, data = cov[, 1])

 vni.garch22sg.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
 vni.garch22sg.fit2 <- ugarchfit(spec = vni.garch22sg.spec2, data = cov[, 1])

#garch sau covid vni 
#(1,1)
vni.garch11n.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "norm")
vni.garch11n.fit3 <- ugarchfit(spec = vni.garch11n.spec3, data = saucov[,1])


vni.garch11t.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "std") 
vni.garch11t.fit3 <- ugarchfit(spec = vni.garch11t.spec3, data = saucov[,1])


vni.garch11st.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "sstd") 
vni.garch11st.fit3 <- ugarchfit(spec = vni.garch11st.spec3, data = saucov[,1])
show(vni.garch11st.fit)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(1,0,1)
## Distribution : sstd 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.000264    0.000279 3582.3203 0.000000
## ar1     0.930879    0.048835   19.0616 0.000000
## ma1    -0.900299    0.062192  -14.4760 0.000000
## omega   0.000011    0.000000   24.4197 0.000000
## alpha1  0.025853    0.012891    2.0055 0.044912
## beta1   0.792915    0.019233   41.2274 0.000000
## gamma1  0.243466    0.048216    5.0494 0.000000
## skew    0.836503    0.028443   29.4098 0.000000
## shape   4.288637    0.436064    9.8349 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.000264    0.000365 2737.4034 0.000000
## ar1     0.930879    0.060099   15.4892 0.000000
## ma1    -0.900299    0.074218  -12.1305 0.000000
## omega   0.000011    0.000001   18.1466 0.000000
## alpha1  0.025853    0.014215    1.8186 0.068966
## beta1   0.792915    0.017740   44.6973 0.000000
## gamma1  0.243466    0.049432    4.9252 0.000001
## skew    0.836503    0.030467   27.4560 0.000000
## shape   4.288637    0.418969   10.2362 0.000000
## 
## LogLikelihood : 4534.214 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -6.2160
## Bayes        -6.1833
## Shibata      -6.2160
## Hannan-Quinn -6.2038
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                      1.292  0.2557
## Lag[2*(p+q)+(p+q)-1][5]     1.634  0.9945
## Lag[4*(p+q)+(p+q)-1][9]     2.177  0.9758
## d.o.f=2
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.8592  0.3540
## Lag[2*(p+q)+(p+q)-1][5]    1.9570  0.6286
## Lag[4*(p+q)+(p+q)-1][9]    3.0046  0.7582
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]     1.197 0.500 2.000  0.2739
## ARCH Lag[5]     1.496 1.440 1.667  0.5933
## ARCH Lag[7]     1.586 2.315 1.543  0.8040
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  43.2216
## Individual Statistics:              
## mu     0.18228
## ar1    0.18077
## ma1    0.19057
## omega  9.47558
## alpha1 0.16663
## beta1  0.17405
## gamma1 0.11933
## skew   0.09849
## shape  0.15482
## 
## 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           0.5779 0.5634    
## Negative Sign Bias  1.0718 0.2840    
## Positive Sign Bias  1.4164 0.1569    
## Joint Effect        4.3477 0.2263    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     35.70    0.0114765
## 2    30     49.03    0.0114712
## 3    40     62.57    0.0096871
## 4    50     86.38    0.0007833
## 
## 
## Elapsed time : 9.016754

vni.garch11g.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "ged") 
vni.garch11g.fit3 <- ugarchfit(spec = vni.garch11g.spec3, data =saucov[,1])
show(vni.garch11g.fit)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(1,0,1)
## Distribution : ged 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.001025    0.000715 1400.1793 0.000000
## ar1     0.909700    0.015946   57.0478 0.000000
## ma1    -0.883610    0.020378  -43.3607 0.000000
## omega   0.000011    0.000000   31.7820 0.000000
## alpha1  0.023010    0.014979    1.5361 0.124513
## beta1   0.794615    0.019142   41.5109 0.000000
## gamma1  0.203300    0.044047    4.6155 0.000004
## shape   1.072843    0.049190   21.8101 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.001025    0.002138 468.20394 0.000000
## ar1     0.909700    0.028486  31.93468 0.000000
## ma1    -0.883610    0.044115 -20.02949 0.000000
## omega   0.000011    0.000000  25.92415 0.000000
## alpha1  0.023010    0.023329   0.98633 0.323970
## beta1   0.794615    0.024818  32.01779 0.000000
## gamma1  0.203300    0.047195   4.30766 0.000016
## shape   1.072843    0.067527  15.88769 0.000000
## 
## LogLikelihood : 4517.522 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -6.1944
## Bayes        -6.1654
## Shibata      -6.1945
## Hannan-Quinn -6.1836
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                      1.171  0.2793
## Lag[2*(p+q)+(p+q)-1][5]     1.520  0.9976
## Lag[4*(p+q)+(p+q)-1][9]     2.022  0.9836
## d.o.f=2
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.5708  0.4500
## Lag[2*(p+q)+(p+q)-1][5]    1.3184  0.7844
## Lag[4*(p+q)+(p+q)-1][9]    2.2034  0.8794
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]    0.9098 0.500 2.000  0.3402
## ARCH Lag[5]    1.0762 1.440 1.667  0.7104
## ARCH Lag[7]    1.1677 2.315 1.543  0.8848
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  37.8862
## Individual Statistics:             
## mu     0.2094
## ar1    0.1819
## ma1    0.2070
## omega  9.4917
## alpha1 0.1882
## beta1  0.1437
## gamma1 0.1369
## shape  0.1316
## 
## 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           0.1435 0.8859    
## Negative Sign Bias  0.4160 0.6775    
## Positive Sign Bias  1.6272 0.1039    
## Joint Effect        3.3146 0.3456    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     49.30    1.659e-04
## 2    30     63.78    2.045e-04
## 3    40     70.54    1.468e-03
## 4    50    113.02    5.715e-07
## 
## 
## Elapsed time : 1.099863

vni.garch11sg.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "sged") 
vni.garch11sg.fit3 <- ugarchfit(spec = vni.garch11sg.spec3, data =saucov[,1])

##(1,2)
vni.garch12n.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "norm")
vni.garch12n.fit3 <- ugarchfit(spec = vni.garch12n.spec3, data = saucov[,1])

 vni.garch12t.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "std") 
 vni.garch12t.fit3 <- ugarchfit(spec = vni.garch12t.spec3, data = saucov[,1])
 show(vni.garch12t.fit)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,2)
## Mean Model   : ARFIMA(1,0,1)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.000994    0.001551 645.38452 0.000000
## ar1     0.714380    0.401676   1.77850 0.075322
## ma1    -0.658274    0.379472  -1.73471 0.082792
## omega   0.000014    0.000001  26.13715 0.000000
## alpha1  0.022502    0.087835   0.25619 0.797808
## beta1   0.619948    0.145308   4.26645 0.000020
## beta2   0.120112    0.132297   0.90790 0.363934
## gamma1  0.315382    0.119164   2.64663 0.008130
## shape   3.924783    0.407975   9.62015 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      1.000994    0.011038 90.685899 0.000000
## ar1     0.714380    2.577869  0.277120 0.781688
## ma1    -0.658274    2.340261 -0.281282 0.778494
## omega   0.000014    0.000004  3.189466 0.001425
## alpha1  0.022502    0.608593  0.036974 0.970506
## beta1   0.619948    0.217627  2.848670 0.004390
## beta2   0.120112    0.195018  0.615899 0.537961
## gamma1  0.315382    0.731983  0.430860 0.666570
## shape   3.924783    1.290143  3.042131 0.002349
## 
## LogLikelihood : 4522.849 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -6.2003
## Bayes        -6.1677
## Shibata      -6.2004
## Hannan-Quinn -6.1882
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                    0.02483  0.8748
## Lag[2*(p+q)+(p+q)-1][5]   0.16530  1.0000
## Lag[4*(p+q)+(p+q)-1][9]   0.48293  1.0000
## d.o.f=2
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                       1.297  0.2547
## Lag[2*(p+q)+(p+q)-1][8]      2.766  0.7283
## Lag[4*(p+q)+(p+q)-1][14]     5.888  0.6538
## d.o.f=3
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[4]    0.2477 0.500 2.000  0.6187
## ARCH Lag[6]    0.3187 1.461 1.711  0.9405
## ARCH Lag[8]    1.4749 2.368 1.583  0.8443
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  40.177
## Individual Statistics:             
## mu     0.2387
## ar1    0.2067
## ma1    0.1955
## omega  5.3938
## alpha1 0.2016
## beta1  0.1989
## beta2  0.2089
## gamma1 0.1709
## shape  0.2124
## 
## 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           0.3345 0.73808    
## Negative Sign Bias  0.9959 0.31946    
## Positive Sign Bias  1.7746 0.07618   *
## Joint Effect        4.1810 0.24257    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     37.21    0.0074593
## 2    30     63.45    0.0002256
## 3    40     73.78    0.0006406
## 4    50     88.23    0.0005000
## 
## 
## Elapsed time : 0.799232

 vni.garch12st.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch12st.fit3 <- ugarchfit(spec = vni.garch12st.spec3, data = saucov[,1])
 
 vni.garch12g.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "ged") 
 vni.garch12g.fit3 <- ugarchfit(spec = vni.garch12g.spec3, data = saucov[,1])
 
 vni.garch12sg.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "sged")
 vni.garch12sg.fit3 <- ugarchfit(spec = vni.garch12sg.spec3, data = saucov[,1])
 
 #(2.1)
 vni.garch21n.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.mode
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "norm")
vni.garch21n.fit3 <- ugarchfit(spec = vni.garch21n.spec3, data = saucov[,1])

 vni.garch21t.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "std") 
vni.garch21t.fit3 <- ugarchfit(spec = vni.garch21t.spec3, data = saucov[,1])

 vni.garch21st.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch21st.fit3 <- ugarchfit(spec = vni.garch21st.spec3, data = saucov[,1])
 
vni.garch21g.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "ged") 
 vni.garch21g.fit3 <- ugarchfit(spec = vni.garch21g.spec3, data = saucov[,1])

 
 vni.garch21sg.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "sged") 
 vni.garch21sg.fit3 <- ugarchfit(spec = vni.garch21sg.spec3, data = saucov[,1])
 
 #(2,2)
vni.garch22n.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "norm")
 vni.garch22n.fit3 <- ugarchfit(spec = vni.garch22n.spec3, data = saucov[,1])
 vni.garch22t.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "std") 
vni.garch22t.fit3 <- ugarchfit(spec = vni.garch22t.spec3, data = saucov[,1])
 
 vni.garch22st.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "sstd") 
 vni.garch22st.fit3 <- ugarchfit(spec = vni.garch22st.spec3, data =saucov[,1])
 
 vni.garch22g.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model 
= list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "ged") 
vni.garch22g.fit3 <- ugarchfit(spec = vni.garch22g.spec3, data = saucov[,1])

 vni.garch22sg.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(0, 1), include.mean = TRUE), distribution.model = "sged") 
 vni.garch22sg.fit3 <- ugarchfit(spec = vni.garch22sg.spec3, data = saucov[,1])

LỰA CHỌN MÔ HÌNH BIÊN PHÙ HỢP CỦA VNI 3 GIAI ĐOẠN

# Lựa chọn mô hình biên phù hợp nhất cho chuỗi VNI trước covid

vni.model.list.truoc <- list(garch11n = vni.garch11n.fit1, 
                             garch11t = vni.garch11t.fit1, 
                             garch11st = vni.garch11st.fit1, 
garch11g = vni.garch11g.fit1, 
garch11sg = vni.garch11sg.fit1,
garch12n = vni.garch12n.fit1, 
garch12t = vni.garch12t.fit1, 
garch12st = vni.garch12st.fit1, 
garch12g = vni.garch12g.fit1,
garch12sg = vni.garch12sg.fit1,
garch21n = vni.garch21n.fit1, 
garch21t = vni.garch21t.fit1,
garch21st = vni.garch21st.fit1, 
garch21g = vni.garch21g.fit1, 
garch21sg = vni.garch21sg.fit1,
garch22n = vni.garch22n.fit1, 
garch22t = vni.garch22t.fit1, 
garch22st = vni.garch22st.fit1,
garch22g = vni.garch22g.fit1,
garch22sg = vni.garch22sg.fit1)

vni.info.mat1 <- sapply(vni.model.list.truoc, infocriteria)
rownames(vni.info.mat1) <- rownames(infocriteria(vni.garch11n.fit1))
 vni.info.mat1

##               garch11n  garch11t garch11st  garch11g garch11sg  garch12n
## Akaike       -6.428317 -6.514462 -6.517343 -6.505187 -6.506760 -6.426460
## Bayes        -6.367737 -6.445228 -6.439455 -6.435952 -6.428872 -6.357225
## Shibata      -6.428729 -6.514999 -6.518021 -6.505724 -6.507438 -6.426997
## Hannan-Quinn -6.404511 -6.487255 -6.486735 -6.477979 -6.476152 -6.399252
##               garch12t garch12st  garch12g garch12sg  garch21n  garch21t
## Akaike       -6.511104 -6.513899 -6.501439 -6.503062 -6.445625 -6.512150
## Bayes        -6.433216 -6.427356 -6.423551 -6.416519 -6.367737 -6.425607
## Shibata      -6.511782 -6.514733 -6.502117 -6.503897 -6.446303 -6.512985
## Hannan-Quinn -6.480496 -6.479890 -6.470831 -6.469053 -6.415017 -6.478141
##              garch21st  garch21g garch21sg  garch22n  garch22t garch22st
## Akaike       -6.513826 -6.501815 -6.503218 -6.441270 -6.508009 -6.509685
## Bayes        -6.418629 -6.415272 -6.408021 -6.354728 -6.412812 -6.405834
## Shibata      -6.514833 -6.502649 -6.504225 -6.442105 -6.509016 -6.510880
## Hannan-Quinn -6.476416 -6.467806 -6.465808 -6.407261 -6.470599 -6.468874
##               garch22g garch22sg
## Akaike       -6.497674 -6.499077
## Bayes        -6.402477 -6.395226
## Shibata      -6.498681 -6.500272
## Hannan-Quinn -6.460264 -6.458266

 vni.inds1 <- which(vni.info.mat1 == min(vni.info.mat1), arr.ind=TRUE)
model.vni1 <- colnames(vni.info.mat1)[vni.inds1[,2]]
 model.vni1

## [1] "garch11st"

# Lựa chọn mô hình biên phù hợp nhất cho chuỗi VNI covid

vni.model.list.trong<- list(garch11n = vni.garch11n.fit2, 
                            garch11t = vni.garch11t.fit2, 
                            garch11st = vni.garch11st.fit2, 
garch11g = vni.garch11g.fit2, 
garch11sg = vni.garch11sg.fit2,
garch12n = vni.garch12n.fit2, 
garch12t = vni.garch12t.fit2, 
garch12st = vni.garch12st.fit2, 
garch12g = vni.garch12g.fit2, 
garch12sg = vni.garch12sg.fit2,
garch21n = vni.garch21n.fit2, 
garch21t = vni.garch21t.fit2, 
garch21st = vni.garch21st.fit2, 
garch21g = vni.garch21g.fit2,
garch21sg = vni.garch21sg.fit2,
garch22n = vni.garch22n.fit2, 
garch22t = vni.garch22t.fit2, 
garch22st = vni.garch22st.fit2,
garch22g = vni.garch22g.fit2,
garch22sg = vni.garch22sg.fit2)

vni.info.mat2 <- sapply(vni.model.list.trong, infocriteria)
rownames(vni.info.mat2) <- rownames(infocriteria(vni.garch11n.fit2))
 vni.info.mat2

##               garch11n  garch11t garch11st  garch11g garch11sg  garch12n
## Akaike       -5.969171 -6.149504 -6.173459 -6.145072 -6.160039 -5.967565
## Bayes        -5.891527 -6.063233 -6.078561 -6.058801 -6.065141 -5.881294
## Shibata      -5.969844 -6.150331 -6.174458 -6.145900 -6.161038 -5.968393
## Hannan-Quinn -5.938665 -6.115607 -6.136173 -6.111176 -6.122753 -5.933669
##               garch12t garch12st  garch12g garch12sg  garch21n  garch21t
## Akaike       -6.137115 -6.154130 -6.128345 -6.156954 -5.964963 -6.142048
## Bayes        -6.042216 -6.050605 -6.033447 -6.053429 -5.870065 -6.038523
## Shibata      -6.138113 -6.155316 -6.129344 -6.158140 -5.965962 -6.143234
## Hannan-Quinn -6.099829 -6.113454 -6.091059 -6.116278 -5.927677 -6.101373
##              garch21st  garch21g garch21sg  garch22n  garch22t garch22st
## Akaike       -6.165674 -6.124554 -6.152468 -5.961252 -6.129040 -6.149300
## Bayes        -6.053521 -6.021028 -6.040315 -5.857726 -6.016887 -6.028520
## Shibata      -6.167061 -6.125739 -6.153855 -5.962437 -6.130427 -6.150905
## Hannan-Quinn -6.121608 -6.083878 -6.108402 -5.920576 -6.084974 -6.101845
##               garch22g garch22sg
## Akaike       -6.119065 -6.147121
## Bayes        -6.006912 -6.026341
## Shibata      -6.120452 -6.148726
## Hannan-Quinn -6.074999 -6.099666

 vni.inds2 <- which(vni.info.mat2 == min(vni.info.mat2), arr.ind=TRUE)
 vni.inds2

##         row col
## Shibata   3   3

model.vni2<- colnames(vni.info.mat2)[vni.inds2[,2]]
 model.vni2

## [1] "garch11st"

# Lựa chọn mô hình biên phù hợp nhất cho chuỗi VNI sau covid

vni.model.list.sau <- list(
garch11n = vni.garch11n.fit3, 
garch11t = vni.garch11t.fit3, 
garch11st = vni.garch11st.fit3, 
garch11g = vni.garch11g.fit3, 
garch11sg = vni.garch11sg.fit3,
garch12n = vni.garch12n.fit3, 
garch12t = vni.garch12t.fit3, 
garch12st = vni.garch12st.fit3, 
garch12g = vni.garch12g.fit3, 
garch12sg = vni.garch12sg.fit3,
garch21n = vni.garch21n.fit3, 
garch21t = vni.garch21t.fit3, 
garch21st = vni.garch21st.fit3,
garch21g = vni.garch21g.fit3, 
garch21sg = vni.garch21sg.fit3,
garch22n = vni.garch22n.fit3, 
garch22t = vni.garch22t.fit3, 
garch22st = vni.garch22st.fit3 )

vni.info.mat3<- sapply(vni.model.list.sau, infocriteria)
rownames(vni.info.mat3) <- rownames(infocriteria(vni.garch11n.fit3))
 vni.info.mat3

##               garch11n  garch11t garch11st  garch11g garch11sg  garch12n
## Akaike       -5.954509 -6.015445 -6.026530 -6.020818 -6.033703 -5.954145
## Bayes        -5.902665 -5.954960 -5.957405 -5.960333 -5.964578 -5.893660
## Shibata      -5.954812 -6.015856 -6.027065 -6.021228 -6.034238 -5.954555
## Hannan-Quinn -5.934138 -5.991678 -5.999368 -5.997051 -6.006541 -5.930378
##               garch12t garch12st  garch12g garch12sg  garch21n  garch21t
## Akaike       -6.014164 -6.025669 -6.018934 -6.031791 -5.954598 -6.011148
## Bayes        -5.945038 -5.947903 -5.949809 -5.954025 -5.885473 -5.933382
## Shibata      -6.014698 -6.026344 -6.019469 -6.032465 -5.955133 -6.011823
## Hannan-Quinn -5.987002 -5.995111 -5.991772 -6.001233 -5.927436 -5.980590
##              garch21st  garch21g garch21sg  garch22n  garch22t garch22st
## Akaike       -6.021362 -6.016904 -6.028108 -5.933075 -6.008959 -6.020045
## Bayes        -5.934956 -5.939138 -5.941702 -5.855309 -5.922553 -5.924998
## Shibata      -6.022193 -6.017579 -6.028939 -5.933750 -6.009790 -6.021048
## Hannan-Quinn -5.987410 -5.986346 -5.994156 -5.902518 -5.975007 -5.982697

 vni.inds3 <- which(vni.info.mat3 == min(vni.info.mat3), arr.ind=TRUE)
model.vni3 <- colnames(vni.info.mat3)[vni.inds3[,2]]
 model.vni3

## [1] "garch11sg"

GARCH S&P500 3 GIAI ĐOẠN

# Các dạng MH GJR-GARCH cho chuỗi sp500sp500
## GJR-GARCH(11)SP500
sp500.garch11n.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
sp500.garch11n.fit1 <- ugarchfit(spec = sp500.garch11n.spec1, data = truoccov[,2])

sp500.garch11t.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
 sp500.garch11t.fit1 <- ugarchfit(spec =sp500.garch11t.spec1, data = truoccov[,2])
 
 sp500.garch11st.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch11st.fit1 <- ugarchfit(spec = sp500.garch11st.spec1, data = truoccov[,2])
 
 sp500.garch11g.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
 sp500.garch11g.fit1 <- ugarchfit(spec =sp500.garch11g.spec1, data = truoccov[,2])

 sp500.garch11sg.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
 sp500.garch11sg.fit1 <- ugarchfit(spec = sp500.garch11sg.spec1, data =truoccov[,2])
## GJR-GARCH(12)vccb
 sp500.garch12n.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
 sp500.garch12n.fit1 <- ugarchfit(spec = sp500.garch12n.spec1, data = truoccov[,2])
 
sp500.garch12t.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
sp500.garch12t.fit1 <- ugarchfit(spec = sp500.garch12t.spec1, data = truoccov[,2])
 
sp500.garch12st.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch12st.fit1 <- ugarchfit(spec = sp500.garch12st.spec1, data = truoccov[,2])
 
sp500.garch12g.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged") 
sp500.garch12g.fit1 <- ugarchfit(spec = sp500.garch12g.spec1, data = truoccov[,2])
 

sp500.garch12sg.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
sp500.garch12sg.fit1 <- ugarchfit(spec = sp500.garch12sg.spec1, data = truoccov[,2])
## GJR-GARCH(21)vcbvcb
sp500.garch21n.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
sp500.garch21n.fit1 <- ugarchfit(spec = sp500.garch21n.spec1, data = truoccov[,2])

sp500.garch21t.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
sp500.garch21t.fit1 <- ugarchfit(spec = sp500.garch21t.spec1, data = truoccov[,2])

sp500.garch21st.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch21st.fit1 <- ugarchfit(spec = sp500.garch21st.spec1, data = truoccov[,2])

sp500.garch21g.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
sp500.garch21g.fit1 <- ugarchfit(spec =sp500.garch21g.spec1, data = truoccov[,2])

sp500.garch21sg.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
sp500.garch21sg.fit1 <- ugarchfit(spec = sp500.garch21sg.spec1, data = truoccov[,2])
## GJR-GARCH(22)SP500
sp500.garch22n.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
sp500.garch22n.fit1 <- ugarchfit(spec = sp500.garch22n.spec1, data = truoccov[,2])

sp500.garch22t.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
sp500.garch22t.fit1 <- ugarchfit(spec = sp500.garch22t.spec1, data = truoccov[,2])

sp500.garch22st.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch22st.fit1<- ugarchfit(spec = sp500.garch22st.spec1, data = truoccov[,2])

sp500.garch22g.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
sp500.garch22g.fit1 <- ugarchfit(spec = sp500.garch22g.spec1, data = truoccov[,2])

sp500.garch22sg.spec1 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
sp500.garch22sg.fit1 <- ugarchfit(spec =sp500.garch22sg.spec1, data = truoccov[,2])

# Các dạng MH GJR-GARCH cho chuỗi trong covid  
## GJR-GARCH(11)SP500
sp500.garch11n.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
sp500.garch11n.fit2 <- ugarchfit(spec = sp500.garch11n.spec2, data = cov[,2])

sp500.garch11t.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
 sp500.garch11t.fit2 <- ugarchfit(spec =sp500.garch11t.spec2, data = cov[,2])
 
 sp500.garch11st.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch11st.fit2 <- ugarchfit(spec = sp500.garch11st.spec2, data = cov[,2])
 
 sp500.garch11g.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
 sp500.garch11g.fit2 <- ugarchfit(spec =sp500.garch11g.spec2, data = cov[,2])

 sp500.garch11sg.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
 sp500.garch11sg.fit2 <- ugarchfit(spec = sp500.garch11sg.spec2, data =cov[,2])
## GJR-GARCH(12)vccb
 sp500.garch12n.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
 sp500.garch12n.fit2 <- ugarchfit(spec = sp500.garch12n.spec2, data = cov[,2])
 
sp500.garch12t.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
sp500.garch12t.fit2 <- ugarchfit(spec = sp500.garch12t.spec2, data = cov[,2])
 
sp500.garch12st.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch12st.fit2 <- ugarchfit(spec = sp500.garch12st.spec2, data = cov[,2])
 
sp500.garch12g.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged") 
sp500.garch12g.fit2 <- ugarchfit(spec = sp500.garch12g.spec2, data = cov[,2])

sp500.garch12sg.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
sp500.garch12sg.fit2 <- ugarchfit(spec = sp500.garch12sg.spec2, data = cov[,2])
## GJR-GARCH(21)vcbvcb
sp500.garch21n.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
sp500.garch21n.fit2 <- ugarchfit(spec = sp500.garch21n.spec2, data = cov[,2])

sp500.garch21t.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
sp500.garch21t.fit2 <- ugarchfit(spec = sp500.garch21t.spec2, data = cov[,2])

sp500.garch21st.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch21st.fit2 <- ugarchfit(spec = sp500.garch21st.spec2, data = cov[,2])

sp500.garch21g.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
sp500.garch21g.fit2 <- ugarchfit(spec =sp500.garch21g.spec2, data = cov[,2])

sp500.garch21sg.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
sp500.garch21sg.fit2 <- ugarchfit(spec = sp500.garch21sg.spec2, data = cov[,2])
## GJR-GARCH(22)SP500
sp500.garch22n.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
sp500.garch22n.fit2 <- ugarchfit(spec = sp500.garch22n.spec2, data = cov[,2])

sp500.garch22t.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
sp500.garch22t.fit2 <- ugarchfit(spec = sp500.garch22t.spec2, data = cov[,2])

sp500.garch22st.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch22st.fit2<- ugarchfit(spec = sp500.garch22st.spec2, data = cov[,2])

sp500.garch22g.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
sp500.garch22g.fit2 <- ugarchfit(spec = sp500.garch22g.spec2, data = cov[,2])

sp500.garch22sg.spec2 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
sp500.garch22sg.fit2 <- ugarchfit(spec =sp500.garch22sg.spec2, data = cov[,2])

# Các dạng MH GJR-GARCH cho chuỗi trong covid  
## GJR-GARCH(11)SP500
sp500.garch11n.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
sp500.garch11n.fit3 <- ugarchfit(spec = sp500.garch11n.spec3, data = saucov[,2])

sp500.garch11t.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
 sp500.garch11t.fit3 <- ugarchfit(spec =sp500.garch11t.spec3, data = saucov[,2])
 
 sp500.garch11st.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch11st.fit3 <- ugarchfit(spec = sp500.garch11st.spec3, data = saucov[,2])
 
 sp500.garch11g.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
 sp500.garch11g.fit3 <- ugarchfit(spec =sp500.garch11g.spec3, data = saucov[,2])

 sp500.garch11sg.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
 sp500.garch11sg.fit3 <- ugarchfit(spec = sp500.garch11sg.spec3, data =saucov[,2])
## GJR-GARCH(12)vccb
 sp500.garch12n.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
 sp500.garch12n.fit3 <- ugarchfit(spec = sp500.garch12n.spec3, data = saucov[,2])
 
sp500.garch12t.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
sp500.garch12t.fit3 <- ugarchfit(spec = sp500.garch12t.spec3, data = saucov[,2])
 
sp500.garch12st.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch12st.fit3 <- ugarchfit(spec = sp500.garch12st.spec3, data = saucov[,2])
 
sp500.garch12g.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged") 
sp500.garch12g.fit3 <- ugarchfit(spec = sp500.garch12g.spec3, data = saucov[,2])
 

sp500.garch12sg.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
sp500.garch12sg.fit3 <- ugarchfit(spec = sp500.garch12sg.spec3, data = saucov[,2])
## GJR-GARCH(21)vcbvcb
sp500.garch21n.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
sp500.garch21n.fit3 <- ugarchfit(spec = sp500.garch21n.spec3, data = saucov[,2])

sp500.garch21t.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
sp500.garch21t.fit3 <- ugarchfit(spec = sp500.garch21t.spec3, data = saucov[,2])

sp500.garch21st.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch21st.fit3 <- ugarchfit(spec = sp500.garch21st.spec3, data = saucov[,2])

sp500.garch21g.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
sp500.garch21g.fit3 <- ugarchfit(spec =sp500.garch21g.spec3, data = saucov[,2])

sp500.garch21sg.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
sp500.garch21sg.fit3 <- ugarchfit(spec = sp500.garch21sg.spec3, data =saucov[,2])
## GJR-GARCH(22)SP500
sp500.garch22n.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
sp500.garch22n.fit3 <- ugarchfit(spec = sp500.garch22n.spec3, data = saucov[,2])

sp500.garch22t.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std") 
sp500.garch22t.fit3 <- ugarchfit(spec = sp500.garch22t.spec3, data =saucov[,2])

sp500.garch22st.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd") 
sp500.garch22st.fit3<- ugarchfit(spec = sp500.garch22st.spec3, data = saucov[,2])

sp500.garch22g.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged") 
sp500.garch22g.fit3 <- ugarchfit(spec = sp500.garch22g.spec3, data = saucov[,2])

sp500.garch22sg.spec3 <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), 
mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged") 
sp500.garch22sg.fit3 <- ugarchfit(spec =sp500.garch22sg.spec3, data = saucov[,2])

LỰA CHỌN MÔ HÌNH BIÊN PHÙ HỢP SP500

# Lựa chọn mô hình biên phù hợp nhất cho chuỗi sp500
sp500.model.list.truoc <- list(garch11n = sp500.garch11n.fit1,
                               garch11t = sp500.garch11t.fit1, 
                               garch11st = sp500.garch11st.fit1, 
                               garch11g = sp500.garch11g.fit1, 
                               garch11sg = sp500.garch11sg.fit1,
                               garch12n = sp500.garch12n.fit1, 
                               garch12t = sp500.garch12t.fit1, 
                               garch12st = sp500.garch12st.fit1, 
                               garch12g = sp500.garch12g.fit1, 
                               garch12sg = sp500.garch12sg.fit1,
                               garch21n = sp500.garch21n.fit1, 
                               garch21t = sp500.garch21t.fit1, 
                               garch21st = sp500.garch21st.fit1, 
                               garch21g = sp500.garch21g.fit1, 
                               garch21sg = sp500.garch21sg.fit1,
                              
                               garch22t =sp500.garch22t.fit1, 
                               garch22st = sp500.garch22st.fit1, 
                               garch22g = sp500.garch22g.fit1, 
                               garch22sg = sp500.garch22sg.fit1)
 sp500.info.mat1 <- sapply(sp500.model.list.truoc, infocriteria) 
 
 rownames(sp500.info.mat1) <- rownames(infocriteria(sp500.garch11n.fit1))
 sp500.info.mat1

##               garch11n  garch11t garch11st  garch11g garch11sg  garch12n
## Akaike       -4.785417 -4.849915 -4.905897 -4.835072 -4.900578 -4.780465
## Bayes        -4.707528 -4.763372 -4.810700 -4.748529 -4.805381 -4.693922
## Shibata      -4.786094 -4.850749 -4.906904 -4.835907 -4.901585 -4.781299
## Hannan-Quinn -4.754809 -4.815905 -4.868487 -4.801063 -4.863168 -4.746456
##               garch12t garch12st  garch12g garch12sg  garch21n  garch21t
## Akaike       -4.844828 -4.904245 -4.827102 -4.896438 -4.805142 -4.849524
## Bayes        -4.749631 -4.800394 -4.731905 -4.792586 -4.709945 -4.745672
## Shibata      -4.845835 -4.905440 -4.828109 -4.897633 -4.806149 -4.850719
## Hannan-Quinn -4.807418 -4.863434 -4.789692 -4.855627 -4.767732 -4.808713
##              garch21st  garch21g garch21sg  garch22t garch22st  garch22g
## Akaike       -4.901684 -4.837177 -4.913904 -4.843763 -4.910554 -4.850483
## Bayes        -4.789179 -4.733325 -4.801399 -4.731257 -4.789394 -4.737977
## Shibata      -4.903083 -4.838372 -4.915303 -4.845162 -4.912172 -4.851881
## Hannan-Quinn -4.857473 -4.796366 -4.869693 -4.799551 -4.862941 -4.806271
##              garch22sg
## Akaike       -4.909764
## Bayes        -4.788604
## Shibata      -4.911382
## Hannan-Quinn -4.862151

sp500.inds1 <- which(sp500.info.mat1 == min(sp500.info.mat1), arr.ind = TRUE)
 model.sp500.1 <- colnames(sp500.info.mat1)[sp500.inds1[,2]]
 model.sp500.1

## [1] "garch21sg"

# Lựa chọn mô hình biên phù hợp nhất cho chuỗi sp500
sp500.model.list.trong <- list(
garch11n = sp500.garch11n.fit2, 
garch11t = sp500.garch11t.fit2, 
garch11st = sp500.garch11st.fit2, 
garch11g = sp500.garch11g.fit2, 
garch11sg = sp500.garch11sg.fit2,
garch12n = sp500.garch12n.fit2, 
garch12t = sp500.garch12t.fit2, 
garch12st = sp500.garch12st.fit2, 
garch12g = sp500.garch12g.fit2, 
garch12sg = sp500.garch12sg.fit2,
garch21n = sp500.garch21n.fit2, 
garch21t = sp500.garch21t.fit2, 
garch21st = sp500.garch21st.fit2, 
garch21g = sp500.garch21g.fit2, 
garch21sg = sp500.garch21sg.fit2,
garch22n = sp500.garch22n.fit2, 
garch22t =sp500.garch22t.fit2, 
garch22st = sp500.garch22st.fit2, 
garch22g = sp500.garch22g.fit2, 
garch22sg = sp500.garch22sg.fit2)
 sp500.info.mat2 <- sapply(sp500.model.list.trong, infocriteria) 
 rownames(sp500.info.mat2) <- rownames(infocriteria(sp500.garch11n.fit2))
 sp500.info.mat2

##               garch11n  garch11t garch11st  garch11g garch11sg  garch12n
## Akaike       -4.358202 -4.464363 -4.525250 -4.431218 -4.516795 -4.373873
## Bayes        -4.280558 -4.378092 -4.430351 -4.344947 -4.421897 -4.287602
## Shibata      -4.358874 -4.465190 -4.526248 -4.432045 -4.517794 -4.374701
## Hannan-Quinn -4.327696 -4.430466 -4.487964 -4.397321 -4.479509 -4.339977
##               garch12t garch12st  garch12g garch12sg  garch21n  garch21t
## Akaike       -4.464026 -4.519489 -4.438242 -4.512894 -4.352254 -4.461770
## Bayes        -4.369127 -4.415964 -4.343344 -4.409369 -4.257356 -4.358245
## Shibata      -4.465024 -4.520675 -4.439241 -4.514079 -4.353253 -4.462955
## Hannan-Quinn -4.426739 -4.478813 -4.400956 -4.472218 -4.314968 -4.421094
##              garch21st  garch21g garch21sg  garch22n  garch22t garch22st
## Akaike       -4.519865 -4.424783 -4.504487 -4.332051 -4.458085 -4.515741
## Bayes        -4.407712 -4.321258 -4.392335 -4.228526 -4.345933 -4.394961
## Shibata      -4.521252 -4.425969 -4.505875 -4.333236 -4.459473 -4.517346
## Hannan-Quinn -4.475799 -4.384108 -4.460422 -4.291375 -4.414020 -4.468286
##               garch22g garch22sg
## Akaike       -4.431810 -4.515201
## Bayes        -4.319657 -4.394422
## Shibata      -4.433197 -4.516806
## Hannan-Quinn -4.387744 -4.467746

sp500.inds2 <- which(sp500.info.mat2 == min(sp500.info.mat2), arr.ind = TRUE)
 model.sp500.2 <- colnames(sp500.info.mat2)[sp500.inds2[,2]]
 model.sp500.2

## [1] "garch11st"

# Lựa chọn mô hình biên phù hợp nhất cho chuỗi sp500
sp500.model.list.sau <- list(
garch11n = sp500.garch11n.fit3, 
garch11t = sp500.garch11t.fit3, 
 

garch12n = sp500.garch12n.fit3, 
garch12t = sp500.garch12t.fit3, 

garch12g = sp500.garch12g.fit3, 
garch12sg = sp500.garch12sg.fit3,

garch21t = sp500.garch21t.fit3, 
garch21st = sp500.garch21st.fit3, 

garch21sg = sp500.garch21sg.fit3,
garch22n = sp500.garch22n.fit3, 
garch22t =sp500.garch22t.fit3, 
garch22st = sp500.garch22st.fit3, 
garch22g = sp500.garch22g.fit3, 
garch22sg = sp500.garch22sg.fit3)
 sp500.info.mat3 <- sapply(sp500.model.list.sau, infocriteria) 
 
rownames(sp500.info.mat3) <- rownames(infocriteria(sp500.garch11n.fit3))
sp500.info.mat3

##               garch11n  garch11t  garch12n  garch12t  garch12g garch12sg
## Akaike       -4.745276 -4.803536 -4.755645 -4.798766 -4.819102 -4.855171
## Bayes        -4.667510 -4.717130 -4.669239 -4.703719 -4.724054 -4.751483
## Shibata      -4.745951 -4.804367 -4.756476 -4.799769 -4.820104 -4.856361
## Hannan-Quinn -4.714719 -4.769584 -4.721693 -4.761418 -4.781754 -4.814428
##               garch21t garch21st garch21sg  garch22n  garch22t garch22st
## Akaike       -4.820964 -4.860739 -4.850959 -4.770730 -4.780739 -4.859242
## Bayes        -4.717276 -4.748410 -4.738630 -4.667042 -4.668411 -4.738273
## Shibata      -4.822155 -4.862132 -4.852352 -4.771920 -4.782132 -4.860854
## Hannan-Quinn -4.780221 -4.816601 -4.806820 -4.729986 -4.736601 -4.811708
##               garch22g garch22sg
## Akaike       -4.808780 -4.858826
## Bayes        -4.696451 -4.737857
## Shibata      -4.810173 -4.860438
## Hannan-Quinn -4.764642 -4.811292

sp500.inds3<- which(sp500.info.mat3 == min(sp500.info.mat3), arr.ind = TRUE)
 model.sp500.3 <- colnames(sp500.info.mat3)[sp500.inds3[,2]]
 model.sp500.3

## [1] "garch21st"

vni.res1 <- residuals(vni.garch11st.fit1)/sigma(vni.garch11st.fit1)
fitdist(distribution = "sstd", vni.res1, control = list())$pars

##         mu      sigma       skew      shape 
## 0.01301075 1.01041242 0.89181824 5.07299725

u1 <- pdist(distribution = "sstd", q = vni.res1, mu = 0.01301075, sigma = 1.01041242 , skew = 0.89181824, shape = 5.07299725 )

vni.res2 <- residuals(vni.garch11st.fit2)/sigma(vni.garch11st.fit2)
fitdist(distribution = "sstd", vni.res2, control = list())$pars

##        mu     sigma      skew     shape 
## 0.0116941 0.9834762 0.7723099 3.9573978

u2<- pdist(distribution = "sstd", q = vni.res2, mu =0.0116941 , sigma =0.9834762 , skew = 0.7723099, shape = 3.9573978 )

vni.res3 <- residuals(vni.garch11sg.fit3)/sigma(vni.garch11sg.fit3)
fitdist(distribution = "sged", vni.res3, control = list())$pars

##          mu       sigma        skew       shape 
## -0.03351554  1.00739992  0.83721133  1.25193828

u3<- pdist(distribution = "sged", q = vni.res3, mu = -0.03351554, sigma = 1.00739992, skew = 0.83721133, shape = 1.25193828  )

sp500.res1<-residuals(sp500.garch21sg.fit1)/sigma(sp500.garch21sg.fit1)
fitdist(distribution = "sged", sp500.res1, control = list())$pars

##           mu        sigma         skew        shape 
## -0.004278287  0.991082927  1.499760046  1.406681719

v1 <- pdist(distribution = "sged", q = sp500.res1, mu = -0.004278287, sigma = 0.991082927 , skew =1.499760046 , shape =1.406681719  )

sp500.res2<-residuals(sp500.garch11st.fit2)/sigma(sp500.garch11st.fit2)
fitdist(distribution = "sstd", sp500.res2, control = list())$pars

##          mu       sigma        skew       shape 
## -0.04184818  0.95201766  1.40195242  4.61777562

v2 <- pdist(distribution = "sstd", q = sp500.res2, mu = -0.04184818, sigma =  0.95201766, skew =1.40195242  , shape = 4.61777562 )

sp500.res3<-residuals(sp500.garch21st.fit3)/sigma(sp500.garch21st.fit3)
fitdist(distribution = "sstd", sp500.res3, control = list())$pars

##         mu      sigma       skew      shape 
## 0.01466194 1.00710418 1.52675449 4.76935597

v3 <- pdist(distribution = "sstd", q = sp500.res3, mu =0.01466194 , sigma =1.00710418 , skew =1.52675449  , shape =4.76935597   )

KẾT QUẢ ƯỚC LƯỢNG

copulatruoc <- BiCopSelect(u1,v1,selectioncrit = "AIC",method = "mle")
copulatrong <- BiCopSelect(u2,v2,selectioncrit = "AIC",method = "mle")
copulasau<- BiCopSelect(u3,v3,selectioncrit = "AIC",method = "mle")

#est
est_copulatruoc <- BiCopEst(u1,v1,family = copulatruoc$family,method = "mle",max.df = 30)
est_copulatrong<- BiCopEst(u2,v2,family = copulatrong$family,method = "mle",max.df = 30)
est_copulasau <- BiCopEst(u3,v3,family = copulasau$family,method = "mle",max.df = 30)
#Trình bày kết quả

kq<- data.frame(mqh = c('Trước Covid' ,'Trong Covid','Sau Covid'),
                    Copula = c('Rotated Gumbel 270 degrees', 'Independence','Gaussian'),
                    Thamso = c(est_copulatruoc$par, est_copulatrong$par, est_copulasau$par),
                  Thamso2 = c(est_copulatruoc$par2, est_copulatrong$par2, est_copulasau$par2),
                   duoi = c(est_copulatruoc$tau, est_copulatrong$tau, est_copulasau$tau),
                  duoiduoi = c(est_copulatruoc$taildep$lower, est_copulatrong$taildep$lower, est_copulasau$taildep$lower),
                  duoitren = c(est_copulatruoc$taildep$upper, est_copulatrong$taildep$upper, est_copulasau$taildep$upper),
                  aic = c(est_copulatruoc$AIC, est_copulatrong$AIC, est_copulasau$AIC),
                  bic = c(est_copulatruoc$BIC, est_copulatrong$BIC, est_copulasau$BIC))

kable(kq, 
  caption = "Bảng 11: Kết quả ước lượng Copula của TSLN VNI và STI từng giai đoạn", 
  col.names = c("CHISO","Copula", "Par","Par2", "HS Kendall","Đuoiuoi","Duoitren","AIC","BIC"), 
  format = 'pandoc') %>% 
  kable_styling(
            bootstrap_options = c("striped", "hover", "condensed"), 
            full_width = F)

## Warning in kable_styling(., bootstrap_options = c("striped", "hover",
## "condensed"), : Please specify format in kable. kableExtra can customize either
## HTML or LaTeX outputs. See https://haozhu233.github.io/kableExtra/ for details.

Bảng 11: Kết quả ước lượng Copula của TSLN VNI và STI từng giai đoạn

CHISO	Copula	Par	Par2	HS Kendall	Đuoiuoi	Duoitren	AIC	BIC
Trước Covid	Rotated Gumbel 270 degrees	-1.0592325	0	-0.0559202	0	0	-3.107264	1.072753
Trong Covid	Independence	0.0000000	0	0.0000000	0	0	0.000000	0.000000
Sau Covid	Gaussian	-0.0805305	0	-0.0513229	0	0	-1.166012	3.016073

years <- 2010:2023
sp500_values <- c(15.06, 2.11, 16.00, 32.39, 13.69, 1.38, 11.96, 21.83, -4.38, 31.49, 18.40, 28.71, -18.11, 26.29)
plot(years, sp500_values, type="o", col="blue", xlab="Năm", ylab="Tỷ lệ tăng trưởng (%)", main="S&P 500 Từ 2010 đến 2023")
abline(h=0, col="red", lty=2) 

library(xlsx)
library(tidyverse)
library(scales)

## 
## Attaching package: 'scales'

## The following object is masked from 'package:purrr':
## 
##     discard

## The following object is masked from 'package:readr':
## 
##     col_factor

h<- read.xlsx("D:/mhnn/thhdvni.xlsx", sheetIndex= 1, header= T)
h %>% ggplot(aes(x =Năm.)) +
  geom_density()

ggplot(h, aes(x=Năm., y=poitvni)) +
  geom_line(color="blue") +
  labs(title="Điểm VNI giai đoạn 2010-2023", x="Năm", y="Điểm VNI") +
  theme_minimal() 

# VẼ CÁC HỌ COPULA

#BIỂU ĐỒ COPULA STUDENT VÀ GAUSSIAN
library(knitr)

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

library(copula)
library(ggplot2)
library(plotly)

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

## 
## Attaching package: 'plotly'

## The following object is masked from 'package:ggplot2':
## 
##     last_plot

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

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

library(gridExtra)

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

## 
## Attaching package: 'gridExtra'

## The following object is masked from 'package:dplyr':
## 
##     combine

library(VC2copula)
library(VineCopula)
library(gridGraphics)

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

library(png)
# Hàm vẽ biểu đồ phân tán
scatter_plot <- function(random_data) {
  ggplot(data.frame(random_data), aes(x = random_data[,1], y = random_data[,2])) +
    geom_point(alpha = 0.5) +
    theme_minimal() +
    labs(x = "u", y = "v")
}

# Hàm vẽ biểu đồ phối cảnh
persp_plot <- function(copula_obj, file_name) {
  png(file_name)
  persp(copula_obj, dCopula, 
        xlab = 'u', ylab = 'v',  ltheta = 120,  
        ticktype = "detailed", cex.axis = 0.8)
  dev.off()
  rasterGrob(readPNG(file_name), interpolate = TRUE)
}

# Mô phỏng dữ liệu
set.seed(123)
cop_nor <- normalCopula(param = 0.8, dim = 2)
random_nor <- rCopula(copula = cop_nor, n =10000)
cop_std <- tCopula(param = 0.8, dim = 2, df = 1)
random_std <- rCopula(copula = cop_std, n = 10000)

# Vẽ biểu đồ phân tán
png('nors.png')
scatter_plot(random_nor)
dev.off()

## png 
##   2

nors <- rasterGrob(readPNG('nors.png'), interpolate = TRUE)

png('stds.png')
scatter_plot(random_std)
dev.off()

## png 
##   2

stds <- rasterGrob(readPNG('stds.png'), interpolate = TRUE)

# Vẽ biểu đồ phối cảnh
nor_per <- persp_plot(cop_nor, 'norp.png')
std_per <- persp_plot(cop_std, 'stdp.png')

# Thêm ghi chú cho biểu đồ
top_note <- textGrob("Biểu đồ phân tán và phối cảnh PDF với Copula Gaussian và Copula t-Student", 
                     gp = gpar(fontsize = 12, font = 1), hjust = 0.5)

                        
                        
# Kết hợp các biểu đồ và ghi chú
grid.arrange(
  top_note,
  arrangeGrob(nors, nor_per, stds, std_per, ncol = 3, 
              layout_matrix = rbind(c(1, 2, 5), c(3, 4, 5)),
              widths = c(2, 2, 1)),
  nrow = 3,
  heights = c(1, 4, 1)
)

# Hàm vẽ biểu đồ phân tán
scatter_plot <- function(random_data,c1) {
  ggplot(data.frame(random_data), aes(x = random_data[,1], y = random_data[,2])) +
    geom_point(alpha = 0.5,col= c1) +
    theme_minimal() +
    labs(x = "u", y = "v")
}

# Hàm vẽ biểu đồ 
persp_plot <- function(copula_obj, file_name,c1){
  png(file_name)
  persp(copula_obj, dCopula, 
        xlab = 'u', ylab = 'v',col=c1,  ltheta = 120,  
        ticktype = "detailed", cex.axis = 0.8)
  dev.off()
  rasterGrob(readPNG(file_name), interpolate = TRUE)
}
set.seed(123)
#Mô phỏng copula clayton với p=4 10000 quan sát 
cop_clay <- claytonCopula(param = 4, dim = 2)
random_clay <- rCopula(copula = cop_clay,n = 10000)
#Vẽ biểu đồ 
png('clays.png')
scatter_plot(random_clay,'#FF0000')
dev.off()

## png 
##   2

clays <- rasterGrob(readPNG('clays.png'), interpolate = TRUE)
clayp <- persp_plot(cop_clay,'clayp.png','#FF0000')
legend <- legendGrob(
  labels = c("Clayton"), pch = 15,
  gp = gpar(col = c('#FF0000'), fill = c('#FF0000'))
)
grid.arrange(clays, clayp,legend, ncol = 3, 
  layout_matrix = rbind(c(1, 2, 3)),
  widths = c(1, 1, 1)
             )

#Mô phỏng copula gumbel với p=5 10000 quan sát 
cop_gum <- gumbelCopula(param = 5, dim = 2)
random_gum <- rCopula(copula = cop_gum,n =10000)
png('gums.png')
scatter_plot(random_gum,'#00FFFF')
dev.off()

## png 
##   2

gums <- rasterGrob(readPNG('gums.png'), interpolate = TRUE)
gump <- persp_plot(cop_gum,'gump.png','#00FFFF')
legend <- legendGrob(
  labels = c( "Gumbel"), pch = 15,
  gp = gpar(col = c( '#00FFFF'), fill = c( '#00FFFF'))
)

grid.arrange( gums, gump, legend, ncol = 3, 
  layout_matrix = rbind(c(1, 2, 3)),
  widths = c(1, 1, 1)
             )

#Mô phỏng copula survival clayton(Rotated-Clayton)với p=4 10000 quan sát 
cop_surclay <- VC2copula::surClaytonCopula(param = 4)
random_surclay <- rCopula(copula = cop_surclay,n = 10000)
png('surclays.png')
scatter_plot(random_surclay,'#808080')
dev.off()

## png 
##   2

surclays <- rasterGrob(readPNG('surclays.png'), interpolate = TRUE)
surclayp <- persp_plot(cop_gum,'surclays.png','#808080')
legend <- legendGrob(
  labels = c( "Survival Clayton"), pch = 15,
  gp = gpar(col = c( '#808080'), fill = c( '#808080'))
)

grid.arrange( surclays, surclayp, legend, ncol = 3, 
  layout_matrix = rbind(c(1, 2, 3)),
  widths = c(1, 1, 1)
             )

#Mô phỏng copula survival gumbel 10000 qs 
cop_surgum <- VC2copula::surGumbelCopula(param = 5)
random_surgum <- rCopula(copula = cop_surgum,n = 10000)
png('surgums.png')
scatter_plot(random_surgum,'#9966FF')
dev.off()

## png 
##   2

surgums <- rasterGrob(readPNG('surgums.png'), interpolate = TRUE)
surgump <- persp_plot(cop_surgum, "surgump.png","#9966FF")
legend <- legendGrob(labels = c("Survival Gumbel"), pch = 15,
                    gp = gpar(col = c('#9966FF'), fill = c('#9966FF' )))

grid.arrange(surgums, surgump, legend, ncol = 3,
             layout_matrix = rbind(c(1,2,3)),
             widths = c(1,1,1)
             )

set.seed(123)
#Mô phỏng copula Frank
cop_frank <- frankCopula(param = 9.2)
#Mô phỏng 7600 quan sát ngẫu nhiên dựa trên copula có sẵn
random_frank <- rCopula(copula = cop_frank,n = 10000)
#Mô phỏng copula survival clayton  với p=4
cop_joe <- joeCopula(param = 3)
#Mô phỏng 7600 quan sát ngẫu nhiên dựa trên copula có sẵn
random_joe <- rCopula(copula = cop_joe,n = 10000)
png('franks.png')
scatter_plot(random_frank,'#FFCCFF')
dev.off()

## png 
##   2

franks <- rasterGrob(readPNG('franks.png'), interpolate = TRUE)

png('joes.png')
scatter_plot(random_joe,'#FFCC66')
dev.off()

## png 
##   2

joes <- rasterGrob(readPNG('joes.png'), interpolate = TRUE)
frankp <- persp_plot(cop_frank, "frankp.png","#FFCCFF")
joep <- persp_plot(cop_joe, "joep.png","#FFCC66")

legend <- legendGrob(labels = c("Frank","Joe"), pch = 15,
                    gp = gpar(col = c('#FFCCFF','#FFCC66'), fill = c('#FFCCFF','#FFCC66')))

grid.arrange(franks, frankp,joes, joep, legend, ncol = 3,
             layout_matrix = rbind(c(1,2,5),c(3,4,5)),
             widths = c(2,2,1)
             )

set.seed(123)
#Mô phỏng copula BB1
cop_bb1 <- VC2copula::BB1Copula(param = c(2,2))
#Mô phỏng 7600 quan sát ngẫu nhiên dựa trên copula có sẵn
random_bb1 <- rCopula(copula = cop_bb1,n = 10000)
#Mô phỏng copula BB6
cop_bb6 <- VC2copula::BB6Copula(param = c(1.5,5))
#Mô phỏng 7600 quan sát ngẫu nhiên dựa trên copula có sẵn
random_bb6 <- rCopula(copula = cop_bb6,n = 10000)
png('bb1s.png')
scatter_plot(random_bb1,'#00EE00')
dev.off()

## png 
##   2

bb1s <- rasterGrob(readPNG('bb1s.png'), interpolate = TRUE)

png('bb6s.png')
scatter_plot(random_bb6,'pink')
dev.off()

## png 
##   2

bb6s <- rasterGrob(readPNG('bb6s.png'), interpolate = TRUE)
bb1p <- persp_plot(cop_bb1, "bb1p.png","#00EE00")
bb6p <- persp_plot(cop_bb6, "bb6p.png","pink")

legend <- legendGrob(labels = c("BB1","BB6"), pch = 15,
                    gp = gpar(col = c('#00EE00','pink'), fill = c('#00EE00','pink')))

grid.arrange(bb1s, bb1p,bb6s, bb6p, legend, ncol = 3,
             layout_matrix = rbind(c(1,2,5),c(3,4,5)),
             widths = c(2,2,1)
             )

set.seed(123)
#Mô phỏng copula BB7
cop_bb7 <- VC2copula::BB7Copula(param = c(2,5))
#Mô phỏng 7600 quan sát ngẫu nhiên dựa trên copula có sẵn
random_bb7 <- rCopula(copula = cop_bb7,n = 10000)
#Mô phỏng copula BB8
cop_bb8 <- VC2copula::BB8Copula(param = c(4,1))
#Mô phỏng 7600 quan sát ngẫu nhiên dựa trên copula có sẵn
random_bb8 <- rCopula(copula = cop_bb8,n = 10000)
png('bb7s.png')
scatter_plot(random_bb7,'yellow')
dev.off()

## png 
##   2

bb7s <- rasterGrob(readPNG('bb7s.png'), interpolate = TRUE)

png('bb8s.png')
scatter_plot(random_bb8,'#FF9966')
dev.off()

## png 
##   2

bb8s <- rasterGrob(readPNG('bb8s.png'), interpolate = TRUE)
bb7p <- persp_plot(cop_bb7, "bb7p.png","yellow")
bb8p <- persp_plot(cop_bb8, "bb8p.png","#FF9966")

legend <- legendGrob(labels = c("BB7","BB8"), pch = 15,
                    gp = gpar(col = c('yellow','#FF9966'), fill = c('yellow','#FF9966')))

grid.arrange(bb7s, bb7p,bb8s, bb8p, legend, ncol = 3,
             layout_matrix = rbind(c(1,2,5),c(3,4,5)),
             widths = c(2,2,1)
             )