Mô Hình Ngẫu Nhiên Của Tôi

#Sử dụng lệnh import file dữ liệu vào R
library(PerformanceAnalytics)

## Loading required package: xts

## Loading required package: zoo

## 
## Attaching package: 'zoo'

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

## 
## Attaching package: 'PerformanceAnalytics'

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

library(xlsx)
data <- read.xlsx("C:/Users/Admin/Desktop/Book1.xlsx", sheetIndex = 1, header = T)
PriceBID <- diff(log(data$BID), lag = 1)
PriceEIB <- diff(log(data$EIB), lag = 1)
mhnn <- data.frame(BID = PriceBID, EIB = PriceEIB)
head(mhnn,10)

##             BID          EIB
## 1  -0.009402353  0.011718678
## 2   0.025317808 -0.002908048
## 3   0.031090587 -0.023681720
## 4  -0.008968670 -0.021168846
## 5   0.014057739  0.010658591
## 6   0.067468868  0.022438968
## 7   0.042954949  0.011753007
## 8   0.005665738 -0.010298462
## 9  -0.013652089 -0.028442367
## 10  0.028234512 -0.016883160

res <- cor(mhnn)
round(res, 2)

##      BID  EIB
## BID 1.00 0.25
## EIB 0.25 1.00

library(Hmisc)

## 
## Attaching package: 'Hmisc'

## The following objects are masked from 'package:base':
## 
##     format.pval, units

res2<-rcorr(as.matrix(mhnn[,1:2]))
res2 

##      BID  EIB
## BID 1.00 0.25
## EIB 0.25 1.00
## 
## n= 497 
## 
## 
## P
##     BID EIB
## BID      0 
## EIB  0

# Hệ số tương quan Pearson
res <- cor(mhnn)
round(res, 2)

##      BID  EIB
## BID 1.00 0.25
## EIB 0.25 1.00

Phần này cung cấp một hàm đơn giản để định dạng ma trận tương quan vào bảng với 4 cột chứa:

Cột 1 : tên hàng

Cột 2 : tên cột

Cột 3 : các hệ số tương quan

Cột 4 : các giá trị p của các tương quan

flattenCorrMatrix <- function(cormat, pmat) {
  ut <- upper.tri(cormat)
  data.frame(
    row = rownames(cormat)[row(cormat)[ut]],
    column = rownames(cormat)[col(cormat)[ut]],
    cor  =(cormat)[ut],
    p = pmat[ut]
    )
}
flattenCorrMatrix(res2$r, res2$P)

##   row column       cor            p
## 1 BID    EIB 0.2522163 1.190725e-08

symnum(res, abbr.colnames = FALSE)

##     BID EIB
## BID 1      
## EIB     1  
## attr(,"legend")
## [1] 0 ' ' 0.3 '.' 0.6 ',' 0.8 '+' 0.9 '*' 0.95 'B' 1

Hàm symnum() là một trong hàm hiển thị ma trận tương quan trong phần mềm R. Nó thay thế cho các hệ số tương quan bằng các ký hiệu theo mức độ tương quan và lấy ma trận tương qaun làm đối số.

Trong đó:

res là ma trận tương quan muốn trực hóa

abbr.colnames là các giá trị logic. Nếu giá trị đúng thì các tên cột sẽ được viết tắt

library(corrplot)

## corrplot 0.92 loaded

corrplot(res, type = "upper", order = "hclust", 
         tl.col = "black", tl.srt = 45)

chart.Correlation(mhnn, histogram=TRUE, pch=19)

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

#-Tương tự cho các cặp biến khác.
library(ggplot2)
library(ggcorrplot)
df <- dplyr::select_if(mhnn, is.numeric)
r <- cor(df, use="complete.obs")
ggcorrplot(r)

2. THỰC HIỆN CÁC KIỂM ĐỊNH

***2.1 KIỂM ĐỊNH PHÂN PHỐI CHUẨN JARQUE - BERA

• Để kiểm định phân phối chuẩn sử dụng kiểm định Jarque-Bera trong R, bạn cần sử dụng hàm “jarque.bera.test()” trong gói “tseries”. Kiểm định Jarque-Bera là một phương pháp thống kê được sử dụng để kiểm tra xem một mẫu dữ liệu có tuân theo phân phối chuẩn hay không. Nó dựa trên việc kiểm tra các đặc trưng thống kê của mẫu dữ liệu, như độ lệch và độ nhọn, để nhận xét về tính chuẩn của phân phối. Giả thiết H0 là không có phân phối chuẩn.

library(tseries)

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

# kiểm định cho chỉ số VNI 
Var1 <- mhnn$BID
# Kiểm định phân phối chuẩn cho VNI 
result1 <-  jarque.bera.test(Var1)
print(result1)

## 
##  Jarque Bera Test
## 
## data:  Var1
## X-squared = 101.6, df = 2, p-value < 2.2e-16

Kết quả của kiểm định sẽ bao gồm giá trị chi-squared = 101.6 và p_value= 0.00000000000000022. Ta có p_value= 0.00000000000000022 < Với alpha = 0.05 thì bác bỏ giả thuyết H0. Kết luận rằng dữ liệu tuân theo phân phối chuẩn.

2.2 Kiểm định tính dừng: Augmented Dickey–Fuller

• Tương tư với Kiểm định phân phối chuẩn: Jarque-Bera thì Kiểm định tính dừng: Augmented Dickey–Fuller cũng sủ dụng gói “tseries”. Kiểm định ADF được sử dụng để kiểm tra xem một chuỗi thời gian có tính dừng hay không. Giả thiết H0 là chuỗi thời gian không có tính dừng.

Dưới đây là cách thực hiện kiểm định ADF

adf.test(Var1)

## Warning in adf.test(Var1): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  Var1
## Dickey-Fuller = -7.7697, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary

print(adf.test(Var1))

## Warning in adf.test(Var1): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  Var1
## Dickey-Fuller = -7.7697, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary

Hàm “adf.test()” sẽ trả về kết quả của kiểm định ADF, bao gồm giá trị của thống kê kiểm định và giá trị p-value. Nếu p-value nhỏ hơn một mức ý nghĩa đã chọn (ví dụ: 0.05), bạn có thể bác bỏ giả thuyết rằng chuỗi thời gian không có tính dừng.

Kết quả chạy kiểm định của kiểm định ADF trên, bao gồm giá trị của thống kê kiểm định về tính dừng là Dickey-Fuller = -7.7697 và giá trị p-value = 0.01 . Ta có p-value = 0.01 < alpha = 0.05, bạn có thể bác bỏ giả thuyết H0 . Kết luận rằng chuỗi thời gian có tính dừng.

2.3 Kiểm định tương quan chuỗi: Ljung-Box

-Trong R, bạn có thể sử dụng hàm Box.test() trong gói “stats” để thực hiện kiểm định tương quan chuỗi Ljung-Box. Kiểm định Ljung-Box được sử dụng để kiểm tra tính tương quan tự do của một chuỗi thời gian và xác định xem chuỗi có phụ thuộc tương quan không gian hay không. Giả thiết H0 là không có tương quan chuỗi Ljung-Box.

# Kiểm định tương quan chuỗi cho BID 
library(stats)
result2 <-  Box.test(Var1, lag = 10, type = "Ljung-Box")
print(result2)

## 
##  Box-Ljung test
## 
## data:  Var1
## X-squared = 17.381, df = 10, p-value = 0.06635

Trong đó, ‘Var1’ là vector chuỗi thời gian mà bạn muốn kiểm tra, ‘lag’ là số lượng lag mà bạn muốn sử dụng trong kiểm định, và type = “Ljung-Box” để chỉ định sử dụng kiểm định Ljung-Box.

Kết quả của kiểm định Ljung-Box sẽ bao gồm giá trị của thống kê kiểm định (Q statistic) và giá trị p-value. Giá trị p-value thường được so sánh với một mức ý nghĩa nhất định (ví dụ: 0.05) để xác định xem có sự tồn tại của tương quan không gian trong chuỗi thời gian hay không. Nếu giá trị p-value nhỏ hơn mức ý nghĩa, ta có thể kết luận rằng có sự tồn tại của tương quan không gian trong chuỗi thời gian.

Kết quả chạy kiểm định của kiểm định Ljung-Box sẽ bao gồm giá trị của thống kê kiểm định (Q statistic) = 17.381 và giá trị p-value = 0.06635. Với giá trị p-value = 0.06635 > 0.05, Chấp nhận rằng không có tương quan không gian trong chuỗi thời gian

Kiểm định mô hình ARIMA chi biến BID

library(tseries)
library(forecast)
modeld <- auto.arima(mhnn$BID)
modeld

## Series: mhnn$BID 
## ARIMA(3,0,1) with zero mean 
## 
## Coefficients:
##          ar1      ar2     ar3      ma1
##       0.7693  -0.0222  0.1357  -0.8617
## s.e.  0.1022   0.0567  0.0449   0.0943
## 
## sigma^2 = 0.0005403:  log likelihood = 1166.32
## AIC=-2322.64   AICc=-2322.52   BIC=-2301.6

Kiểm định mô hình ARIMA chi biến EIB

library(tseries)
library(forecast)
modeld1 <- auto.arima(mhnn$EIB)
modeld1

## Series: mhnn$EIB 
## ARIMA(1,0,1) with zero mean 
## 
## Coefficients:
##          ar1      ma1
##       0.7338  -0.6183
## s.e.  0.1441   0.1670
## 
## sigma^2 = 0.000801:  log likelihood = 1067.5
## AIC=-2129   AICc=-2128.95   BIC=-2116.37

# Trích xuất phần dư
d <- residuals(modeld1)
d

## Time Series:
## Start = 1 
## End = 497 
## Frequency = 1 
##   [1]  1.155294e-02 -4.441149e-03 -2.423002e-02 -1.872809e-02  1.461712e-02
##   [6]  2.365028e-02  9.908452e-03 -1.279636e-02 -2.879717e-02 -1.381762e-02
##  [11]  3.845277e-03  1.010046e-02  2.479752e-02  9.489128e-03  2.911668e-02
##  [16]  4.509742e-03 -3.113575e-03  5.612816e-02 -4.954224e-02 -7.603445e-03
##  [21] -2.512202e-02  8.945211e-03  2.389459e-02  1.894065e-02  1.548940e-02
##  [26] -4.408533e-02  1.023753e-02 -3.957462e-03 -1.761519e-02 -6.053956e-03
##  [31] -5.633233e-02  2.637313e-02  4.103410e-02 -3.302354e-02  1.997436e-03
##  [36] -5.494375e-02  8.787940e-03 -1.299083e-02  6.174248e-02 -9.737914e-03
##  [41]  4.552694e-02 -1.946512e-02  2.910726e-02  2.816175e-02  3.809340e-03
##  [46]  6.476072e-03 -2.101788e-02 -2.446961e-02  7.537888e-03  1.945442e-03
##  [51]  1.935438e-02 -2.123199e-02  1.600329e-02 -2.541449e-03  1.963697e-02
##  [56] -5.342517e-03 -1.482161e-02  8.817015e-03 -1.403298e-02 -9.687080e-03
##  [61]  6.167808e-03 -1.023586e-02 -2.495674e-02 -3.355472e-02  1.577437e-02
##  [66] -5.567233e-03 -1.773856e-01 -2.808960e-02  1.038468e-02  1.183183e-02
##  [71] -1.089086e-02  4.268852e-02 -4.779220e-02  2.068021e-02  3.572301e-03
##  [76] -2.529208e-02  3.674605e-03 -1.963135e-02  2.418440e-02 -1.165262e-02
##  [81] -5.353221e-03  1.656376e-03  6.839423e-02 -2.385963e-03 -1.446915e-02
##  [86] -8.419876e-03  1.232595e-02 -1.773562e-03 -3.664879e-02  1.973643e-02
##  [91] -1.369175e-03  2.432175e-02  2.553539e-02 -4.831808e-03  4.507205e-02
##  [96] -1.035018e-02 -2.804514e-02 -2.116208e-02 -1.450798e-02 -1.065313e-02
## [101]  2.208648e-03 -2.807690e-02  2.456428e-02 -2.346302e-02  5.014742e-03
## [106]  1.821200e-02  1.217863e-02 -2.129250e-02 -2.233627e-03  2.525564e-02
## [111] -5.843496e-04  1.676274e-03  5.008949e-03  3.184503e-03 -1.415876e-02
## [116]  5.365012e-04  6.501094e-02 -5.458080e-02  9.727131e-04  1.300265e-02
## [121] -1.060325e-03  2.442598e-03 -1.626260e-02 -1.920160e-02 -3.204124e-03
## [126] -1.351548e-02  1.653718e-02 -4.152578e-03 -3.881116e-03  7.645286e-03
## [131] -9.768686e-03  2.773899e-03  2.108702e-03 -1.492812e-03  3.484040e-03
## [136] -9.959196e-03 -1.223017e-02 -1.202913e-03  5.786886e-05  2.902442e-03
## [141]  5.572173e-03  4.749111e-03  1.565462e-02 -1.045170e-02 -5.425847e-03
## [146] -6.330018e-03  9.212837e-04 -6.110540e-03  1.123696e-03 -9.586093e-04
## [151]  2.273945e-03  1.927390e-04  1.191722e-04 -3.235854e-03 -6.272020e-03
## [156]  7.738041e-03  6.523413e-03 -4.195756e-03 -3.448770e-03  4.285179e-02
## [161] -1.279708e-02 -1.660368e-02 -4.478967e-03 -8.303832e-04  7.200702e-04
## [166]  2.126212e-03  9.877187e-03 -2.699464e-03 -5.398796e-03  1.494978e-02
## [171]  6.572167e-02  5.715157e-02 -4.756000e-02  1.914901e-02  6.199454e-03
## [176] -2.744009e-02  1.569603e-02 -1.194711e-02  1.141372e-02  1.001346e-02
## [181] -1.631883e-02  4.907071e-02 -7.731441e-02 -2.174487e-02 -1.818212e-02
## [186]  7.354278e-02  5.775021e-02 -2.624681e-03 -6.555408e-03 -9.434855e-03
## [191] -1.884657e-03  2.022690e-02 -2.730415e-02  3.532601e-03  1.876626e-04
## [196]  1.454594e-03 -1.421404e-03 -5.307343e-03 -7.501963e-03  6.760131e-02
## [201]  1.602888e-02  4.445015e-02 -7.405182e-02 -6.174941e-02 -1.945091e-02
## [206] -4.761097e-02  3.894350e-02 -6.563502e-02 -6.097264e-02  1.425781e-03
## [211] -6.195102e-02 -5.750351e-02 -5.426864e-02 -5.156477e-02 -5.136496e-02
## [216] -5.109012e-02 -5.067283e-02  8.791085e-02 -6.670123e-02  7.869561e-02
## [221]  7.257296e-03 -2.723227e-02  1.015567e-02  1.863578e-02  6.528628e-02
## [226]  4.727020e-02 -5.846176e-02  2.150026e-02  1.669523e-02 -7.318248e-02
## [231] -4.509545e-02  7.578600e-02  6.493822e-02  5.797684e-02  5.344799e-02
## [236]  4.853310e-02  1.162144e-02 -3.576195e-02  1.187200e-02  1.536591e-02
## [241]  4.355411e-03 -3.316804e-02 -5.210338e-03 -6.033751e-02  4.124151e-02
## [246]  2.983448e-02 -3.566230e-02  3.657326e-02 -2.266865e-02 -8.547978e-03
## [251]  1.786851e-02  1.692604e-02  2.188349e-02 -2.910010e-02 -6.996934e-02
## [256] -3.879660e-02  4.001503e-02  4.112589e-02 -2.520773e-03 -3.413068e-03
## [261]  1.409518e-02 -7.731956e-03 -3.654360e-02  3.702939e-03 -9.323192e-03
## [266] -1.295833e-02  3.519468e-03  2.174057e-02 -3.241482e-02 -1.914898e-02
## [271]  1.259907e-02 -6.960257e-02 -6.289268e-02  4.862594e-02 -4.623749e-02
## [276]  5.533927e-02  4.625184e-02 -7.858863e-03  5.042657e-02 -3.307734e-02
## [281] -7.152952e-03 -2.388233e-02 -4.861380e-02 -3.809351e-03  5.777302e-03
## [286]  2.285534e-02 -1.930147e-02  1.601798e-02  6.600628e-02  3.735086e-02
## [291] -1.002795e-02 -1.295711e-03 -2.410610e-02 -3.849683e-02  3.716897e-02
## [296]  1.264104e-03 -2.634722e-02 -3.953115e-02 -4.538290e-03  2.909650e-02
## [301]  3.723666e-04  5.433421e-03  4.779161e-03 -1.132932e-02 -4.636344e-03
## [306]  3.635954e-03 -2.292295e-03  3.685857e-02 -6.418484e-03  4.210226e-04
## [311] -1.700763e-02 -9.656190e-03  1.696305e-03  8.925804e-03  1.518830e-02
## [316]  5.860617e-04  6.121453e-03 -1.804323e-03 -1.386308e-02  2.363573e-02
## [321] -1.226145e-02 -2.576388e-02 -5.023103e-03 -1.314274e-02  8.801199e-03
## [326]  1.203334e-02 -1.075764e-02 -6.910274e-03  6.903861e-03  5.598334e-03
## [331]  7.490374e-03  2.217753e-02 -1.371808e-02 -9.138073e-04  2.053824e-03
## [336] -5.835212e-03 -2.337419e-02  1.076148e-02  3.448327e-03  2.867707e-02
## [341] -5.645373e-04 -9.962254e-03 -8.212782e-03  1.089697e-02  3.433573e-02
## [346]  5.282625e-03 -1.138009e-02  2.513115e-02  1.259534e-02 -3.072435e-02
## [351]  1.469717e-02  2.211463e-02 -3.442511e-02 -3.532687e-03  3.228986e-02
## [356]  4.265637e-03 -2.127646e-02 -1.606626e-02  4.700505e-03 -1.335869e-02
## [361]  1.451993e-02  4.843003e-03  1.142462e-02 -1.688063e-03 -1.043744e-03
## [366] -1.733779e-02  3.914308e-03  1.026783e-02  1.109184e-02 -3.280861e-02
## [371] -1.223905e-02 -1.665096e-03 -9.898951e-03  1.793503e-02  5.088137e-03
## [376] -4.795539e-04 -2.965123e-04 -5.124201e-03  2.901675e-03  3.394654e-02
## [381] -1.590377e-02 -1.558934e-02 -3.127177e-02  1.939637e-02  9.686341e-04
## [386]  1.047136e-02 -8.179658e-03 -2.082871e-03  1.780467e-02  2.721502e-02
## [391]  1.445269e-02  6.270607e-02 -3.060506e-02  5.177897e-02 -2.936137e-03
## [396] -1.837055e-04 -5.863379e-04 -1.279769e-03 -2.328265e-03  2.899140e-02
## [401] -1.646604e-02  1.473515e-02 -1.874354e-02 -7.107540e-02  8.354840e-03
## [406]  2.879181e-02  4.655752e-04  2.390077e-03  1.674316e-02  5.863476e-02
## [411] -2.804102e-02  9.167007e-03  2.417034e-02 -2.251724e-02 -1.123195e-03
## [416] -6.944813e-04 -2.417246e-03 -1.985152e-02  1.814072e-02 -4.320729e-04
## [421] -2.671544e-04 -1.651839e-04 -6.725499e-02 -2.436583e-02  2.992761e-02
## [426] -1.871855e-02  9.705560e-03 -6.941801e-02 -3.251889e-02  4.715618e-02
## [431] -3.693519e-02  3.427404e-02 -1.356366e-02 -5.326105e-02  1.941875e-02
## [436] -1.456070e-02  2.784085e-02  1.435020e-02  1.538388e-02 -2.668682e-04
## [441] -1.364284e-02 -7.303204e-05 -1.157266e-02 -1.599385e-03 -1.350043e-02
## [446]  1.120713e-02  3.495042e-02 -8.748351e-04  2.790467e-02 -1.612764e-02
## [451] -5.291063e-02  3.899951e-02 -2.953945e-02 -2.371302e-02  2.232540e-02
## [456]  2.675501e-02  8.836529e-03  8.345420e-03 -1.984601e-02  2.791901e-02
## [461] -5.929824e-03 -2.393281e-02  4.367786e-03  6.587703e-02  3.330323e-03
## [466] -1.084659e-02 -2.940145e-02 -9.524825e-03  1.016286e-02  2.954454e-02
## [471] -4.051051e-02  1.852314e-02 -2.203705e-02 -5.989691e-03 -4.225826e-04
## [476]  7.272639e-03  5.933231e-03  2.127022e-02 -1.076868e-02  1.794357e-02
## [481]  5.283610e-03  8.733587e-05 -7.118809e-03 -5.496585e-04 -3.398586e-04
## [486] -2.687838e-02 -1.065570e-02 -1.596909e-02  2.643604e-02  8.291769e-03
## [491] -9.026653e-03  4.089572e-04 -2.483118e-03  4.723211e-04  2.920403e-04
## [496]  5.645065e-03 -5.194382e-04

Kiểm định Arch LM cho biến BID

library(lmtest)
library(fGarch)

## NOTE: Packages 'fBasics', 'timeDate', and 'timeSeries' are no longer
## attached to the search() path when 'fGarch' is attached.
## 
## If needed attach them yourself in your R script by e.g.,
##         require("timeSeries")

## 
## Attaching package: 'fGarch'

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

library(rugarch)

## Loading required package: parallel

## 
## Attaching package: 'rugarch'

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

# Kiểm định hiệu ứng ARCH - LM  cho chỉ số chứng khoán 
arch_spec <- ugarchspec(variance.model = list(model = "sGARCH"))
arch_BID <- ugarchfit(spec = arch_spec, data = mhnn$BID)

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

## 
##  studentized Breusch-Pagan test
## 
## data:  arch_lm_model
## BP = 10.165, df = 1, p-value = 0.001431

Kiểm định Arch LM cho biến EIB

library(lmtest)
library(fGarch)
library(rugarch)
# Kiểm định hiệu ứng ARCH - LM  cho chỉ số chứng khoán 
arch_spec1 <- ugarchspec(variance.model = list(model = "sGARCH"))
arch_EIB <- ugarchfit(spec = arch_spec1, data = mhnn$EIB)

residuals1 <- residuals(arch_EIB)
n1 <- length(residuals1)
x1 <- 1:n
# Tạo mô hình tuyến tính
arch_lm_model1 <- lm(residuals1^2 ~ x)
# Kiểm định hiệu ứng ARCH-LM
arch1 <- bptest(arch_lm_model1)
# Hiển thị kết quả
arch1

## 
##  studentized Breusch-Pagan test
## 
## data:  arch_lm_model1
## BP = 1.8834, df = 1, p-value = 0.1699

Chạy mô hình Garch cho biến BID

library(rugarch)
BIDts<- ts(mhnn$BID)
print(BIDts)

## Time Series:
## Start = 1 
## End = 497 
## Frequency = 1 
##   [1] -0.009402353  0.025317808  0.031090587 -0.008968670  0.014057739
##   [6]  0.067468868  0.042954949  0.005665738 -0.013652089  0.028234512
##  [11] -0.028234512  0.067540882  0.013822655 -0.009549144  0.043802623
##  [16] -0.018538121 -0.010449416  0.007326040 -0.011536573 -0.001055409
##  [21]  0.021932994  0.000000000 -0.010384309 -0.068024060  0.031888353
##  [26] -0.022989518  0.018651117 -0.028667895  0.012229169  0.016438726
##  [31] -0.008733680 -0.022173857 -0.001121705 -0.019264052  0.009111680
##  [36] -0.038132870  0.008211190  0.011614532 -0.024548281 -0.015504187
##  [41] -0.026798193  0.011049836  0.021739987 -0.013229297  0.019185241
##  [46] -0.011947573  0.044660771  0.009153382 -0.002280503 -0.006872879
##  [51] -0.002301497 -0.006936444  0.008087855 -0.043510684  0.019048195
##  [56]  0.026761341 -0.001148765  0.019351771 -0.002257337 -0.021702736
##  [61]  0.004608303 -0.010398707 -0.027076404 -0.035219183  0.011063420
##  [66] -0.009828089 -0.030077455 -0.034955015  0.000000000  0.000000000
##  [71]  0.014388737  0.000000000 -0.071314674  0.028867984  0.008097210
##  [76] -0.013532006 -0.104603914  0.000000000  0.025183175 -0.031921908
##  [81] -0.071382260  0.038439124  0.008338084 -0.071783893 -0.055049652
##  [86]  0.012501704  0.067554634  0.012967147 -0.007194042 -0.004334867
##  [91] -0.033918447  0.011924297  0.033523059  0.005698938  0.005698568
##  [96]  0.012656991 -0.012656991 -0.004254849 -0.012906736 -0.010118571
## [101] -0.004372777 -0.017718406  0.020613811  0.005831111 -0.020492723
## [106] -0.056299787  0.010909518 -0.009358802  0.009358802 -0.021903706
## [111] -0.068784023  0.026760727  0.006561290  0.016271844  0.006449765
## [116]  0.017472071  0.058118221  0.036465713 -0.040929631  0.045214915
## [121]  0.000000000  0.035034776 -0.019466784  0.019466784 -0.036450432
## [126] -0.014398537  0.053608105 -0.009674836  0.002778256 -0.009710639
## [131] -0.008439936  0.004213067  0.020834087  0.002751544 -0.027798697
## [136] -0.002797382  0.004224844  0.000000000  0.026371236  0.021683549
## [141]  0.044551587 -0.012883141  0.020539838  0.000000000 -0.007656697
## [146] -0.005127548 -0.003870278 -0.006493719 -0.002615226  0.023236908
## [151]  0.044886626 -0.012278576 -0.012403043 -0.010051474 -0.006337446
## [156] -0.023147371  0.026948951 -0.005091107  0.000000000  0.002548794
## [161] -0.010205490  0.020307880  0.005027265 -0.012587341  0.013826150
## [166] -0.057830625 -0.029528692  0.008134601 -0.002683829 -0.002721673
## [171] -0.008178873 -0.020776241 -0.007022456 -0.037287468  0.027398084
## [176] -0.011446384  0.011446384 -0.011446384 -0.039624206  0.008934629
## [181] -0.005936328  0.000000000  0.011870866 -0.071862867 -0.017584138
## [186]  0.025482286 -0.025482286 -0.059807042  0.027031760 -0.051289340
## [191]  0.066165740  0.063622147  0.016804803 -0.009124965  0.003028011
## [196]  0.006096953  0.004531447 -0.016728186 -0.071529382  0.030821165
## [201]  0.012700287  0.067123606 -0.002962866  0.021928895 -0.014554672
## [206] -0.010345895 -0.020984399  0.009042452  0.000000000  0.046935250
## [211]  0.035182616 -0.040946694  0.036792061 -0.002789839 -0.072166076
## [216]  0.066594505 -0.001421464  0.008404601 -0.012617668  0.026408414
## [221]  0.025728915  0.015932424  0.051299225 -0.012587341  0.037268959
## [226]  0.002443210 -0.052459974  0.054869877  0.001230097 -0.053531615
## [231] -0.002568359  0.000000000  0.005130138 -0.028458390  0.015612478
## [236]  0.002588226  0.005127548 -0.002574972 -0.002552576 -0.007755593
## [241]  0.002572424  0.010310717  0.000000000 -0.005127548  0.030462693
## [246]  0.046404759 -0.046404759 -0.035645862  0.065180594 -0.009729896
## [251] -0.001243661  0.021855057 -0.015734614  0.007284510 -0.001201300
## [256]  0.004823752  0.008419677  0.067066125  0.005581129  0.003328790
## [261]  0.018689357 -0.030957907 -0.001113614  0.013382164 -0.052344611
## [266]  0.008155176  0.004611845  0.037376323 -0.027031760  0.015850862
## [271] -0.011307325 -0.024159396  0.033210385 -0.022769970  0.013718980
## [276]  0.022488223  0.017598965  0.030125753 -0.020331835 -0.027392883
## [281]  0.012146402 -0.021076044 -0.007888937 -0.003392817  0.034532517
## [286]  0.016307104 -0.010841803 -0.002187459  0.023754779  0.023180082
## [291] -0.007328112 -0.010555944 -0.019256887 -0.026291644  0.038111769
## [296] -0.011820125  0.001071498 -0.020731355  0.000000000  0.016414012
## [301] -0.004360614 -0.007640021  0.009822705  0.000000000  0.004326736
## [306]  0.000000000  0.000000000 -0.006509420  0.002182684 -0.010936608
## [311]  0.010936608 -0.007647986 -0.021029774 -0.006728581  0.000000000
## [316]  0.012309710 -0.011193582  0.012321105 -0.008929641 -0.004507592
## [321]  0.004507592 -0.009010099 -0.011384446 -0.003435586  0.012548378
## [326] -0.004558850 -0.009154621  0.005734672 -0.006875189  0.028356732
## [331]  0.008909919 -0.002201267  0.000000000  0.000000000 -0.002231220
## [336]  0.002231220 -0.004467430 -0.003351100 -0.005618703  0.000000000
## [341] -0.012463130 -0.008024503  0.005734672 -0.008017008  0.011436957
## [346] -0.002261514  0.004543537 -0.002282023  0.018061593  0.000000000
## [351]  0.002241222 -0.010087178 -0.014769578 -0.005741197  0.004605918
## [356]  0.015904857 -0.007933614 -0.003412141 -0.003423823 -0.009196599
## [361]  0.004595919 -0.002282336  0.012591440  0.007917091  0.000000000
## [366]  0.000000000  0.023431698 -0.018913924 -0.026195425  0.026195425
## [371] -0.011307325  0.007933614 -0.009061154  0.007917091  0.058109067
## [376] -0.008557259  0.003214543  0.004286065 -0.003224878 -0.011833023
## [381]  0.010771836 -0.009674796  0.000000000  0.010735983  0.001084142
## [386]  0.007436762  0.004245278 -0.013827369  0.000000000  0.010657039
## [391]  0.020955915  0.018508109 -0.011263304 -0.003091839  0.009246986
## [396] -0.004091498 -0.009308454 -0.035893234  0.004280280  0.019096910
## [401] -0.012698659  0.010589429 -0.008457768 -0.063537332  0.031174094
## [406]  0.004364612 -0.002167595  0.002167595 -0.013176335  0.004427978
## [411]  0.008748357  0.008696879  0.016114551  0.011644964 -0.004208030
## [416]  0.001047719 -0.007429117 -0.010678531  0.010678531  0.000000000
## [421] -0.005337064  0.001084142 -0.022697253 -0.012093125  0.011008740
## [426] -0.011008740  0.018623800 -0.020845164 -0.016755875  0.001117375
## [431] -0.001117375  0.000000000 -0.009061154 -0.056161953  0.022606044
## [436] -0.021413406  0.014335331 -0.005945862  0.002387949 -0.001206677
## [441]  0.003562202  0.008280463 -0.020195132 -0.008450104 -0.031966129
## [446]  0.004974086  0.007428957 -0.004937180  0.024500266 -0.013404953
## [451] -0.004906795  0.035114318 -0.024087081 -0.019707532 -0.004974086
## [456]  0.040416233 -0.003604975  0.007197001  0.000000000  0.025972030
## [461] -0.001156465 -0.015290534 -0.002379458  0.021161588  0.026379930
## [466] -0.009102510 -0.019612552  0.005814579  0.018372405 -0.008006118
## [471] -0.013845734  0.015008150 -0.015008150  0.017972643  0.011516442
## [476] -0.011516442  0.014057739  0.010101096 -0.003775964  0.008788506
## [481]  0.014888612  0.031517760 -0.012004946  0.012004946 -0.007185660
## [486]  0.000000000 -0.002406740 -0.012121361  0.004866190  0.002424244
## [491]  0.012033840  0.015430573  0.017513582 -0.004640380  0.000000000
## [496] -0.007001195  0.016260521

library(lmtest)
BIDspec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,1)), mean.model = list(armaOrder = c(3,1), include.mean =TRUE), distribution.model = 'norm')
print(BIDspec)

## 
## *---------------------------------*
## *       GARCH Model Spec          *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## ------------------------------------
## GARCH Model      : gjrGARCH(1,1)
## Variance Targeting   : FALSE 
## 
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model       : ARFIMA(3,0,1)
## Include Mean     : TRUE 
## GARCH-in-Mean        : FALSE 
## 
## Conditional Distribution
## ------------------------------------
## Distribution :  norm 
## Includes Skew    :  FALSE 
## Includes Shape   :  FALSE 
## Includes Lambda  :  FALSE

BIDfit <- ugarchfit(spec = BIDspec, BIDts)
print(BIDfit)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(3,0,1)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu     -0.000113    0.001082  -0.10476 0.916564
## ar1     0.788022    0.091605   8.60234 0.000000
## ar2     0.005128    0.062224   0.08242 0.934313
## ar3     0.100704    0.048986   2.05578 0.039804
## ma1    -0.880250    0.083035 -10.60096 0.000000
## omega   0.000005    0.000005   0.95662 0.338761
## alpha1  0.014630    0.016861   0.86768 0.385570
## beta1   0.939977    0.013106  71.71924 0.000000
## gamma1  0.067348    0.025143   2.67854 0.007394
## 
## Robust Standard Errors:
##         Estimate  Std. Error    t value Pr(>|t|)
## mu     -0.000113    0.002106  -0.053825 0.957075
## ar1     0.788022    0.058473  13.476756 0.000000
## ar2     0.005128    0.061995   0.082725 0.934070
## ar3     0.100704    0.049300   2.042676 0.041085
## ma1    -0.880250    0.038689 -22.752143 0.000000
## omega   0.000005    0.000021   0.237317 0.812411
## alpha1  0.014630    0.040916   0.357568 0.720666
## beta1   0.939977    0.014531  64.689743 0.000000
## gamma1  0.067348    0.043319   1.554693 0.120019
## 
## LogLikelihood : 1206.888 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -4.8205
## Bayes        -4.7443
## Shibata      -4.8211
## Hannan-Quinn -4.7906
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                   0.0001522  0.9902
## Lag[2*(p+q)+(p+q)-1][11] 3.7751289  1.0000
## Lag[4*(p+q)+(p+q)-1][19] 6.6676625  0.9345
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                    0.09649  0.7561
## Lag[2*(p+q)+(p+q)-1][5]   3.27964  0.3583
## Lag[4*(p+q)+(p+q)-1][9]   4.73773  0.4689
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]    0.9825 0.500 2.000  0.3216
## ARCH Lag[5]    1.8882 1.440 1.667  0.4965
## ARCH Lag[7]    2.8504 2.315 1.543  0.5422
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  1.1488
## Individual Statistics:              
## mu     0.04957
## ar1    0.20316
## ar2    0.20940
## ar3    0.16055
## ma1    0.25087
## omega  0.08611
## alpha1 0.16855
## beta1  0.18953
## gamma1 0.11350
## 
## 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          0.56258 0.5740    
## Negative Sign Bias 0.05868 0.9532    
## Positive Sign Bias 0.05887 0.9531    
## Joint Effect       0.51794 0.9149    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     33.26      0.02242
## 2    30     42.09      0.05507
## 3    40     57.77      0.02685
## 4    50     64.07      0.07285
## 
## 
## Elapsed time : 0.7578611

bidst.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(3, 1), include.mean = TRUE), distribution.model = "std")

bidst1<- ugarchfit(bidst.spec,BIDts) 
print(bidst1)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(3,0,1)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      0.000019    0.000656  0.029132 0.976760
## ar1     0.755217    0.102993  7.332726 0.000000
## ar2     0.071969    0.054799  1.313313 0.189077
## ar3     0.069317    0.040126  1.727481 0.084081
## ma1    -0.910602    0.094302 -9.656242 0.000000
## omega   0.000003    0.000006  0.515175 0.606430
## alpha1  0.017523    0.022937  0.763960 0.444891
## beta1   0.948742    0.021952 43.219088 0.000000
## gamma1  0.056696    0.027662  2.049628 0.040401
## shape   4.205016    0.932747  4.508206 0.000007
## 
## Robust Standard Errors:
##         Estimate  Std. Error    t value Pr(>|t|)
## mu      0.000019    0.000673   0.028394 0.977348
## ar1     0.755217    0.054167  13.942500 0.000000
## ar2     0.071969    0.052481   1.371333 0.170271
## ar3     0.069317    0.036909   1.878060 0.060373
## ma1    -0.910602    0.034414 -26.459834 0.000000
## omega   0.000003    0.000016   0.178942 0.857984
## alpha1  0.017523    0.042124   0.415986 0.677420
## beta1   0.948742    0.049240  19.267893 0.000000
## gamma1  0.056696    0.035047   1.617720 0.105723
## shape   4.205016    1.525640   2.756232 0.005847
## 
## LogLikelihood : 1228.797 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -4.9046
## Bayes        -4.8199
## Shibata      -4.9054
## Hannan-Quinn -4.8714
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                       1.552  0.2128
## Lag[2*(p+q)+(p+q)-1][11]     6.583  0.1658
## Lag[4*(p+q)+(p+q)-1][19]    10.088  0.4537
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.1257  0.7229
## Lag[2*(p+q)+(p+q)-1][5]    3.4429  0.3321
## Lag[4*(p+q)+(p+q)-1][9]    5.8213  0.3193
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]     1.278 0.500 2.000  0.2583
## ARCH Lag[5]     2.276 1.440 1.667  0.4135
## ARCH Lag[7]     4.313 2.315 1.543  0.3036
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  2.0145
## Individual Statistics:              
## mu     0.09987
## ar1    0.05554
## ar2    0.05071
## ar3    0.05488
## ma1    0.05836
## omega  0.36771
## alpha1 0.10863
## beta1  0.09946
## gamma1 0.10358
## shape  0.09945
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          2.29 2.54 3.05
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value   prob sig
## Sign Bias          0.63823 0.5236    
## Negative Sign Bias 0.15660 0.8756    
## Positive Sign Bias 0.07355 0.9414    
## Joint Effect       0.57288 0.9026    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     20.22       0.3813
## 2    30     34.61       0.2176
## 3    40     30.89       0.8197
## 4    50     55.21       0.2515
## 
## 
## Elapsed time : 0.8513491

# Phân phối Student đối xứng (sstd)
bidst1.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(3, 1), include.mean = TRUE), distribution.model = "sstd")

bidst2<- ugarchfit(bidst1.spec,BIDts) 
print(bidst2)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(3,0,1)
## Distribution : sstd 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error  t value Pr(>|t|)
## mu      0.000050    0.000728  0.06831 0.945539
## ar1     0.755251    0.104380  7.23562 0.000000
## ar2     0.071419    0.055179  1.29431 0.195557
## ar3     0.069505    0.040257  1.72655 0.084249
## ma1    -0.910398    0.095654 -9.51760 0.000000
## omega   0.000003    0.000006  0.51177 0.608815
## alpha1  0.017469    0.022958  0.76089 0.446723
## beta1   0.948727    0.022025 43.07574 0.000000
## gamma1  0.056841    0.027790  2.04540 0.040816
## skew    1.005537    0.056541 17.78435 0.000000
## shape   4.197873    0.934579  4.49172 0.000007
## 
## Robust Standard Errors:
##         Estimate  Std. Error    t value Pr(>|t|)
## mu      0.000050    0.000803   0.061942 0.950609
## ar1     0.755251    0.057039  13.240938 0.000000
## ar2     0.071419    0.053587   1.332772 0.182607
## ar3     0.069505    0.036995   1.878748 0.060279
## ma1    -0.910398    0.035916 -25.348241 0.000000
## omega   0.000003    0.000016   0.177326 0.859253
## alpha1  0.017469    0.042414   0.411862 0.680440
## beta1   0.948727    0.049563  19.142006 0.000000
## gamma1  0.056841    0.035246   1.612686 0.106813
## skew    1.005537    0.056181  17.898107 0.000000
## shape   4.197873    1.512106   2.776176 0.005500
## 
## LogLikelihood : 1228.802 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -4.9006
## Bayes        -4.8075
## Shibata      -4.9016
## Hannan-Quinn -4.8641
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                       1.543  0.2142
## Lag[2*(p+q)+(p+q)-1][11]     6.567  0.1724
## Lag[4*(p+q)+(p+q)-1][19]    10.070  0.4566
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.1255  0.7231
## Lag[2*(p+q)+(p+q)-1][5]    3.4426  0.3321
## Lag[4*(p+q)+(p+q)-1][9]    5.8318  0.3180
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]     1.279 0.500 2.000  0.2582
## ARCH Lag[5]     2.272 1.440 1.667  0.4142
## ARCH Lag[7]     4.325 2.315 1.543  0.3021
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  2.2114
## Individual Statistics:              
## mu     0.09839
## ar1    0.05551
## ar2    0.05035
## ar3    0.05402
## ma1    0.05823
## omega  0.36844
## alpha1 0.10962
## beta1  0.10006
## gamma1 0.10461
## skew   0.12719
## shape  0.09949
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          2.49 2.75 3.27
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value   prob sig
## Sign Bias          0.63786 0.5239    
## Negative Sign Bias 0.15810 0.8744    
## Positive Sign Bias 0.07102 0.9434    
## Joint Effect       0.57316 0.9025    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     20.14       0.3860
## 2    30     33.52       0.2571
## 3    40     30.24       0.8414
## 4    50     58.03       0.1767
## 
## 
## Elapsed time : 1.16914

# Phân phối Generalized Error Distribution(ged)
bidged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(3, 1), include.mean = TRUE), distribution.model = "ged")

bidged1 <- ugarchfit(bidged.spec,BIDts) 
print(bidged1)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(3,0,1)
## Distribution : ged 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error    t value Pr(>|t|)
## mu      0.000073    0.000045    1.61362  0.10661
## ar1     0.836107    0.008185  102.15098  0.00000
## ar2     0.087804    0.004732   18.55520  0.00000
## ar3     0.041928    0.004085   10.26358  0.00000
## ma1    -0.987153    0.001298 -760.25737  0.00000
## omega   0.000004    0.000005    0.89496  0.37081
## alpha1  0.014703    0.017627    0.83416  0.40419
## beta1   0.945961    0.016285   58.08836  0.00000
## gamma1  0.055075    0.023186    2.37540  0.01753
## shape   1.080325    0.092369   11.69574  0.00000
## 
## Robust Standard Errors:
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.000073    0.000008     9.34967  0.00000
## ar1     0.836107    0.005602   149.25218  0.00000
## ar2     0.087804    0.000752   116.77545  0.00000
## ar3     0.041928    0.000603    69.50738  0.00000
## ma1    -0.987153    0.000619 -1595.86546  0.00000
## omega   0.000004    0.000011     0.40313  0.68685
## alpha1  0.014703    0.017616     0.83464  0.40392
## beta1   0.945961    0.014620    64.70417  0.00000
## gamma1  0.055075    0.024792     2.22146  0.02632
## shape   1.080325    0.091677    11.78401  0.00000
## 
## LogLikelihood : 1232.26 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -4.9186
## Bayes        -4.8339
## Shibata      -4.9193
## Hannan-Quinn -4.8853
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic   p-value
## Lag[1]                       1.485 2.229e-01
## Lag[2*(p+q)+(p+q)-1][11]    10.052 8.080e-09
## Lag[4*(p+q)+(p+q)-1][19]    16.010 1.328e-02
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.1387  0.7096
## Lag[2*(p+q)+(p+q)-1][5]    3.7653  0.2848
## Lag[4*(p+q)+(p+q)-1][9]    5.7616  0.3265
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]    0.9756 0.500 2.000  0.3233
## ARCH Lag[5]    2.4168 1.440 1.667  0.3863
## ARCH Lag[7]    3.8238 2.315 1.543  0.3727
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  1.1319
## Individual Statistics:              
## mu     0.13956
## ar1    0.04719
## ar2    0.04430
## ar3    0.05003
## ma1    0.09364
## omega  0.08297
## alpha1 0.11221
## beta1  0.09392
## gamma1 0.06809
## shape  0.04957
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          2.29 2.54 3.05
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value   prob sig
## Sign Bias           1.1230 0.2620    
## Negative Sign Bias  0.2211 0.8251    
## Positive Sign Bias  0.2423 0.8087    
## Joint Effect        1.6610 0.6456    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     19.18       0.4455
## 2    30     27.25       0.5585
## 3    40     32.82       0.7467
## 4    50     48.77       0.4822
## 
## 
## Elapsed time : 1.773942

# Phân phối Generalized Error Distribution đối xứng ("sged")
bidged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(3, 1), include.mean = TRUE), distribution.model = "sged")

bidged2 <- ugarchfit(bidged.spec,BIDts) 
print(bidged2)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,1)
## Mean Model   : ARFIMA(3,0,1)
## Distribution : sged 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error    t value Pr(>|t|)
## mu      0.000074    0.000085    0.86619 0.386385
## ar1     0.836390    0.008064  103.72168 0.000000
## ar2     0.087384    0.004593   19.02538 0.000000
## ar3     0.042156    0.003870   10.89325 0.000000
## ma1    -0.987204    0.001266 -779.53639 0.000000
## omega   0.000004    0.000005    0.89620 0.370145
## alpha1  0.014635    0.017630    0.83015 0.406453
## beta1   0.946002    0.016230   58.28651 0.000000
## gamma1  0.055089    0.023276    2.36681 0.017942
## skew    1.000386    0.022491   44.47894 0.000000
## shape   1.080407    0.092363   11.69746 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.000074    0.000025     2.94729 0.003206
## ar1     0.836390    0.005602   149.30365 0.000000
## ar2     0.087384    0.000790   110.57957 0.000000
## ar3     0.042156    0.000595    70.81190 0.000000
## ma1    -0.987204    0.000617 -1598.86225 0.000000
## omega   0.000004    0.000011     0.40383 0.686340
## alpha1  0.014635    0.017624     0.83040 0.406311
## beta1   0.946002    0.014509    65.20130 0.000000
## gamma1  0.055089    0.024757     2.22518 0.026069
## skew    1.000386    0.013511    74.04217 0.000000
## shape   1.080407    0.091713    11.78027 0.000000
## 
## LogLikelihood : 1232.26 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -4.9145
## Bayes        -4.8214
## Shibata      -4.9155
## Hannan-Quinn -4.8780
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic   p-value
## Lag[1]                       1.474 2.248e-01
## Lag[2*(p+q)+(p+q)-1][11]    10.030 9.385e-09
## Lag[4*(p+q)+(p+q)-1][19]    15.982 1.357e-02
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.1384  0.7099
## Lag[2*(p+q)+(p+q)-1][5]    3.7624  0.2852
## Lag[4*(p+q)+(p+q)-1][9]    5.7579  0.3270
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]    0.9715 0.500 2.000  0.3243
## ARCH Lag[5]    2.4151 1.440 1.667  0.3866
## ARCH Lag[7]    3.8213 2.315 1.543  0.3731
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  1.3655
## Individual Statistics:              
## mu     0.13926
## ar1    0.04720
## ar2    0.04276
## ar3    0.04966
## ma1    0.09121
## omega  0.08293
## alpha1 0.11269
## beta1  0.09418
## gamma1 0.06832
## skew   0.06332
## shape  0.04960
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          2.49 2.75 3.27
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value   prob sig
## Sign Bias           0.9436 0.3458    
## Negative Sign Bias  0.1294 0.8971    
## Positive Sign Bias  0.1587 0.8740    
## Joint Effect        1.2908 0.7313    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     19.18       0.4455
## 2    30     27.73       0.5325
## 3    40     34.11       0.6924
## 4    50     49.18       0.4660
## 
## 
## Elapsed time : 2.474279

# Tạo danh sách bao gồm các phân phối và ước lượng
BID_list <- list(BIDfit,bidst1,bidst2,bidged1,bidged2)
# Tính toán các thông tin
sii_info_mat <- sapply(BID_list, infocriteria) 
print(sii_info_mat)

##           [,1]      [,2]      [,3]      [,4]      [,5]
## [1,] -4.820475 -4.904617 -4.900612 -4.918553 -4.914529
## [2,] -4.744263 -4.819937 -4.807465 -4.833873 -4.821381
## [3,] -4.821116 -4.905406 -4.901564 -4.919342 -4.915480
## [4,] -4.790562 -4.871380 -4.864052 -4.885316 -4.877968

rownames(sii_info_mat)<-rownames(infocriteria(BIDfit))
print(rownames(sii_info_mat))

## [1] "Akaike"       "Bayes"        "Shibata"      "Hannan-Quinn"

# Ước lượng mô hình Garch(2,2) với phân phối Student đối xứng (sttd)
bidst.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(3, 1), include.mean = TRUE), distribution.model = "sstd")

bidst2 <- ugarchfit(bidst.spec,BIDts) 
print(bidst2)

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(2,2)
## Mean Model   : ARFIMA(3,0,1)
## Distribution : sstd 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      0.000028    0.000724  0.038327 0.969427
## ar1     0.770523    0.117506  6.557315 0.000000
## ar2     0.060427    0.054872  1.101235 0.270794
## ar3     0.063152    0.039519  1.598009 0.110041
## ma1    -0.908374    0.108951 -8.337468 0.000000
## omega   0.000004    0.000006  0.666968 0.504792
## alpha1  0.021484    0.088328  0.243230 0.807827
## alpha2  0.000001    0.085305  0.000017 0.999986
## beta1   0.653087    0.063230 10.328745 0.000000
## beta2   0.280700    0.057115  4.914613 0.000001
## gamma1  0.212493    0.142424  1.491975 0.135706
## gamma2 -0.135209    0.130408 -1.036816 0.299821
## skew    1.006292    0.057230 17.583189 0.000000
## shape   4.231502    0.874678  4.837783 0.000001
## 
## Robust Standard Errors:
##         Estimate  Std. Error    t value Pr(>|t|)
## mu      0.000028    0.000757   0.036693 0.970730
## ar1     0.770523    0.057578  13.382242 0.000000
## ar2     0.060427    0.054141   1.116106 0.264377
## ar3     0.063152    0.038205   1.653000 0.098331
## ma1    -0.908374    0.035783 -25.385334 0.000000
## omega   0.000004    0.000012   0.322552 0.747034
## alpha1  0.021484    0.112165   0.191540 0.848102
## alpha2  0.000001    0.106044   0.000014 0.999989
## beta1   0.653087    0.013307  49.079763 0.000000
## beta2   0.280700    0.033648   8.342343 0.000000
## gamma1  0.212493    0.142970   1.486278 0.137206
## gamma2 -0.135209    0.129933  -1.040603 0.298060
## skew    1.006292    0.057326  17.553736 0.000000
## shape   4.231502    0.998305   4.238687 0.000022
## 
## LogLikelihood : 1229.938 
## 
## Information Criteria
## ------------------------------------
##                     
## Akaike       -4.8931
## Bayes        -4.7746
## Shibata      -4.8946
## Hannan-Quinn -4.8466
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                       1.185  0.2764
## Lag[2*(p+q)+(p+q)-1][11]     6.257  0.3248
## Lag[4*(p+q)+(p+q)-1][19]     9.967  0.4738
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                      0.8558  0.3549
## Lag[2*(p+q)+(p+q)-1][11]    6.7278  0.3438
## Lag[4*(p+q)+(p+q)-1][19]    8.4891  0.6201
## d.o.f=4
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[5]    0.4761 0.500 2.000  0.4902
## ARCH Lag[7]    2.3982 1.473 1.746  0.4225
## ARCH Lag[9]    2.5709 2.402 1.619  0.6469
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  1.9044
## Individual Statistics:              
## mu     0.10249
## ar1    0.04944
## ar2    0.04302
## ar3    0.05107
## ma1    0.05009
## omega  0.22021
## alpha1 0.10068
## alpha2 0.09055
## beta1  0.10095
## beta2  0.10152
## gamma1 0.08624
## gamma2 0.08409
## skew   0.12932
## shape  0.09004
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          3.08 3.34 3.9
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value   prob sig
## Sign Bias           0.4827 0.6295    
## Negative Sign Bias  0.7732 0.4398    
## Positive Sign Bias  0.0247 0.9803    
## Joint Effect        0.6297 0.8896    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     18.86       0.4662
## 2    30     21.33       0.8468
## 3    40     31.05       0.8141
## 4    50     38.31       0.8646
## 
## 
## Elapsed time : 1.799646

# Trích xuất chuỗi phần dư v của chuỗi lợi suất AGR
bid.res <- residuals(bidst2)/sigma(bidst2)
fitdist(distribution = "sstd", bid.res, control = list())

## $pars
##         mu      sigma       skew      shape 
## 0.01715115 1.03799308 1.01914732 3.89117200 
## 
## $convergence
## [1] 0
## 
## $values
## [1] 709.5176 678.7749 678.7749
## 
## $lagrange
## [1] 0
## 
## $hessian
##             [,1]      [,2]        [,3]      [,4]
## [1,]  675.905857 -42.46921 -266.742764 -4.640171
## [2,]  -42.469209 458.27743   12.771585 36.568972
## [3,] -266.742764  12.77159  384.524076  3.936309
## [4,]   -4.640171  36.56897    3.936309  4.586604
## 
## $ineqx0
## NULL
## 
## $nfuneval
## [1] 91
## 
## $outer.iter
## [1] 2
## 
## $elapsed
## Time difference of 0.06324887 secs
## 
## $vscale
## [1] 1 1 1 1 1

bid.res

##            m.c.seq.row..seq.n...seq.col..drop...FALSE.
## 0001-01-01                                 -0.40583360
## 0002-01-01                                  1.08837996
## 0003-01-01                                  1.33681674
## 0004-01-01                                 -0.24558645
## 0005-01-01                                  0.54821985
## 0006-01-01                                  3.02281350
## 0007-01-01                                  2.16277883
## 0008-01-01                                  0.59034688
## 0009-01-01                                 -0.53016249
## 0010-01-01                                  1.05801230
##        ...                                            
## 0488-01-01                                 -0.90168342
## 0489-01-01                                  0.18701453
## 0490-01-01                                  0.15494975
## 0491-01-01                                  0.91411870
## 0492-01-01                                  1.26633042
## 0493-01-01                                  1.50235198
## 0494-01-01                                 -0.10439694
## 0495-01-01                                  0.01947996
## 0496-01-01                                 -0.58421005
## 0497-01-01                                  1.13152899

s = pdist("sstd",bid.res, mu = 0.01715115, sigma =  1.03799308, skew = 1.01914732, shape = 3.89117200 )
s

##   [1] 0.298244028 0.891854823 0.926824003 0.371593439 0.749421987 0.992088614
##   [7] 0.977827242 0.764618276 0.248071153 0.886519085 0.081706523 0.985444438
##  [13] 0.837336033 0.395286601 0.964115848 0.213684991 0.265154216 0.569968729
##  [19] 0.235986740 0.422585427 0.864584540 0.547675952 0.270125284 0.004611508
##  [25] 0.745603179 0.101237345 0.762390263 0.097944597 0.653212725 0.779363279
##  [31] 0.380787973 0.136942924 0.400069780 0.143375001 0.617582729 0.042802852
##  [37] 0.556893468 0.705898065 0.137983197 0.192011690 0.081562682 0.613280694
##  [43] 0.857543289 0.310529780 0.827180395 0.286916209 0.968464714 0.777255758
##  [49] 0.540323153 0.344126099 0.412668830 0.314357387 0.657544090 0.021156788
##  [55] 0.719024975 0.922117172 0.582598845 0.870028173 0.501546699 0.116962996
##  [61] 0.525389293 0.236846288 0.067148565 0.041207477 0.577866027 0.263053570
##  [67] 0.070366551 0.051219964 0.381096132 0.452612036 0.770520072 0.547772637
##  [73] 0.006735004 0.720995299 0.654541052 0.324862682 0.002923602 0.364236728
##  [79] 0.772995550 0.186599139 0.026805102 0.745314448 0.627336457 0.038874938
##  [85] 0.073490138 0.503793735 0.951039436 0.750209364 0.492726015 0.444514878
##  [91] 0.144519100 0.583709731 0.847338229 0.644871077 0.617663286 0.682894334
##  [97] 0.348662811 0.420946404 0.291445165 0.319079237 0.394445890 0.226125409
## [103] 0.752279293 0.622215294 0.222387890 0.027836948 0.519962812 0.307032060
## [109] 0.636464848 0.193676407 0.017886848 0.671027783 0.596694353 0.755063886
## [115] 0.642016982 0.773129534 0.970503181 0.937330699 0.112678314 0.911979820
## [121] 0.550396569 0.913109489 0.262618941 0.773915028 0.081212549 0.239073363
## [127] 0.954776507 0.437524112 0.581305744 0.316661715 0.321973100 0.537028860
## [133] 0.824591710 0.607973805 0.110519237 0.374582659 0.534064130 0.502696938
## [139] 0.895154680 0.886842602 0.975817493 0.378971008 0.858837567 0.531237353
## [145] 0.346213740 0.346342951 0.368350219 0.316835758 0.397514605 0.893898837
## [151] 0.983342542 0.379872120 0.233410797 0.210171668 0.284771905 0.074450639
## [157] 0.881845315 0.415192748 0.522525016 0.552198257 0.246152430 0.876986634
## [163] 0.685932785 0.223896405 0.793203751 0.005089747 0.093496727 0.499448557
## [169] 0.421549891 0.444092083 0.309548297 0.121133957 0.289317839 0.033088537
## [175] 0.819797024 0.280460047 0.731858137 0.274615644 0.034659066 0.547355799
## [181] 0.336124175 0.498474276 0.740055800 0.006078666 0.203163978 0.801219142
## [187] 0.165265773 0.021886708 0.705432727 0.032351490 0.946836145 0.979476474
## [193] 0.849673316 0.458237769 0.541107166 0.590209517 0.587380022 0.250060008
## [199] 0.013843242 0.703932383 0.694131000 0.974847633 0.604711627 0.826290919
## [205] 0.313715016 0.323503195 0.173429215 0.579562148 0.491521519 0.951562191
## [211] 0.934639973 0.093497553 0.878939567 0.481925202 0.013712358 0.919595823
## [217] 0.543836007 0.678484638 0.312403632 0.825877626 0.859769712 0.798996289
## [223] 0.966237637 0.412989775 0.925633098 0.604511910 0.033274727 0.921224732
## [229] 0.582921375 0.040322405 0.356977694 0.421122155 0.575020240 0.127040025
## [235] 0.677802400 0.545340659 0.610195625 0.462433155 0.445055252 0.337937717
## [241] 0.520416663 0.689738430 0.528089364 0.400534866 0.916178540 0.977026005
## [247] 0.045335485 0.068372555 0.968064095 0.433632682 0.527922522 0.830805170
## [253] 0.255576761 0.621054952 0.464513719 0.600988008 0.680472192 0.991807752
## [259] 0.775202341 0.669413880 0.836371637 0.075359170 0.405450204 0.726515000
## [265] 0.017444497 0.520063761 0.542773580 0.945417962 0.139290931 0.751846981
## [271] 0.270167060 0.111544883 0.897269694 0.147614344 0.732945884 0.875083754
## [277] 0.861649684 0.943430434 0.198106369 0.079447955 0.627431055 0.119281567
## [283] 0.295655993 0.359673969 0.944324958 0.865363860 0.348009001 0.428643870
## [289] 0.892623691 0.919979915 0.426862449 0.251936843 0.102747927 0.062573400
## [295] 0.932352078 0.295005044 0.543326883 0.103256738 0.429900663 0.820508096
## [301] 0.442025801 0.312948068 0.706431138 0.518733264 0.632392061 0.511733769
## [307] 0.502761554 0.307201221 0.532955004 0.197076445 0.753866501 0.287010484
## [313] 0.069083921 0.242150639 0.423511609 0.812074289 0.225624379 0.806548917
## [319] 0.253801066 0.341062615 0.606830024 0.228756541 0.158850932 0.318791723
## [325] 0.824693072 0.391626600 0.214255094 0.640807884 0.266124415 0.971988851
## [331] 0.851537117 0.530875518 0.504023125 0.486560535 0.405177130 0.569395707
## [337] 0.324154300 0.341953766 0.251882366 0.453098433 0.103261053 0.182180318
## [343] 0.645527407 0.210912172 0.843249679 0.445669309 0.699486186 0.417372054
## [349] 0.947749510 0.597278220 0.644447904 0.144019062 0.068247895 0.212870645
## [355] 0.613710506 0.929618611 0.279193846 0.351251479 0.308755202 0.149648488
## [361] 0.622855177 0.395088039 0.894122104 0.840010990 0.583618965 0.518213572
## [367] 0.977137635 0.061391015 0.023114184 0.913282952 0.174125140 0.753395275
## [373] 0.201724764 0.735937331 0.997945841 0.494364594 0.688261674 0.629926451
## [379] 0.400038605 0.143602916 0.762092013 0.198884371 0.468313725 0.812868456
## [385] 0.588559989 0.775308785 0.689819546 0.114847466 0.430147411 0.820140832
## [391] 0.960632983 0.958501352 0.230486123 0.355925056 0.774604461 0.365560553
## [397] 0.171435013 0.007758264 0.461802873 0.925260391 0.218942580 0.785537711
## [403] 0.247956616 0.002165401 0.781075347 0.630224035 0.512004937 0.552083273
## [409] 0.213309826 0.564809039 0.704525839 0.741073725 0.863040305 0.819879448
## [415] 0.451854812 0.528071383 0.286378760 0.202298644 0.723218307 0.517687405
## [421] 0.355948950 0.504774300 0.057964729 0.165190790 0.711375272 0.217432450
## [427] 0.884502712 0.089083452 0.118530744 0.424019902 0.434576920 0.497781827
## [433] 0.237459635 0.004244073 0.712033949 0.076240904 0.746818039 0.368545064
## [439] 0.563428656 0.468748433 0.591752292 0.713304104 0.120983112 0.255793851
## [445] 0.033049099 0.499497382 0.659188161 0.412525900 0.918445021 0.250247544
## [451] 0.366521177 0.963515280 0.111400770 0.116224647 0.280340227 0.972820476
## [457] 0.542671527 0.731180537 0.515608431 0.938689827 0.562397313 0.167061811
## [463] 0.367497370 0.900495665 0.956182827 0.374735763 0.093426847 0.557169436
## [469] 0.889426930 0.343444751 0.152753311 0.803125793 0.144675960 0.868093620
## [475] 0.831321932 0.241569458 0.831189852 0.805425956 0.443093472 0.761142806
## [481] 0.885844021 0.981591674 0.279045899 0.830851010 0.277653735 0.478926849
## [487] 0.381996734 0.137040490 0.591211003 0.575236361 0.857432204 0.918319235
## [493] 0.943252082 0.442110472 0.506025824 0.228305442 0.898998955

library("copula")
library("scatterplot3d")
#Chuyển đôi dữ liệu phân phối đều
u <- pobs(s)
u

##   [1] 0.295180723 0.883534137 0.923694779 0.373493976 0.744979920 0.995983936
##   [7] 0.983935743 0.765060241 0.238955823 0.877510040 0.088353414 0.991967871
##  [13] 0.833333333 0.395582329 0.961847390 0.198795181 0.259036145 0.588353414
##  [19] 0.222891566 0.425702811 0.857429719 0.566265060 0.263052209 0.008032129
##  [25] 0.740963855 0.100401606 0.763052209 0.098393574 0.670682731 0.783132530
##  [31] 0.383534137 0.132530120 0.401606426 0.140562249 0.638554217 0.052208835
##  [37] 0.576305221 0.708835341 0.136546185 0.174698795 0.086345382 0.634538153
##  [43] 0.847389558 0.305220884 0.821285141 0.283132530 0.967871486 0.781124498
##  [49] 0.550200803 0.341365462 0.411646586 0.313253012 0.674698795 0.026104418
##  [55] 0.718875502 0.917670683 0.600401606 0.863453815 0.497991968 0.120481928
##  [61] 0.532128514 0.224899598 0.064257028 0.050200803 0.594377510 0.257028112
##  [67] 0.072289157 0.056224900 0.385542169 0.461847390 0.767068273 0.568273092
##  [73] 0.014056225 0.720883534 0.672690763 0.329317269 0.004016064 0.361445783
##  [79] 0.769076305 0.172690763 0.032128514 0.738955823 0.648594378 0.046184739
##  [85] 0.074297189 0.504016064 0.947791165 0.746987952 0.485943775 0.453815261
##  [91] 0.146586345 0.606425703 0.839357430 0.666666667 0.640562249 0.688755020
##  [97] 0.349397590 0.419678715 0.289156627 0.321285141 0.391566265 0.212851406
## [103] 0.751004016 0.644578313 0.206827309 0.034136546 0.524096386 0.297188755
## [109] 0.658634538 0.176706827 0.024096386 0.680722892 0.618473896 0.757028112
## [115] 0.662650602 0.771084337 0.969879518 0.931726908 0.114457831 0.899598394
## [121] 0.570281124 0.901606426 0.255020080 0.773092369 0.084337349 0.228915663
## [127] 0.951807229 0.443775100 0.598393574 0.315261044 0.323293173 0.548192771
## [133] 0.813253012 0.630522088 0.108433735 0.375502008 0.546184739 0.500000000
## [139] 0.891566265 0.879518072 0.977911647 0.379518072 0.849397590 0.542168675
## [145] 0.343373494 0.345381526 0.369477912 0.317269076 0.397590361 0.887550201
## [151] 0.989959839 0.381526104 0.220883534 0.190763052 0.279116466 0.076305221
## [157] 0.871485944 0.415662651 0.530120482 0.574297189 0.234939759 0.867469880
## [163] 0.690763052 0.208835341 0.789156627 0.010040161 0.094377510 0.493975904
## [169] 0.423694779 0.451807229 0.303212851 0.128514056 0.287148594 0.040160643
## [175] 0.805220884 0.277108434 0.728915663 0.267068273 0.044176707 0.564257028
## [181] 0.331325301 0.491967871 0.734939759 0.012048193 0.188755020 0.793172691
## [187] 0.160642570 0.028112450 0.706827309 0.036144578 0.943775100 0.985943775
## [193] 0.841365462 0.465863454 0.552208835 0.612449799 0.608433735 0.240963855
## [199] 0.020080321 0.702811245 0.698795181 0.975903614 0.626506024 0.819277108
## [205] 0.311244980 0.325301205 0.166666667 0.596385542 0.483935743 0.949799197
## [211] 0.929718876 0.096385542 0.869477912 0.479919679 0.018072289 0.911646586
## [217] 0.560240964 0.684738956 0.307228916 0.817269076 0.851405622 0.791164659
## [223] 0.963855422 0.413654618 0.921686747 0.624497992 0.042168675 0.915662651
## [229] 0.602409639 0.048192771 0.357429719 0.421686747 0.590361446 0.130522088
## [235] 0.682730924 0.562248996 0.632530120 0.469879518 0.455823293 0.333333333
## [241] 0.528112450 0.694779116 0.538152610 0.403614458 0.905622490 0.979919679
## [247] 0.054216867 0.068273092 0.965863454 0.439759036 0.534136546 0.823293173
## [253] 0.251004016 0.642570281 0.471887550 0.622489960 0.686746988 0.993975904
## [259] 0.777108434 0.678714859 0.831325301 0.078313253 0.407630522 0.724899598
## [265] 0.022088353 0.526104418 0.556224900 0.941767068 0.138554217 0.748995984
## [271] 0.265060241 0.112449799 0.893574297 0.150602410 0.730923695 0.865461847
## [277] 0.853413655 0.937751004 0.180722892 0.082329317 0.650602410 0.124497992
## [283] 0.293172691 0.359437751 0.939759036 0.859437751 0.347389558 0.433734940
## [289] 0.885542169 0.913654618 0.431726908 0.246987952 0.102409639 0.062248996
## [295] 0.927710843 0.291164659 0.558232932 0.104417671 0.435742972 0.811244980
## [301] 0.445783133 0.309236948 0.710843373 0.522088353 0.656626506 0.512048193
## [307] 0.502008032 0.299196787 0.544176707 0.178714859 0.755020080 0.285140562
## [313] 0.070281124 0.232931727 0.427710843 0.801204819 0.210843373 0.799196787
## [319] 0.248995984 0.335341365 0.628514056 0.216867470 0.156626506 0.319277108
## [325] 0.815261044 0.389558233 0.200803213 0.660642570 0.261044177 0.971887550
## [331] 0.843373494 0.540160643 0.506024096 0.481927711 0.405622490 0.586345382
## [337] 0.327309237 0.337349398 0.244979920 0.463855422 0.106425703 0.170682731
## [343] 0.668674699 0.192771084 0.837349398 0.457831325 0.700803213 0.417670683
## [349] 0.945783133 0.620481928 0.664658635 0.144578313 0.066265060 0.194779116
## [355] 0.636546185 0.925702811 0.273092369 0.351405622 0.301204819 0.152610442
## [361] 0.646586345 0.393574297 0.889558233 0.835341365 0.604417671 0.520080321
## [367] 0.981927711 0.060240964 0.030120482 0.903614458 0.168674699 0.753012048
## [373] 0.184738956 0.732931727 0.997991968 0.487951807 0.692771084 0.652610442
## [379] 0.399598394 0.142570281 0.761044177 0.182730924 0.473895582 0.803212851
## [385] 0.610441767 0.779116466 0.696787149 0.116465863 0.437751004 0.809236948
## [391] 0.957831325 0.955823293 0.218875502 0.353413655 0.775100402 0.363453815
## [397] 0.164658635 0.016064257 0.467871486 0.919678715 0.204819277 0.787148594
## [403] 0.236947791 0.002008032 0.785140562 0.654618474 0.514056225 0.572289157
## [409] 0.196787149 0.584337349 0.704819277 0.736947791 0.855421687 0.807228916
## [415] 0.459839357 0.536144578 0.281124498 0.186746988 0.722891566 0.518072289
## [421] 0.355421687 0.508032129 0.058232932 0.158634538 0.712851406 0.202811245
## [427] 0.873493976 0.090361446 0.122489960 0.429718876 0.441767068 0.489959839
## [433] 0.226907631 0.006024096 0.714859438 0.080321285 0.742971888 0.371485944
## [439] 0.582329317 0.475903614 0.616465863 0.716867470 0.126506024 0.253012048
## [445] 0.038152610 0.495983936 0.676706827 0.409638554 0.909638554 0.242971888
## [451] 0.365461847 0.959839357 0.110441767 0.118473896 0.275100402 0.973895582
## [457] 0.554216867 0.726907631 0.516064257 0.933734940 0.580321285 0.162650602
## [463] 0.367469880 0.897590361 0.953815261 0.377510040 0.092369478 0.578313253
## [469] 0.881526104 0.339357430 0.154618474 0.795180723 0.148594378 0.861445783
## [475] 0.829317269 0.230923695 0.827309237 0.797188755 0.449799197 0.759036145
## [481] 0.875502008 0.987951807 0.271084337 0.825301205 0.269076305 0.477911647
## [487] 0.387550201 0.134538153 0.614457831 0.592369478 0.845381526 0.907630522
## [493] 0.935742972 0.447791165 0.510040161 0.214859438 0.895582329

k <- pobs(d)
k

##   [1] 0.730923695 0.395582329 0.152610442 0.202811245 0.759036145 0.847389558
##   [7] 0.700803213 0.269076305 0.120481928 0.246987952 0.608433735 0.704819277
##  [13] 0.859437751 0.694779116 0.893574297 0.618473896 0.417670683 0.961847390
##  [19] 0.058232932 0.341365462 0.144578313 0.690763052 0.849397590 0.811244980
##  [25] 0.773092369 0.072289157 0.710843373 0.401606426 0.208835341 0.361445783
##  [31] 0.038152610 0.867469880 0.925702811 0.100401606 0.564257028 0.040160643
##  [37] 0.680722892 0.263052209 0.971887550 0.315261044 0.939759036 0.190763052
##  [43] 0.891566265 0.881526104 0.606425703 0.656626506 0.182730924 0.148594378
##  [49] 0.668674699 0.562248996 0.815261044 0.178714859 0.781124498 0.425702811
##  [55] 0.821285141 0.377510040 0.232931727 0.684738956 0.242971888 0.317269076
##  [61] 0.652610442 0.303212851 0.146586345 0.094377510 0.779116466 0.369477912
##  [67] 0.002008032 0.122489960 0.714859438 0.734939759 0.287148594 0.931726908
##  [73] 0.062248996 0.827309237 0.598393574 0.142570281 0.602409639 0.188755020
##  [79] 0.853413655 0.279116466 0.375502008 0.556224900 0.989959839 0.433734940
##  [85] 0.238955823 0.331325301 0.742971888 0.447791165 0.084337349 0.823293173
##  [91] 0.459839357 0.855421687 0.865461847 0.387550201 0.937751004 0.301204819
##  [97] 0.126506024 0.180722892 0.236947791 0.297188755 0.572289157 0.124497992
## [103] 0.857429719 0.162650602 0.630522088 0.805220884 0.740963855 0.174698795
## [109] 0.439759036 0.863453815 0.485943775 0.558232932 0.628514056 0.586345382
## [115] 0.240963855 0.536144578 0.977911647 0.042168675 0.546184739 0.748995984
## [121] 0.469879518 0.578313253 0.220883534 0.196787149 0.415662651 0.255020080
## [127] 0.787148594 0.399598394 0.403614458 0.670682731 0.313253012 0.580321285
## [133] 0.568273092 0.455823293 0.592369478 0.309236948 0.275100402 0.465863454
## [139] 0.514056225 0.584337349 0.640562249 0.622489960 0.775100402 0.299196787
## [145] 0.371485944 0.355421687 0.542168675 0.359437751 0.548192771 0.473895582
## [151] 0.574297189 0.522088353 0.518072289 0.413654618 0.357429719 0.672690763
## [157] 0.658634538 0.397590361 0.409638554 0.933734940 0.267068273 0.214859438
## [163] 0.393574297 0.479919679 0.540160643 0.570281124 0.698795181 0.421686747
## [169] 0.373493976 0.765060241 0.981927711 0.963855422 0.066265060 0.813253012
## [175] 0.654618474 0.130522088 0.777108434 0.277108434 0.726907631 0.702811245
## [181] 0.218875502 0.951807229 0.004016064 0.172690763 0.206827309 0.991967871
## [187] 0.965863454 0.423694779 0.351405622 0.323293173 0.443775100 0.825301205
## [193] 0.132530120 0.596385542 0.520080321 0.554216867 0.457831325 0.379518072
## [199] 0.343373494 0.987951807 0.785140562 0.935742972 0.006024096 0.028112450
## [205] 0.192771084 0.064257028 0.919678715 0.022088353 0.030120482 0.552208835
## [211] 0.026104418 0.036144578 0.044176707 0.050200803 0.052208835 0.054216867
## [217] 0.056224900 0.997991968 0.020080321 0.995983936 0.662650602 0.134538153
## [223] 0.706827309 0.809236948 0.979919679 0.945783133 0.034136546 0.831325301
## [229] 0.789156627 0.008032129 0.070281124 0.993975904 0.975903614 0.967871486
## [235] 0.957831325 0.947791165 0.732931727 0.088353414 0.736947791 0.769076305
## [241] 0.614457831 0.096385542 0.381526104 0.032128514 0.929718876 0.897590361
## [247] 0.090361446 0.911646586 0.166666667 0.329317269 0.797188755 0.793172691
## [253] 0.835341365 0.118473896 0.012048193 0.078313253 0.923694779 0.927710843
## [259] 0.427710843 0.411646586 0.751004016 0.339357430 0.086345382 0.604417671
## [265] 0.325301205 0.265060241 0.594377510 0.833333333 0.106425703 0.198795181
## [271] 0.746987952 0.014056225 0.024096386 0.949799197 0.068273092 0.959839357
## [277] 0.941767068 0.337349398 0.953815261 0.098393574 0.345381526 0.158634538
## [283] 0.060240964 0.405622490 0.646586345 0.843373494 0.194779116 0.783132530
## [289] 0.985943775 0.917670683 0.305220884 0.461847390 0.154618474 0.080321285
## [295] 0.915662651 0.550200803 0.138554217 0.076305221 0.391566265 0.889558233
## [301] 0.526104418 0.638554217 0.624497992 0.285140562 0.389558233 0.600401606
## [307] 0.437751004 0.913654618 0.353413655 0.530120482 0.212851406 0.319277108
## [313] 0.560240964 0.688755020 0.767068273 0.538152610 0.650602410 0.445783133
## [319] 0.244979920 0.845381526 0.271084337 0.140562249 0.385542169 0.261044177
## [325] 0.682730924 0.738955823 0.293172691 0.349397590 0.660642570 0.642570281
## [331] 0.666666667 0.839357430 0.248995984 0.475903614 0.566265060 0.367469880
## [337] 0.164658635 0.718875502 0.590361446 0.883534137 0.487951807 0.307228916
## [343] 0.333333333 0.720883534 0.907630522 0.634538153 0.283132530 0.861445783
## [349] 0.744979920 0.110441767 0.761044177 0.837349398 0.092369478 0.407630522
## [355] 0.901606426 0.612449799 0.176706827 0.224899598 0.620481928 0.259036145
## [361] 0.757028112 0.626506024 0.728915663 0.449799197 0.471887550 0.210843373
## [367] 0.610441767 0.712851406 0.722891566 0.102409639 0.273092369 0.451807229
## [373] 0.311244980 0.799196787 0.632530120 0.493975904 0.502008032 0.383534137
## [379] 0.582329317 0.903614458 0.228915663 0.230923695 0.108433735 0.817269076
## [385] 0.544176707 0.716867470 0.335341365 0.441767068 0.795180723 0.873493976
## [391] 0.755020080 0.973895582 0.112449799 0.955823293 0.419678715 0.508032129
## [397] 0.483935743 0.463855422 0.435742972 0.887550201 0.216867470 0.763052209
## [403] 0.200803213 0.010040161 0.678714859 0.885542169 0.532128514 0.576305221
## [409] 0.791164659 0.969879518 0.128514056 0.692771084 0.851405622 0.168674699
## [415] 0.467871486 0.481927711 0.431726908 0.184738956 0.803212851 0.495983936
## [421] 0.504016064 0.510040161 0.018072289 0.150602410 0.899598394 0.204819277
## [427] 0.696787149 0.016064257 0.104417671 0.943775100 0.082329317 0.905622490
## [433] 0.253012048 0.046184739 0.819277108 0.234939759 0.875502008 0.753012048
## [439] 0.771084337 0.506024096 0.251004016 0.512048193 0.281124498 0.453815261
## [445] 0.257028112 0.724899598 0.909638554 0.477911647 0.877510040 0.222891566
## [451] 0.048192771 0.921686747 0.114457831 0.160642570 0.841365462 0.871485944
## [457] 0.686746988 0.676706827 0.186746988 0.879518072 0.365461847 0.156626506
## [463] 0.616465863 0.983935743 0.588353414 0.289156627 0.116465863 0.321285141
## [469] 0.708835341 0.895582329 0.074297189 0.807228916 0.170682731 0.363453815
## [475] 0.497991968 0.664658635 0.648594378 0.829317269 0.291164659 0.801204819
## [481] 0.636546185 0.516064257 0.347389558 0.489959839 0.500000000 0.136546185
## [487] 0.295180723 0.226907631 0.869477912 0.674698795 0.327309237 0.528112450
## [493] 0.429718876 0.534136546 0.524096386 0.644578313 0.491967871

# Tạo copula
copula_model <- normalCopula(dim = 2)

# Ước lượng copula từ dữ liệu chuẩn hóa
fit_copula <- fitCopula(copula_model, cbind(u,k), method = "ml")

# Xem kết quả ước lượng
summary(fit_copula)

## Call: fitCopula(copula_model, data = cbind(u, k), ... = pairlist(method = "ml"))
## Fit based on "maximum likelihood" and 497 2-dimensional observations.
## Normal copula, dim. d = 2 
##       Estimate Std. Error
## rho.1   0.3023       0.04
## The maximized loglikelihood is 22.93 
## Optimization converged
## Number of loglikelihood evaluations:
## function gradient 
##        7        7

# Kiểm định Anderson_Darling
library(nortest)
ad.test(s)

## 
##  Anderson-Darling normality test
## 
## data:  s
## A = 4.9749, p-value = 2.564e-12

# Kiểm định Cramer-von Mises
cvm.test(s)

## 
##  Cramer-von Mises normality test
## 
## data:  s
## W = 0.6398, p-value = 1.755e-07

# Kiểm định Kolmogorov-Smirnov
ks.test(s, y = "punif")

## 
##  Asymptotic one-sample Kolmogorov-Smirnov test
## 
## data:  s
## D = 0.025954, p-value = 0.8913
## alternative hypothesis: two-sided

#
mycop<-normalCopula(c(0.25),dim=2,dispstr="ex")
mymvd<-mvdc(copula=mycop,margins =c("norm","norm"),paramMargins=list(list(mean=0,sd=1),list(mean=1,2)))
#
r<-rMvdc(497,mymvd)
#
dens<-dMvdc(r,mymvd)
dist<-pMvdc(r,mymvd)
#
x<-r[,1]
y<-r[,2]
scatterplot3d(x,y,dens,highlight.3d = T)

scatterplot3d(x,y,dist,highlight.3d = T)

2.2 See the copula itself

The copula function can also be visualized,it will be this look.

u<-rCopula(497,mycop)
a<-u[,1]
b<-u[,2]
copdens<-dCopula(u,mycop)
copdist<-pCopula(u,mycop)
scatterplot3d(a,b,copdens,highlight.3d = T)

scatterplot3d(a,b,copdist,highlight.3d = T)