library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ ggplot2 3.4.2 ✔ tibble 3.2.1
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.1
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## ✖ dplyr::filter() masks stats::filter()
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(readxl)
library(rugarch)## Warning: package 'rugarch' was built under R version 4.3.1## Loading required package: parallel
##
## Attaching package: 'rugarch'
##
## The following object is masked from 'package:purrr':
##
## reduce
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## The following object is masked from 'package:stats':
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## sigmalibrary(VineCopula)## Warning: package 'VineCopula' was built under R version 4.3.1library(goftest)
data <- read_excel('C:/Users/Thanh Lan/Documents/DATAlast.xlsx')databf <- data %>% filter(DATE < ymd(20200101))
TSXbf <- ts(databf$TSX)
TSVNbf <- ts(databf$TSVN)autoarfima(TSXbf, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000791 0.000000 -9051.698 0
## ar1 0.000000 NA NA NA
## ar2 0.706610 0.007644 92.438 0
## ma1 -0.115667 0.000053 -2187.891 0
## ma2 -0.918501 0.000015 -60981.410 0
## sigma 0.050613 0.001308 38.701 0
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000791 0.000000 -11663.247 0
## ar1 0.000000 NA NA NA
## ar2 0.706610 0.018171 38.887 0
## ma1 -0.115667 0.000081 -1431.834 0
## ma2 -0.918501 0.000021 -44037.964 0
## sigma 0.050613 0.002960 17.100 0
##
## LogLikelihood : 762.1124
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.1093
## Bayes -3.0663
## Shibata -3.1095
## Hannan-Quinn -3.0924
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1667 6.831e-01
## Lag[2*(p+q)+(p+q)-1][11] 18.5096 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 35.8677 3.513e-12
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.426 0.2325
## Lag[2*(p+q)+(p+q)-1][2] 1.689 0.3200
## Lag[4*(p+q)+(p+q)-1][5] 3.330 0.3501
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 2.040 2 3.606e-01
## ARCH Lag[5] 6.855 5 2.317e-01
## ARCH Lag[10] 68.713 10 7.854e-11
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 6.1962
## Individual Statistics:
## mu 0.005382
## ar2 0.013610
## ma1 0.005936
## ma2 0.005978
## sigma 0.195077
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.101733
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 0 1 1 1 1 0 -3.109291 1
## 2 1 1 0 1 0 0 -3.079920 1
## 3 1 1 0 1 1 0 -3.078241 1
## 4 1 1 1 1 0 0 -3.077839 1
## 5 1 1 1 1 1 0 -3.077299 1
## 6 0 1 1 1 0 0 -3.077053 1
## 7 1 0 1 0 0 0 -3.072672 1
## 8 1 0 1 0 1 0 -3.072211 1
## 9 1 1 1 0 0 0 -3.071854 1
## 10 1 0 1 1 0 0 -3.071295 1
## 11 1 1 1 0 1 0 -3.071232 1
## 12 1 0 1 1 1 0 -3.070706 1
## 13 0 1 0 1 0 0 -3.057465 1
## 14 0 1 0 1 1 0 -3.053915 1
## 15 0 0 1 0 0 0 -3.009988 1
## 16 1 0 0 0 0 0 -3.009944 1
## 17 0 0 0 1 0 0 -3.008819 1
## 18 0 1 0 0 0 0 -3.008802 1
## 19 0 0 0 0 1 0 -3.008697 1
## 20 0 0 1 1 0 0 -3.006166 1
## 21 1 0 0 1 0 0 -3.006130 1
## 22 0 1 1 0 0 0 -3.006108 1
## 23 1 1 0 0 0 0 -3.006074 1
## 24 0 0 1 0 1 0 -3.005980 1
## 25 1 0 0 0 1 0 -3.005936 1
## 26 0 0 0 1 1 0 -3.004806 1
## 27 0 1 0 0 1 0 -3.004787 1
## 28 0 0 1 1 1 0 -3.002161 1
## 29 1 0 0 1 1 0 -3.002125 1
## 30 0 1 1 0 1 0 -3.002102 1
## 31 1 1 0 0 1 0 -3.002068 1autoarfima(TSVNbf, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 -0.407927 0.037818 -10.787 0
## ar2 0.557276 0.040686 13.697 0
## ma1 0.000000 NA NA NA
## ma2 -0.916797 0.020924 -43.816 0
## sigma 0.043588 0.001397 31.205 0
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 -0.407927 0.053298 -7.6538 0
## ar2 0.557276 0.052907 10.5331 0
## ma1 0.000000 NA NA NA
## ma2 -0.916797 0.017733 -51.6994 0
## sigma 0.043588 0.002131 20.4532 0
##
## LogLikelihood : 834.7337
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.4116
## Bayes -3.3772
## Shibata -3.4118
## Hannan-Quinn -3.3981
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01843 0.8920
## Lag[2*(p+q)+(p+q)-1][11] 4.83658 0.9791
## Lag[4*(p+q)+(p+q)-1][19] 8.41593 0.7332
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 47.55 5.354e-12
## Lag[2*(p+q)+(p+q)-1][2] 56.64 1.110e-15
## Lag[4*(p+q)+(p+q)-1][5] 76.26 0.000e+00
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 53.66 2 2.223e-12
## ARCH Lag[5] 59.96 5 1.237e-11
## ARCH Lag[10] 62.86 10 1.038e-09
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 5.0015
## Individual Statistics:
## ar1 0.04744
## ar2 0.07879
## ma2 0.08999
## sigma 4.28695
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.0619452
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 1 0 1 0 0 -3.411637 1
## 2 1 1 0 1 1 0 -3.410908 1
## 3 1 0 1 0 0 0 -3.406675 1
## 4 1 0 1 0 1 0 -3.405789 1
## 5 1 1 1 0 0 0 -3.403499 1
## 6 1 0 1 1 0 0 -3.403451 1
## 7 0 1 1 1 0 0 -3.403292 1
## 8 1 0 1 1 1 0 -3.402663 1
## 9 1 1 1 0 1 0 -3.402641 1
## 10 0 1 1 1 1 0 -3.402408 1
## 11 1 1 1 1 0 0 -3.399415 1
## 12 1 1 1 1 1 0 -3.398556 1
## 13 0 0 1 1 0 0 -3.335949 1
## 14 0 0 1 1 1 0 -3.332806 1
## 15 1 0 0 1 0 0 -3.304910 1
## 16 1 0 0 1 1 0 -3.300912 1
## 17 0 1 1 0 0 0 -3.298028 1
## 18 0 1 1 0 1 0 -3.293992 1
## 19 0 0 1 0 0 0 -3.291296 1
## 20 0 0 1 0 1 0 -3.287280 1
## 21 1 1 0 0 0 0 -3.285792 1
## 22 1 1 0 0 1 0 -3.281749 1
## 23 1 0 0 0 0 0 -3.263267 1
## 24 1 0 0 0 1 0 -3.259225 1
## 25 0 0 0 1 0 0 -3.210717 1
## 26 0 1 0 0 0 0 -3.210228 1
## 27 0 1 0 1 0 0 -3.207387 1
## 28 0 0 0 1 1 0 -3.206653 1
## 29 0 1 0 0 1 0 -3.206164 1
## 30 0 1 0 1 1 0 -3.203325 1
## 31 0 0 0 0 1 0 -3.201651 1# PHÂN PHỐI CHUẨN
TSXbf11n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXbf11n <- ugarchfit(spec = TSXbf11n.spec, TSXbf)
# PHÂN PHỐI STUDENT
TSXbf11std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXbf11std <- ugarchfit(TSXbf11std.spec, TSXbf)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXbf11sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXbf11sstd <- ugarchfit(TSXbf11sstd.spec, TSXbf)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXbf11ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
TSXbf11ged <- ugarchfit(TSXbf11ged.spec, TSXbf)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXbf11sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXbf11sged <- ugarchfit(TSXbf11sged.spec, TSXbf)# PHÂN PHỐI CHUẨN
TSXbf12n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXbf12n <- ugarchfit(TSXbf12n.spec, TSXbf)
# PHÂN PHỐI STUDENT
TSXbf12std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXbf12std <- ugarchfit(TSXbf12std.spec, TSXbf)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXbf12sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXbf12sstd <- ugarchfit(TSXbf12sstd.spec, TSXbf)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXbf12ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSXbf12ged <- ugarchfit(TSXbf12ged.spec, TSXbf)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXbf12sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXbf12sged <- ugarchfit(TSXbf12sged.spec, TSXbf)# PHÂN PHỐI CHUẨN
TSXbf21n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXbf21n <- ugarchfit(TSXbf21n.spec, TSXbf)
# PHÂN PHỐI STUDENT
TSXbf21std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXbf21std <- ugarchfit(TSXbf21std.spec, TSXbf)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXbf21sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXbf21sstd <- ugarchfit(TSXbf21sstd.spec, TSXbf)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXbf21ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSXbf21ged <- ugarchfit(TSXbf21ged.spec, TSXbf)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXbf21sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXbf21sged <- ugarchfit(TSXbf21sged.spec, TSXbf)# PHÂN PHỐI CHUẨN
TSXbf22n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXbf22n <- ugarchfit(TSXbf22n.spec, TSXbf)
# PHÂN PHỐI STUDENT
TSXbf22std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXbf22std <- ugarchfit(TSXbf22std.spec, TSXbf)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXbf22sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXbf22sstd <- ugarchfit(TSXbf22sstd.spec, TSXbf)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXbf22ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSXbf22ged <- ugarchfit(TSXbf22ged.spec, TSXbf)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXbf22sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXbf22sged <- ugarchfit(TSXbf22sged.spec, TSXbf)# PHÂN PHỐI CHUẨN
TSVNbf11n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSVNbf11n <- ugarchfit(TSVNbf11n.spec, TSVNbf)
# PHÂN PHỐI STUDENT
TSVNbf11std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSVNbf11std <- ugarchfit(spec = TSVNbf11std.spec, data = TSVNbf)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNbf11sstd.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSVNbf11sstd <- ugarchfit(TSVNbf11sstd.spec, TSVNbf)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNbf11ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSVNbf11ged <- ugarchfit(TSVNbf11ged.spec, TSVNbf)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNbf11sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSVNbf11sged <- ugarchfit(TSVNbf11sged.spec, TSVNbf)# PHÂN PHỐI CHUẨN
TSVNbf12n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSVNbf12n <- ugarchfit(TSVNbf12n.spec, TSVNbf)
# PHÂN PHỐI STUDENT
TSVNbf12std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSVNbf12std <- ugarchfit(TSVNbf12std.spec, TSVNbf)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNbf12sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSVNbf12sstd <- ugarchfit(TSVNbf12sstd.spec, TSVNbf)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNbf12ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSVNbf12ged <- ugarchfit(TSVNbf12ged.spec, TSVNbf)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNbf12sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSVNbf12sged <- ugarchfit(TSVNbf12sged.spec, TSVNbf)# PHÂN PHỐI CHUẨN
TSVNbf21n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSVNbf21n <- ugarchfit(TSVNbf21n.spec, TSVNbf)
# PHÂN PHỐI STUDENT
TSVNbf21std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSVNbf21std <- ugarchfit(TSVNbf21std.spec, TSVNbf)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNbf21sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSVNbf21sstd <- ugarchfit(TSVNbf21sstd.spec, TSVNbf)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNbf21ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSVNbf21ged <- ugarchfit(TSVNbf21ged.spec, TSVNbf)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNbf21sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSVNbf21sged <- ugarchfit(TSVNbf21sged.spec, TSVNbf)# PHÂN PHỐI CHUẨN
TSVNbf22n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSVNbf22n <- ugarchfit(TSVNbf22n.spec, TSVNbf)
# PHÂN PHỐI STUDENT
TSVNbf22std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSVNbf22std <- ugarchfit(TSVNbf22std.spec, TSVNbf)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNbf22sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSVNbf22sstd <- ugarchfit(TSVNbf22sstd.spec, TSVNbf)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNbf22ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSVNbf22ged <- ugarchfit(TSVNbf22ged.spec, TSVNbf)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNbf22sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSVNbf22sged <- ugarchfit(TSVNbf22sged.spec, TSVNbf)TSXbf.model.list <- list(garch11n = TSXbf11n,
garch11std = TSXbf11std,
garch11sstd = TSXbf11sstd,
garch11ged = TSXbf11ged,
garch11sged = TSXbf11sged,
garch12n = TSXbf12n,
garch12std = TSXbf12std,
garch12sstd = TSXbf12sstd,
garch12ged = TSXbf12ged,
garch12sged = TSXbf12sged,
garch21n = TSXbf21n,
garch21std = TSXbf21std,
garch21sstd = TSXbf21sstd,
garch21ged = TSXbf21ged,
garch21sged = TSXbf21sged,
garch22n = TSXbf22n,
garch22sstd = TSXbf22sstd)
TSXbf.info.mat <- sapply(TSXbf.model.list, infocriteria)
rownames(TSXbf.info.mat) <- rownames(infocriteria(TSXbf11n))
TSXbf.info.mat## garch11n garch11std garch11sstd garch11ged garch11sged garch12n
## Akaike -3.166518 -4.286883 -4.288578 -4.318377 -4.311625 -3.162415
## Bayes -3.089116 -4.200881 -4.193977 -4.232376 -4.217023 -3.076413
## Shibata -3.167184 -4.287703 -4.289569 -4.319198 -4.312615 -3.163236
## Hannan-Quinn -3.136112 -4.253098 -4.251415 -4.284593 -4.274462 -3.128630
## garch12std garch12sstd garch12ged garch12sged garch21n garch21std
## Akaike -4.279452 -4.289255 -4.288580 -4.282941 -3.187011 -4.281015
## Bayes -4.184851 -4.186054 -4.193978 -4.179740 -3.092410 -4.177814
## Shibata -4.280443 -4.290431 -4.289570 -4.284117 -3.188002 -4.282191
## Hannan-Quinn -4.242289 -4.248714 -4.251417 -4.242400 -3.149848 -4.240474
## garch21sstd garch21ged garch21sged garch22n garch22sstd
## Akaike -4.244497 -4.128885 -4.078341 -3.178386 -4.268268
## Bayes -4.132696 -4.025684 -3.966539 -3.075184 -4.147866
## Shibata -4.245874 -4.130061 -4.079718 -3.179562 -4.269860
## Hannan-Quinn -4.200577 -4.088344 -4.034421 -3.137844 -4.220969TSXbf.inds <- which(TSXbf.info.mat == min(TSXbf.info.mat), arr.ind = TRUE)
colnames(TSXbf.info.mat)[TSXbf.inds[,2]]## [1] "garch11ged"TSXbf11ged##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000000 0.000003 -5.7011e-02 0.95454
## ar1 0.475031 0.000201 2.3684e+03 0.00000
## ar2 0.314639 0.000296 1.0645e+03 0.00000
## ma1 -0.475063 0.000193 -2.4606e+03 0.00000
## ma2 -0.314630 0.000293 -1.0729e+03 0.00000
## omega 0.000008 0.000001 8.3310e+00 0.00000
## alpha1 0.009835 0.019940 4.9323e-01 0.62185
## beta1 0.995959 0.000917 1.0855e+03 0.00000
## gamma1 -0.018896 0.041606 -4.5416e-01 0.64971
## shape 0.402339 0.024327 1.6539e+01 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000000 0.000060 -0.003114 0.99752
## ar1 0.475031 0.013380 35.502512 0.00000
## ar2 0.314639 0.009226 34.102886 0.00000
## ma1 -0.475063 0.013407 -35.434075 0.00000
## ma2 -0.314630 0.009240 -34.049525 0.00000
## omega 0.000008 0.000001 8.671350 0.00000
## alpha1 0.009835 0.022450 0.438083 0.66133
## beta1 0.995959 0.000291 3420.975511 0.00000
## gamma1 -0.018896 0.046596 -0.405530 0.68509
## shape 0.402339 0.040344 9.972638 0.00000
##
## LogLikelihood : 1061.525
##
## Information Criteria
## ------------------------------------
##
## Akaike -4.3184
## Bayes -4.2324
## Shibata -4.3192
## Hannan-Quinn -4.2846
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7268 3.939e-01
## Lag[2*(p+q)+(p+q)-1][11] 20.0060 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 40.1603 1.166e-14
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.517 0.2180791
## Lag[2*(p+q)+(p+q)-1][5] 4.470 0.2009705
## Lag[4*(p+q)+(p+q)-1][9] 20.209 0.0001774
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 1.576 0.500 2.000 0.2093
## ARCH Lag[5] 3.523 1.440 1.667 0.2224
## ARCH Lag[7] 4.579 2.315 1.543 0.2707
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 22.142
## Individual Statistics:
## mu 0.13163
## ar1 2.97390
## ar2 0.79306
## ma1 2.97419
## ma2 0.79320
## omega 0.07523
## alpha1 0.04590
## beta1 0.03226
## gamma1 0.03545
## shape 0.04485
##
## 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 1.8693 0.06219 *
## Negative Sign Bias 1.1483 0.25142
## Positive Sign Bias 0.9156 0.36034
## Joint Effect 6.2832 0.09861 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 67.37 2.499e-07
## 2 30 81.40 7.218e-07
## 3 40 97.89 5.741e-07
## 4 50 117.41 1.521e-07
##
##
## Elapsed time : 1.263251TSVNbf.model.list <- list(TSVNbf11n = TSVNbf11n,
TSVNbf11std = TSVNbf11std,
TSVNbf11sstd = TSVNbf11sstd,
TSVNbf11ged = TSVNbf11ged,
TSVNbf12n = TSVNbf12n,
TSVNbf12std = TSVNbf12std,
TSVNbf12sstd = TSVNbf12sstd,
TSVNbf12ged = TSVNbf12ged,
TSVNbf12sged = TSVNbf12sged,
TSVNbf21n = TSVNbf21n,
TSVNbf21std = TSVNbf21std,
TSVNbf21sstd = TSVNbf21sstd,
TSVNbf21sged = TSVNbf21sged,
TSVNbf22n = TSVNbf22n,
TSVNbf22std = TSVNbf22std,
TSVNbf22sstd = TSVNbf22sstd,
TSVNbf22ged = TSVNbf22ged,
TSVNbf22sged = TSVNbf22sged)
TSVNbf.info.mat <- sapply(TSVNbf.model.list, infocriteria)
rownames(TSVNbf.info.mat) <- rownames(infocriteria(TSVNbf11n))
TSVNbf.info.mat## TSVNbf11n TSVNbf11std TSVNbf11sstd TSVNbf11ged TSVNbf12n
## Akaike -3.583890 -4.163137 -4.166940 -4.029580 -3.593860
## Bayes -3.506489 -4.077136 -4.072339 -3.943578 -3.507858
## Shibata -3.584557 -4.163958 -4.167931 -4.030401 -3.594680
## Hannan-Quinn -3.553484 -4.129353 -4.129777 -3.995795 -3.560075
## TSVNbf12std TSVNbf12sstd TSVNbf12ged TSVNbf12sged TSVNbf21n
## Akaike -4.160047 -4.164031 -4.167389 -4.056741 -3.639699
## Bayes -4.065446 -4.060830 -4.072788 -3.953539 -3.545098
## Shibata -4.161038 -4.165207 -4.168380 -4.057916 -3.640690
## Hannan-Quinn -4.122884 -4.123490 -4.130226 -4.016199 -3.602536
## TSVNbf21std TSVNbf21sstd TSVNbf21sged TSVNbf22n TSVNbf22std
## Akaike -4.155229 -4.159176 -4.114584 -3.635594 -4.136810
## Bayes -4.052028 -4.047374 -4.002782 -3.532392 -4.025008
## Shibata -4.156405 -4.160552 -4.115960 -3.636770 -4.138186
## Hannan-Quinn -4.114688 -4.115256 -4.070664 -3.595052 -4.092890
## TSVNbf22sstd TSVNbf22ged TSVNbf22sged
## Akaike -4.155891 -4.116216 -4.148033
## Bayes -4.035489 -4.004414 -4.027632
## Shibata -4.157483 -4.117592 -4.149626
## Hannan-Quinn -4.108592 -4.072296 -4.100735TSVNbf.inds <- which(TSVNbf.info.mat == min(TSVNbf.info.mat), arr.ind = TRUE)
model.TSVNbf <- colnames(TSVNbf.info.mat)[TSVNbf.inds[,2]]
model.TSVNbf## [1] "TSVNbf12ged"TSVNbf12ged##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001036 0.000067 15.37430 0.000000
## ar1 -0.091680 0.005698 -16.08873 0.000000
## ar2 0.072038 0.004718 15.26747 0.000000
## ma1 -0.165265 0.007350 -22.48391 0.000000
## ma2 -0.186385 0.007237 -25.75527 0.000000
## omega 0.000281 0.000076 3.72430 0.000196
## alpha1 0.787735 0.218791 3.60039 0.000318
## beta1 0.236487 0.139148 1.69953 0.089220
## beta2 0.045636 0.081045 0.56309 0.573371
## gamma1 -0.141714 0.278501 -0.50885 0.610860
## shape 0.665742 0.043688 15.23850 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001036 0.000067 15.39571 0.000000
## ar1 -0.091680 0.004848 -18.91219 0.000000
## ar2 0.072038 0.003939 18.28906 0.000000
## ma1 -0.165265 0.006404 -25.80684 0.000000
## ma2 -0.186385 0.005932 -31.42183 0.000000
## omega 0.000281 0.000089 3.15205 0.001621
## alpha1 0.787735 0.169507 4.64722 0.000003
## beta1 0.236487 0.108305 2.18353 0.028997
## beta2 0.045636 0.056377 0.80947 0.418246
## gamma1 -0.141714 0.239772 -0.59104 0.554495
## shape 0.665742 0.043591 15.27234 0.000000
##
## LogLikelihood : 1025.759
##
## Information Criteria
## ------------------------------------
##
## Akaike -4.1674
## Bayes -4.0728
## Shibata -4.1684
## Hannan-Quinn -4.1302
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.6582 0.417184
## Lag[2*(p+q)+(p+q)-1][11] 8.2783 0.000317
## Lag[4*(p+q)+(p+q)-1][19] 13.6639 0.072341
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4667 0.4945
## Lag[2*(p+q)+(p+q)-1][8] 2.4916 0.7774
## Lag[4*(p+q)+(p+q)-1][14] 5.7772 0.6687
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.1215 0.500 2.000 0.7274
## ARCH Lag[6] 1.1534 1.461 1.711 0.7042
## ARCH Lag[8] 1.3318 2.368 1.583 0.8703
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 8.9338
## Individual Statistics:
## mu 0.05655
## ar1 0.10306
## ar2 0.41075
## ma1 0.05948
## ma2 0.16407
## omega 0.53678
## alpha1 6.11820
## beta1 2.77097
## beta2 2.18698
## gamma1 4.06298
## shape 1.35327
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.49 2.75 3.27
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.0478 0.2953
## Negative Sign Bias 1.5782 0.1152
## Positive Sign Bias 0.6542 0.5133
## Joint Effect 3.5536 0.3139
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 33.37 0.02178
## 2 30 35.32 0.19421
## 3 40 50.58 0.10139
## 4 50 67.93 0.03793
##
##
## Elapsed time : 2.019631TSXbf.res <- residuals(TSXbf11ged)/sigma(TSXbf11ged)
fitdist(distribution = 'ged' , TSXbf.res, control = list())$pars## mu sigma shape
## 9.969367e-06 9.525559e-01 4.123138e-01sb <- pdist(distribution = 'ged' , q = TSXbf.res, mu = 9.969367e-06 , sigma = 9.525559e-01, shape = 4.123138e-01 )TSVNbf.res <- residuals(TSVNbf12ged)/sigma(TSVNbf12ged)
fitdist(distribution = 'ged' , TSVNbf.res, control = list())$pars## mu sigma shape
## 0.0006281056 1.1209131383 0.6240881095vb <- pdist(distribution = 'ged' , q = TSVNbf.res, mu = 0.0006281056 , sigma = 1.1209131383, shape = 0.6240881095)# Kiểm định Anderson-Darling
ad.test(sb, 'punif')##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: sb
## An = 3.1224, p-value = 0.02375ad.test(vb, 'punif')##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: vb
## An = 1.2671, p-value = 0.2433# Kiểm định Cramer-von Mises
cvm.test(sb, 'punif')##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: sb
## omega2 = 0.57379, p-value = 0.02595cvm.test(vb, 'punif')##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: vb
## omega2 = 0.19182, p-value = 0.2839# Kiểm định ks-test
ks.test(sb, 'punif')##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: sb
## D = 0.079042, p-value = 0.004553
## alternative hypothesis: two-sidedks.test(vb, 'punif')##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: vb
## D = 0.056215, p-value = 0.09209
## alternative hypothesis: two-sidedBiCopSelect(sb, vb, familyset = NA, selectioncrit = 'AIC' , indeptest = FALSE , level = 0.05)## Bivariate copula: t (par = -0.07, par2 = 4.11, tau = -0.04)hehe <- BiCopEst(sb,vb, family = 2, method = 'mle', se = T, max.df = 10)
summary(hehe)## Family
## ------
## No: 2
## Name: t
##
## Parameter(s)
## ------------
## par: -0.07 (SE = 0.05)
## par2: 4.11 (SE = 0.84)
## Dependence measures
## -------------------
## Kendall's tau: -0.04 (empirical = -0.04, p value = 0.15)
## Upper TD: 0.06
## Lower TD: 0.06
##
## Fit statistics
## --------------
## logLik: 18.49
## AIC: -32.98
## BIC: -24.61dataing <- data %>% filter(DATE > ymd(20200101), DATE < ymd(20220101))
TSXing <- ts(dataing$TSX)
TSVNing <- ts(dataing$TSVN)autoarfima(TSXing, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 1.808067 0.017787 101.649 0
## ar2 -0.881999 0.016569 -53.231 0
## ma1 -1.917991 0.000009 -214617.997 0
## ma2 0.943341 0.000037 25444.924 0
## sigma 0.059876 0.001914 31.278 0
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 1.808067 0.017522 103.189 0
## ar2 -0.881999 0.012159 -72.539 0
## ma1 -1.917991 0.000007 -276777.843 0
## ma2 0.943341 0.000030 31822.332 0
## sigma 0.059876 0.003352 17.861 0
##
## LogLikelihood : 684.308
##
## Information Criteria
## ------------------------------------
##
## Akaike -2.7727
## Bayes -2.7299
## Shibata -2.7729
## Hannan-Quinn -2.7559
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7768 3.781e-01
## Lag[2*(p+q)+(p+q)-1][11] 12.1996 4.441e-16
## Lag[4*(p+q)+(p+q)-1][19] 26.9366 2.274e-07
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.063 0.3025
## Lag[2*(p+q)+(p+q)-1][2] 1.389 0.3876
## Lag[4*(p+q)+(p+q)-1][5] 3.924 0.2637
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 1.751 2 0.416655
## ARCH Lag[5] 9.476 5 0.091520
## ARCH Lag[10] 28.437 10 0.001536
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.1979
## Individual Statistics:
## ar1 0.1217
## ar2 0.1438
## ma1 0.2585
## ma2 0.2106
## sigma 0.4184
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.04762697
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 1 1 1 0 0 -2.772686 1
## 2 1 1 1 1 1 0 -2.769076 1
## 3 1 1 1 0 0 0 -2.684227 1
## 4 1 0 1 1 0 0 -2.677857 1
## 5 0 1 1 1 0 0 -2.676412 1
## 6 1 1 0 1 0 0 -2.674548 1
## 7 1 0 1 1 1 0 -2.673882 1
## 8 1 1 0 1 1 0 -2.670798 1
## 9 0 1 0 1 0 0 -2.635408 1
## 10 0 1 0 1 1 0 -2.631334 1
## 11 0 0 0 1 0 0 -2.622441 1
## 12 0 1 0 0 0 0 -2.622373 1
## 13 0 0 1 0 0 0 -2.621007 1
## 14 1 0 0 0 0 0 -2.620988 1
## 15 0 0 0 0 1 0 -2.620769 1
## 16 1 0 0 1 0 0 -2.618583 1
## 17 0 0 1 1 0 0 -2.618570 1
## 18 1 1 0 0 0 0 -2.618516 1
## 19 0 1 1 0 0 0 -2.618504 1
## 20 0 0 0 1 1 0 -2.618360 1
## 21 0 1 0 0 1 0 -2.618291 1
## 22 0 0 1 0 1 0 -2.616926 1
## 23 1 0 1 0 0 0 -2.616913 1
## 24 1 0 0 0 1 0 -2.616907 1
## 25 1 0 0 1 1 0 -2.614502 1
## 26 0 0 1 1 1 0 -2.614488 1
## 27 1 1 0 0 1 0 -2.614435 1
## 28 1 0 1 0 1 0 -2.612831 1
## 29 0 1 1 1 1 0 -2.537056 1
## 30 0 1 1 0 1 0 NA 0
## 31 1 1 1 0 1 0 NA 0autoarfima(TSVNing, ar.max = 2, ma.max = 2, criterion = 'AIC', method = 'full')## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(1,0,1)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000937 0.000565 1.6594 0.09703
## ar1 0.604656 0.060079 10.0643 0.00000
## ma1 -0.924889 0.034327 -26.9435 0.00000
## sigma 0.063198 0.002019 31.3039 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000937 0.000584 1.6055 0.10838
## ar1 0.604656 0.079896 7.5680 0.00000
## ma1 -0.924889 0.069410 -13.3249 0.00000
## sigma 0.063198 0.004427 14.2760 0.00000
##
## LogLikelihood : 657.8492
##
## Information Criteria
## ------------------------------------
##
## Akaike -2.6688
## Bayes -2.6345
## Shibata -2.6689
## Hannan-Quinn -2.6553
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.05836 0.8091
## Lag[2*(p+q)+(p+q)-1][5] 1.56789 0.9966
## Lag[4*(p+q)+(p+q)-1][9] 2.87135 0.9092
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 6.880 0.008716
## Lag[2*(p+q)+(p+q)-1][2] 7.447 0.009067
## Lag[4*(p+q)+(p+q)-1][5] 8.171 0.026720
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 6.598 2 0.036922
## ARCH Lag[5] 8.899 5 0.113163
## ARCH Lag[10] 25.584 10 0.004342
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.2169
## Individual Statistics:
## mu 0.23547
## ar1 0.32215
## ma1 0.05813
## sigma 1.50546
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.172915
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 0 1 0 1 0 -2.668772 1
## 2 1 0 1 0 0 0 -2.667597 1
## 3 1 0 1 1 1 0 -2.665108 1
## 4 1 0 1 1 0 0 -2.663847 1
## 5 0 1 1 1 1 0 -2.632676 1
## 6 0 1 1 1 0 0 -2.630571 1
## 7 1 1 1 1 1 0 -2.628719 1
## 8 1 1 1 1 0 0 -2.626589 1
## 9 1 1 0 1 1 0 -2.626128 1
## 10 1 1 0 1 0 0 -2.625550 1
## 11 0 0 1 1 0 0 -2.625346 1
## 12 0 0 1 1 1 0 -2.622456 1
## 13 1 1 1 0 1 0 -2.621754 1
## 14 1 1 1 0 0 0 -2.620782 1
## 15 1 0 0 1 0 0 -2.614259 1
## 16 1 0 0 1 1 0 -2.610934 1
## 17 0 0 1 0 0 0 -2.592626 1
## 18 0 1 1 0 0 0 -2.589301 1
## 19 0 0 1 0 1 0 -2.589069 1
## 20 0 1 1 0 1 0 -2.585846 1
## 21 1 1 0 0 0 0 -2.583314 1
## 22 1 1 0 0 1 0 -2.579718 1
## 23 1 0 0 0 0 0 -2.570131 1
## 24 1 0 0 0 1 0 -2.566379 1
## 25 0 1 0 1 0 0 -2.551443 1
## 26 0 1 0 1 1 0 -2.547824 1
## 27 0 0 0 1 0 0 -2.546146 1
## 28 0 1 0 0 0 0 -2.544337 1
## 29 0 0 0 1 1 0 -2.542323 1
## 30 0 1 0 0 1 0 -2.540495 1
## 31 0 0 0 0 1 0 -2.527137 1# PHÂN PHỐI CHUẨN
TSXing11n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXing11n <- ugarchfit(spec = TSXing11n.spec, TSXing)
# PHÂN PHỐI STUDENT
TSXing11std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXing11std <- ugarchfit(TSXing11std.spec, TSXing)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXing11sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXing11sstd <- ugarchfit(TSXing11sstd.spec, TSXing)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXing11ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
TSXing11ged <- ugarchfit(TSXing11ged.spec, TSXing)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXing11sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXing11sged <- ugarchfit(TSXing11sged.spec, TSXing)# PHÂN PHỐI CHUẨN
TSXing12n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXing12n <- ugarchfit(TSXing12n.spec, TSXing)
# PHÂN PHỐI STUDENT
TSXing12std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXing12std <- ugarchfit(TSXing12std.spec, TSXing)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXing12sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXing12sstd <- ugarchfit(TSXing12sstd.spec, TSXing)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXing12ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSXing12ged <- ugarchfit(TSXing12ged.spec, TSXing)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXing12sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXing12sged <- ugarchfit(TSXing12sged.spec, TSXing)# PHÂN PHỐI CHUẨN
TSXing21n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXing21n <- ugarchfit(TSXing21n.spec, TSXing)
# PHÂN PHỐI STUDENT
TSXing21std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXing21std <- ugarchfit(TSXing21std.spec, TSXing)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXing21sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXing21sstd <- ugarchfit(TSXing21sstd.spec, TSXing)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXing21ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSXing21ged <- ugarchfit(TSXing21ged.spec, TSXing)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXing21sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXing21sged <- ugarchfit(TSXing21sged.spec, TSXing)# PHÂN PHỐI CHUẨN
TSXing22n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXing22n <- ugarchfit(TSXing22n.spec, TSXing)
# PHÂN PHỐI STUDENT
TSXing22std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXing22std <- ugarchfit(TSXing22std.spec, TSXing)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXing22sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXing22sstd <- ugarchfit(TSXing22sstd.spec, TSXing)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXing22ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSXing22ged <- ugarchfit(TSXing22ged.spec, TSXing)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXing22sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXing22sged <- ugarchfit(TSXing22sged.spec, TSXing)# PHÂN PHỐI CHUẨN
TSVNing11n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'norm')
TSVNing11n <- ugarchfit(spec = TSVNing11n.spec, TSVNing)
# PHÂN PHỐI STUDENT
TSVNing11std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'std')
TSVNing11std <- ugarchfit(TSVNing11std.spec, TSVNing)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNing11sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'sstd')
TSVNing11sstd <- ugarchfit(TSVNing11sstd.spec, TSVNing)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNing11ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = "ged")
TSVNing11ged <- ugarchfit(TSVNing11ged.spec, TSVNing)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNing11sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'sged')
TSVNing11sged <- ugarchfit(TSVNing11sged.spec, TSVNing)# PHÂN PHỐI CHUẨN
TSVNing12n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'norm')
TSVNing12n <- ugarchfit(TSVNing12n.spec, TSVNing)
# PHÂN PHỐI STUDENT
TSVNing12std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'std')
TSVNing12std <- ugarchfit(TSVNing12std.spec, TSVNing)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNing12sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'sstd')
TSVNing12sstd <- ugarchfit(TSVNing12sstd.spec, TSVNing)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNing12ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = "ged")
TSVNing12ged <- ugarchfit(TSVNing12ged.spec, TSVNing)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNing12sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'sged')
TSVNing12sged <- ugarchfit(TSVNing12sged.spec, TSVNing)# PHÂN PHỐI CHUẨN
TSVNing21n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'norm')
TSVNing21n <- ugarchfit(TSVNing21n.spec, TSVNing)
# PHÂN PHỐI STUDENT
TSVNing21std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'std')
TSVNing21std <- ugarchfit(TSVNing21std.spec, TSVNing)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNing21sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'sstd')
TSVNing21sstd <- ugarchfit(TSVNing21sstd.spec, TSVNing)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNing21ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = "ged")
TSVNing21ged <- ugarchfit(TSVNing21ged.spec, TSVNing)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNing21sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'sged')
TSVNing21sged <- ugarchfit(TSVNing21sged.spec, TSVNing)# PHÂN PHỐI CHUẨN
TSVNing22n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'norm')
TSVNing22n <- ugarchfit(TSVNing22n.spec, TSVNing)
# PHÂN PHỐI STUDENT
TSVNing22std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'std')
TSVNing22std <- ugarchfit(TSVNing22std.spec, TSVNing)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNing22sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'sstd')
TSVNing22sstd <- ugarchfit(TSVNing22sstd.spec, TSVNing)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNing22ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = "ged")
TSVNing22ged <- ugarchfit(TSVNing22ged.spec, TSVNing)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNing22sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(1,1), include.mean = TRUE), distribution.model = 'sged')
TSVNing22sged <- ugarchfit(TSVNing22sged.spec, TSVNing)TSXing.model.list <- list(garch11n = TSXing11n,
garch11std = TSXing11std,
garch11sstd = TSXing11sstd,
garch11ged = TSXing11ged,
garch11sged = TSXing11sged,
garch12n = TSXing12n,
garch12std = TSXing12std,
garch12sstd = TSXing12sstd,
garch12ged = TSXing12ged,
garch12sged = TSXing12sged,
garch21n = TSXing21n,
garch21std = TSXing21std,
garch21ged = TSXing21ged,
garch22n = TSXing22n,
garch22std = TSXing22std,
garch22sstd = TSXing22sstd,
garch22ged = TSXing22ged)
TSXing.info.mat <- sapply(TSXing.model.list, infocriteria)
rownames(TSXing.info.mat) <- rownames(infocriteria(TSXing11n))
TSXing.info.mat## garch11n garch11std garch11sstd garch11ged garch11sged garch12n
## Akaike -2.762436 -4.058712 -4.044594 -4.141586 -3.965044 -2.796488
## Bayes -2.685396 -3.973112 -3.950434 -4.055986 -3.870884 -2.710888
## Shibata -2.763094 -4.059523 -4.045572 -4.142397 -3.966023 -2.797299
## Hannan-Quinn -2.732179 -4.025093 -4.007614 -4.107968 -3.928064 -2.762870
## garch12std garch12sstd garch12ged garch12sged garch21n garch21std
## Akaike -4.054523 -4.044480 -4.099929 -4.057761 -2.773750 -4.038621
## Bayes -3.960363 -3.941760 -4.005769 -3.955041 -2.679590 -3.935901
## Shibata -4.055502 -4.045642 -4.100908 -4.058923 -2.774729 -4.039782
## Hannan-Quinn -4.017543 -4.004139 -4.062949 -4.017419 -2.736770 -3.998279
## garch21ged garch22n garch22std garch22sstd garch22ged
## Akaike -4.107073 -2.715481 -4.045682 -4.042605 -4.077941
## Bayes -4.004353 -2.612761 -3.934401 -3.922765 -3.966661
## Shibata -4.108235 -2.716643 -4.047041 -4.044178 -4.079301
## Hannan-Quinn -4.066731 -2.675139 -4.001978 -3.995540 -4.034237TSXing.inds <- which(TSXing.info.mat == min(TSXing.info.mat), arr.ind = TRUE)
model.TSXing <- colnames(TSXing.info.mat)[TSXing.inds[,2]]
model.TSXing## [1] "garch11ged"TSXing11ged##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.001036 0.000011 -94.755551 0.000000
## ar1 0.205347 0.000243 843.382832 0.000000
## ar2 0.137399 0.000346 397.139832 0.000000
## ma1 -0.187813 0.000250 -752.486925 0.000000
## ma2 -0.136621 0.000305 -447.860816 0.000000
## omega 0.000009 0.000004 2.439229 0.014719
## alpha1 0.003639 0.018120 0.200844 0.840821
## beta1 0.994366 0.001603 620.444594 0.000000
## gamma1 -0.002814 0.036870 -0.076325 0.939161
## shape 0.387873 0.024990 15.520857 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.001036 0.000316 -3.28282 0.001028
## ar1 0.205347 0.031668 6.48428 0.000000
## ar2 0.137399 0.023330 5.88929 0.000000
## ma1 -0.187813 0.031288 -6.00275 0.000000
## ma2 -0.136621 0.022835 -5.98299 0.000000
## omega 0.000009 0.000004 2.27435 0.022945
## alpha1 0.003639 0.020811 0.17487 0.861182
## beta1 0.994366 0.002042 486.97065 0.000000
## gamma1 -0.002814 0.042521 -0.06618 0.947234
## shape 0.387873 0.050303 7.71074 0.000000
##
## LogLikelihood : 1024.689
##
## Information Criteria
## ------------------------------------
##
## Akaike -4.1416
## Bayes -4.0560
## Shibata -4.1424
## Hannan-Quinn -4.1080
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.001071 9.739e-01
## Lag[2*(p+q)+(p+q)-1][11] 16.153606 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 36.767814 1.079e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.899 0.168194
## Lag[2*(p+q)+(p+q)-1][5] 6.144 0.083181
## Lag[4*(p+q)+(p+q)-1][9] 14.822 0.003949
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 2.387 0.500 2.000 0.12231
## ARCH Lag[5] 5.533 1.440 1.667 0.07727
## ARCH Lag[7] 10.013 2.315 1.543 0.01828
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 25.6065
## Individual Statistics:
## mu 0.03829
## ar1 0.50811
## ar2 0.58192
## ma1 0.49585
## ma2 0.57635
## omega 0.04473
## alpha1 0.02361
## beta1 0.01404
## gamma1 0.01327
## shape 0.07904
##
## 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 0.6060 0.5448
## Negative Sign Bias 0.8155 0.4152
## Positive Sign Bias 0.9193 0.3584
## Joint Effect 2.0424 0.5637
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 54.73 2.552e-05
## 2 30 77.43 2.738e-06
## 3 40 95.80 1.109e-06
## 4 50 107.55 2.841e-06
##
##
## Elapsed time : 1.157415TSVNing.model.list <- list(garch11n = TSVNing11n,
garch11std = TSVNing11std,
garch11sstd = TSVNing11sstd,
garch11ged = TSVNing11ged,
garch12n = TSVNing12n,
garch12std = TSVNing12std,
garch12sstd = TSVNing12sstd,
garch12ged = TSVNing12ged,
garch21n = TSVNing21n,
garch21std = TSVNing21std,
garch21sstd = TSVNing21sstd,
garch22n = TSVNing22n,
garch22std = TSVNing22std,
garch22sstd = TSVNing22sstd,
garch22ged = TSVNing22ged)
TSVNing.info.mat <- sapply(TSVNing.model.list, infocriteria)
rownames(TSVNing.info.mat) <- rownames(infocriteria(TSVNing11n))
TSVNing.info.mat## garch11n garch11std garch11sstd garch11ged garch12n garch12std
## Akaike -2.711955 -3.369840 -3.372863 -3.420731 -2.698609 -3.357546
## Bayes -2.652035 -3.301360 -3.295823 -3.352251 -2.630129 -3.280506
## Shibata -2.712356 -3.370362 -3.373522 -3.421253 -2.699130 -3.358204
## Hannan-Quinn -2.688422 -3.342946 -3.342607 -3.393837 -2.671714 -3.327289
## garch12sstd garch12ged garch21n garch21std garch21sstd garch22n
## Akaike -3.359778 -3.428538 -2.732027 -3.386084 -3.385674 -2.746152
## Bayes -3.274178 -3.351498 -2.654987 -3.300484 -3.291514 -2.660552
## Shibata -3.360589 -3.429197 -2.732686 -3.386895 -3.386653 -2.746963
## Hannan-Quinn -3.326160 -3.398282 -2.701770 -3.352466 -3.348694 -2.712534
## garch22std garch22sstd garch22ged
## Akaike -3.382003 -3.381016 -3.400268
## Bayes -3.287843 -3.278296 -3.306108
## Shibata -3.382981 -3.382178 -3.401246
## Hannan-Quinn -3.345023 -3.340674 -3.363288TSVNing.inds <- which(TSVNing.info.mat == min(TSVNing.info.mat), arr.ind = TRUE)
model.TSVNing <- colnames(TSVNing.info.mat)[TSVNing.inds[,2]]
model.TSVNing## [1] "garch12ged"TSVNing12ged##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(1,0,1)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001672 0.000002 816.17 0
## ar1 0.155997 0.000679 229.59 0
## ma1 -0.127693 0.000938 -136.15 0
## omega 0.000026 0.000000 366.47 0
## alpha1 0.044033 0.000062 706.40 0
## beta1 0.708876 0.000496 1430.46 0
## beta2 0.300999 0.000235 1282.37 0
## gamma1 -0.110367 0.000068 -1634.46 0
## shape 0.437139 0.025297 17.28 0
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001672 0.000106 15.7204 0.00000
## ar1 0.155997 0.019928 7.8279 0.00000
## ma1 -0.127693 0.017022 -7.5016 0.00000
## omega 0.000026 0.000001 19.6976 0.00000
## alpha1 0.044033 0.000771 57.0968 0.00000
## beta1 0.708876 0.013389 52.9437 0.00000
## beta2 0.300999 0.004106 73.3082 0.00000
## gamma1 -0.110367 0.001700 -64.9061 0.00000
## shape 0.437139 0.373159 1.1715 0.24141
##
## LogLikelihood : 848.9918
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.4285
## Bayes -3.3515
## Shibata -3.4292
## Hannan-Quinn -3.3983
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 17.47 2.913e-05
## Lag[2*(p+q)+(p+q)-1][5] 24.47 0.000e+00
## Lag[4*(p+q)+(p+q)-1][9] 26.88 7.141e-12
## d.o.f=2
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 14.22 0.0001624
## Lag[2*(p+q)+(p+q)-1][8] 15.32 0.0018463
## Lag[4*(p+q)+(p+q)-1][14] 22.20 0.0006630
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.5009 0.500 2.000 0.4791
## ARCH Lag[6] 0.5184 1.461 1.711 0.8868
## ARCH Lag[8] 0.7504 2.368 1.583 0.9574
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 3.5371
## Individual Statistics:
## mu 0.03673
## ar1 0.28998
## ma1 0.28602
## omega 0.01947
## alpha1 0.01973
## beta1 0.02978
## beta2 0.01085
## gamma1 0.01953
## shape 0.35068
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.1 2.32 2.82
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.7440 8.179e-02 *
## Negative Sign Bias 4.6931 3.507e-06 ***
## Positive Sign Bias 0.9295 3.531e-01
## Joint Effect 22.9674 4.102e-05 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 46.73 0.0003897
## 2 30 65.80 0.0001114
## 3 40 71.31 0.0012097
## 4 50 82.86 0.0017881
##
##
## Elapsed time : 1.045662TSXing.res <- residuals(TSXing11ged)/sigma(TSXing11ged)
fitdist(distribution = 'ged' , TSXing.res, control = list())$pars## mu sigma shape
## 1.988807e-06 7.919871e-01 4.351004e-01si <- pdist(distribution = 'ged' , q = TSXing.res, mu = 1.988807e-06, sigma = 7.919871e-01, shape = 4.351004e-01)TSVNing.res <- residuals(TSVNing12ged)/sigma(TSVNing12ged)
fitdist(distribution = 'ged' , TSVNing.res, control = list())$pars## mu sigma shape
## -3.156577e-05 1.146166e+00 4.177457e-01vi <- pdist(distribution = 'ged' , q = TSVNing.res, mu = -0.001569485 , sigma = 1.084206215, shape = 0.423689743) # Kiểm định Anderson-Darling
ad.test(si, 'punif')##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: si
## An = 2.3557, p-value = 0.05905ad.test(vi, 'punif')##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: vi
## An = 2.7523, p-value = 0.03664# Kiểm định Cramer-von Mises
cvm.test(si, 'punif')##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: si
## omega2 = 0.31697, p-value = 0.1211cvm.test(vi, 'punif')##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: vi
## omega2 = 0.44125, p-value = 0.05631# Kiểm định ks-test
ks.test(si, 'punif')##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: si
## D = 0.064405, p-value = 0.03432
## alternative hypothesis: two-sidedks.test(vi, 'punif')##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: vi
## D = 0.060394, p-value = 0.05606
## alternative hypothesis: two-sidedBiCopSelect(si, vi, familyset = NA, selectioncrit = 'AIC' , indeptest = FALSE , level = 0.05)## Bivariate copula: Rotated Tawn type 2 180 degrees (par = 1.58, par2 = 0.1, tau = 0.07)yeah <- BiCopEst(si, vi, family = 214, method = 'mle', se = T, max.df = 10)
summary(yeah)## Family
## ------
## No: 214
## Name: Rotated Tawn type 2 180 degrees
##
## Parameter(s)
## ------------
## par: 1.58 (SE = 0.18)
## par2: 0.1 (SE = 0.03)
## Dependence measures
## -------------------
## Kendall's tau: 0.07 (empirical = 0.02, p value = 0.48)
## Upper TD: 0
## Lower TD: 0.09
##
## Fit statistics
## --------------
## logLik: 15.6
## AIC: -27.2
## BIC: -18.81dataaft <- data %>% filter(DATE > ymd(20211231))
TSXaft <- ts(dataaft$TSX)
TSVNaft <- ts(dataaft$TSVN)autoarfima(TSXaft, ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.767947 0.003185 241.087 0
## ar2 0.009244 0.000232 39.902 0
## ma1 -0.994890 0.000023 -42778.101 0
## ma2 -0.027939 0.000059 -470.650 0
## sigma 0.070298 0.002615 26.883 0
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.767947 0.010055 76.377 0
## ar2 0.009244 0.000545 16.947 0
## ma1 -0.994890 0.000047 -21131.155 0
## ma2 -0.027939 0.000119 -235.515 0
## sigma 0.070298 0.005651 12.441 0
##
## LogLikelihood : 436.6717
##
## Information Criteria
## ------------------------------------
##
## Akaike -2.4049
## Bayes -2.3508
## Shibata -2.4052
## Hannan-Quinn -2.3833
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.575 1.086e-01
## Lag[2*(p+q)+(p+q)-1][11] 9.649 1.203e-07
## Lag[4*(p+q)+(p+q)-1][19] 26.451 3.989e-07
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.690 0.4062
## Lag[2*(p+q)+(p+q)-1][2] 1.236 0.4277
## Lag[4*(p+q)+(p+q)-1][5] 2.685 0.4675
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 1.817 2 0.4031
## ARCH Lag[5] 4.856 5 0.4338
## ARCH Lag[10] 9.906 10 0.4488
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 8.9673
## Individual Statistics:
## ar1 0.03336
## ar2 0.03352
## ma1 0.03328
## ma2 0.03337
## sigma 0.57966
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.05600214
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 1 1 1 0 0 -2.404856 1
## 2 1 1 1 0 0 0 -2.383456 1
## 3 0 1 1 1 1 0 -2.376003 1
## 4 1 1 0 1 0 0 -2.361318 1
## 5 1 1 0 1 1 0 -2.355749 1
## 6 0 1 0 1 1 0 -2.311608 1
## 7 0 0 1 0 0 0 -2.304061 1
## 8 1 0 0 0 0 0 -2.304059 1
## 9 0 0 0 1 0 0 -2.304005 1
## 10 0 1 0 0 0 0 -2.303993 1
## 11 0 0 0 0 1 0 -2.303938 1
## 12 0 0 1 1 0 0 -2.298569 1
## 13 1 0 0 1 0 0 -2.298561 1
## 14 0 1 1 0 0 0 -2.298548 1
## 15 1 1 0 0 0 0 -2.298543 1
## 16 0 0 1 0 1 0 -2.298490 1
## 17 1 0 0 0 1 0 -2.298488 1
## 18 1 0 1 0 0 0 -2.298488 1
## 19 0 0 0 1 1 0 -2.298434 1
## 20 0 1 0 0 1 0 -2.298422 1
## 21 0 1 0 1 0 0 -2.298375 1
## 22 0 0 1 1 1 0 -2.292999 1
## 23 1 0 1 1 0 0 -2.292993 1
## 24 1 0 0 1 1 0 -2.292990 1
## 25 1 1 0 0 1 0 -2.292972 1
## 26 1 0 1 0 1 0 -2.292918 1
## 27 0 1 1 1 0 0 -2.292896 1
## 28 1 0 1 1 1 0 -2.287422 1
## 29 1 1 1 1 1 0 -2.283200 1
## 30 0 1 1 0 1 0 NA 0
## 31 1 1 1 0 1 0 NA 0autoarfima(TSVNaft, ar.max = 2, ma.max = 2, criterion = 'AIC', method = 'full')## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000785 0.000373 -2.1042 0.035364
## ar1 0.273134 0.061085 4.4714 0.000008
## ar2 0.228172 0.059479 3.8362 0.000125
## ma1 -0.363711 0.029784 -12.2115 0.000000
## ma2 -0.591012 0.029491 -20.0401 0.000000
## sigma 0.069531 0.002595 26.7940 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000785 0.000344 -2.2795 0.022635
## ar1 0.273134 0.040623 6.7237 0.000000
## ar2 0.228172 0.050440 4.5236 0.000006
## ma1 -0.363711 0.013873 -26.2177 0.000000
## ma2 -0.591012 0.012310 -48.0100 0.000000
## sigma 0.069531 0.006120 11.3619 0.000000
##
## LogLikelihood : 447.6868
##
## Information Criteria
## ------------------------------------
##
## Akaike -2.4607
## Bayes -2.3957
## Shibata -2.4612
## Hannan-Quinn -2.4348
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 4.305e-04 0.98345
## Lag[2*(p+q)+(p+q)-1][11] 7.481e+00 0.01042
## Lag[4*(p+q)+(p+q)-1][19] 1.212e+01 0.18059
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1965 0.65757
## Lag[2*(p+q)+(p+q)-1][2] 5.6344 0.02753
## Lag[4*(p+q)+(p+q)-1][5] 9.1311 0.01533
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 10.84 2 0.004425
## ARCH Lag[5] 12.44 5 0.029285
## ARCH Lag[10] 14.52 10 0.150732
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 3.2039
## Individual Statistics:
## mu 0.39025
## ar1 0.08921
## ar2 0.15602
## ma1 0.37754
## ma2 0.44053
## sigma 1.05160
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.03275704
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 1 1 1 1 0 -2.460651 1
## 2 1 1 1 1 0 0 -2.458731 1
## 3 1 0 1 1 1 0 -2.457749 1
## 4 1 0 1 1 0 0 -2.456311 1
## 5 0 1 1 1 1 0 -2.453854 1
## 6 0 1 1 1 0 0 -2.452359 1
## 7 1 1 0 1 0 0 -2.421220 1
## 8 1 1 0 1 1 0 -2.421176 1
## 9 0 1 0 1 0 0 -2.394706 1
## 10 0 1 0 1 1 0 -2.389320 1
## 11 0 0 0 1 0 0 -2.375237 1
## 12 1 0 0 1 0 0 -2.369935 1
## 13 0 0 1 1 0 0 -2.369844 1
## 14 0 0 0 1 1 0 -2.369785 1
## 15 1 0 0 1 1 0 -2.364479 1
## 16 0 0 1 1 1 0 -2.364397 1
## 17 0 1 0 0 0 0 -2.355538 1
## 18 0 1 1 0 0 0 -2.350974 1
## 19 1 1 1 0 0 0 -2.350888 1
## 20 1 1 0 0 0 0 -2.350358 1
## 21 0 1 0 0 1 0 -2.350059 1
## 22 0 1 1 0 1 0 -2.345489 1
## 23 1 1 1 0 1 0 -2.345398 1
## 24 1 1 0 0 1 0 -2.344876 1
## 25 1 0 1 0 0 0 -2.323858 1
## 26 1 0 1 0 1 0 -2.318338 1
## 27 0 0 1 0 0 0 -2.305028 1
## 28 1 0 0 0 0 0 -2.304826 1
## 29 0 0 0 0 1 0 -2.304632 1
## 30 0 0 1 0 1 0 -2.299510 1
## 31 1 0 0 0 1 0 -2.299308 1# PHÂN PHỐI CHUẨN
TSXaft11n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXaft11n <- ugarchfit(spec = TSXaft11n.spec, TSXaft)
# PHÂN PHỐI STUDENT
TSXaft11std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXaft11std <- ugarchfit(TSXaft11std.spec, TSXaft)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXaft11sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXaft11sstd <- ugarchfit(TSXaft11sstd.spec, TSXaft)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXaft11ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
TSXaft11ged <- ugarchfit(TSXaft11ged.spec, TSXaft)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXaft11sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXaft11sged <- ugarchfit(TSXaft11sged.spec, TSXaft)# PHÂN PHỐI CHUẨN
TSXaft12n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXaft12n <- ugarchfit(TSXaft12n.spec, TSXaft)
# PHÂN PHỐI STUDENT
TSXaft12std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXaft12std <- ugarchfit(TSXaft12std.spec, TSXaft)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXaft12sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXaft12sstd <- ugarchfit(TSXaft12sstd.spec, TSXaft)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXaft12ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSXaft12ged <- ugarchfit(TSXaft12ged.spec, TSXaft)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXaft12sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXaft12sged <- ugarchfit(TSXaft12sged.spec, TSXaft)# PHÂN PHỐI CHUẨN
TSXaft21n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXaft21n <- ugarchfit(TSXaft21n.spec, TSXaft)
# PHÂN PHỐI STUDENT
TSXaft21std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXaft21std <- ugarchfit(TSXaft21std.spec, TSXaft)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXaft21sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXaft21sstd <- ugarchfit(TSXaft21sstd.spec, TSXaft)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXaft21ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSXaft21ged <- ugarchfit(TSXaft21ged.spec, TSXaft)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXaft21sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXaft21sged <- ugarchfit(TSXaft21sged.spec, TSXaft)# PHÂN PHỐI CHUẨN
TSXaft22n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSXaft22n <- ugarchfit(TSXaft22n.spec, TSXaft)
# PHÂN PHỐI STUDENT
TSXaft22std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSXaft22std <- ugarchfit(TSXaft22std.spec, TSXaft)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSXaft22sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSXaft22sstd <- ugarchfit(TSXaft22sstd.spec, TSXaft)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSXaft22ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSXaft22ged <- ugarchfit(TSXaft22ged.spec, TSXaft)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSXaft22sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSXaft22sged <- ugarchfit(TSXaft22sged.spec, TSXaft)# PHÂN PHỐI CHUẨN
TSVNaft11n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSVNaft11n <- ugarchfit(TSVNaft11n.spec, TSVNaft)
# PHÂN PHỐI STUDENT
TSVNaft11std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSVNaft11std <- ugarchfit(TSVNaft11std.spec, TSVNaft)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNaft11sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSVNaft11sstd <- ugarchfit(TSVNaft11sstd.spec, TSVNaft)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNaft11ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
TSVNaft11ged <- ugarchfit(TSVNaft11ged.spec, TSVNaft)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNaft11sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSVNaft11sged <- ugarchfit(TSVNaft11sged.spec, TSVNaft)# PHÂN PHỐI CHUẨN
TSVNaft12n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSVNaft12n <- ugarchfit(TSVNaft12n.spec, TSVNaft)
# PHÂN PHỐI STUDENT
TSVNaft12std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSVNaft12std <- ugarchfit(TSVNaft12std.spec, TSVNaft)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNaft12sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSVNaft12sstd <- ugarchfit(TSVNaft12sstd.spec, TSVNaft)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNaft12ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSVNaft12ged <- ugarchfit(TSVNaft12ged.spec, TSVNaft)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNaft12sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSVNaft12sged <- ugarchfit(TSVNaft12sged.spec, TSVNaft)# PHÂN PHỐI CHUẨN
TSVNaft21n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSVNaft21n <- ugarchfit(TSVNaft21n.spec, TSVNaft)
# PHÂN PHỐI STUDENT
TSVNaft21std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSVNaft21std <- ugarchfit(TSVNaft21std.spec, TSVNaft)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNaft21sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSVNaft21sstd <- ugarchfit(TSVNaft21sstd.spec, TSVNaft)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNaft21ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSVNaft21ged <- ugarchfit(TSVNaft21ged.spec, TSVNaft)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNaft21sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSVNaft21sged <- ugarchfit(TSVNaft21sged.spec, TSVNaft)# PHÂN PHỐI CHUẨN
TSVNaft22n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
TSVNaft22n <- ugarchfit(TSVNaft22n.spec, TSVNaft)
# PHÂN PHỐI STUDENT
TSVNaft22std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
TSVNaft22std <- ugarchfit(TSVNaft22std.spec, TSVNaft)
# PHÂN PHỐI ĐỐI XỨNG (sstd)
TSVNaft22sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
TSVNaft22sstd <- ugarchfit(TSVNaft22sstd.spec, TSVNaft)
# PHÂN PHỐI Generalized Error Distribution (ged)
TSVNaft22ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = "ged")
TSVNaft22ged <- ugarchfit(TSXaft22ged.spec, TSVNaft)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
TSVNaft22sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
TSVNaft22sged <- ugarchfit(TSXaft22sged.spec, TSVNaft)TSXaft.model.list <- list(garch11n = TSXaft11n,
garch11std = TSXaft11std,
garch11sstd = TSXaft11sstd,
garch11sged = TSXaft11sged,
garch12n = TSXaft12n,
garch12std = TSXaft12std,
garch12sstd = TSXaft12sstd,
garch12ged = TSXaft12ged,
garch12sged = TSXaft12sged,
garch21std = TSXaft21std,
garch21sged = TSXaft21sged,
garch22n = TSXaft22n,
garch22std = TSXaft22std,
garch22sstd = TSXaft22sstd,
garch22ged = TSXaft22ged)
TSXaft.info.mat <- sapply(TSXaft.model.list, infocriteria)
rownames(TSXaft.info.mat) <- rownames(infocriteria(TSXaft11n))
TSXaft.info.mat## garch11n garch11std garch11sstd garch11sged garch12n garch12std
## Akaike -2.495518 -3.784704 -3.804895 -3.848287 -2.446719 -3.778958
## Bayes -2.398164 -3.676533 -3.685908 -3.729300 -2.338548 -3.659971
## Shibata -2.496734 -3.786200 -3.806700 -3.850092 -2.448215 -3.780763
## Hannan-Quinn -2.456804 -3.741689 -3.757579 -3.800971 -2.403703 -3.731642
## garch12sstd garch12ged garch12sged garch21std garch21sged
## Akaike -3.666447 -3.910292 -3.795799 -3.732425 -3.766929
## Bayes -3.536643 -3.791304 -3.665995 -3.602620 -3.626307
## Shibata -3.668587 -3.912096 -3.797939 -3.734565 -3.769431
## Hannan-Quinn -3.614829 -3.862975 -3.744181 -3.680807 -3.711009
## garch22n garch22std garch22sstd garch22ged
## Akaike -2.478526 -3.786280 -3.814525 -3.807111
## Bayes -2.348721 -3.645658 -3.663086 -3.666489
## Shibata -2.480666 -3.788783 -3.817417 -3.809613
## Hannan-Quinn -2.426908 -3.730360 -3.754304 -3.751191TSXaft.inds <- which(TSXaft.info.mat == min(TSXaft.info.mat), arr.ind = TRUE)
model.TSXaft <- colnames(TSXaft.info.mat)[TSXaft.inds[,2]]
model.TSXaft## [1] "garch12ged"TSXaft12ged##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001221 0.000007 176.138941 0.00000
## ar1 0.650099 0.002014 322.757437 0.00000
## ar2 0.287367 0.001109 259.192558 0.00000
## ma1 -0.639971 0.003439 -186.095729 0.00000
## ma2 -0.318577 0.001472 -216.360421 0.00000
## omega 0.000017 0.000082 0.211008 0.83288
## alpha1 0.007377 0.051346 0.143680 0.88575
## beta1 0.395598 0.010401 38.033722 0.00000
## beta2 0.594802 0.010051 59.178162 0.00000
## gamma1 0.000710 0.099671 0.007122 0.99432
## shape 0.367340 0.027173 13.518468 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001221 0.000959 1.273562 0.202819
## ar1 0.650099 0.204715 3.175633 0.001495
## ar2 0.287367 0.117658 2.442396 0.014590
## ma1 -0.639971 0.302088 -2.118492 0.034133
## ma2 -0.318577 0.135992 -2.342621 0.019149
## omega 0.000017 0.000590 0.029319 0.976610
## alpha1 0.007377 0.699389 0.010548 0.991584
## beta1 0.395598 0.007851 50.387359 0.000000
## beta2 0.594802 0.017794 33.426988 0.000000
## gamma1 0.000710 1.140485 0.000622 0.999503
## shape 0.367340 0.085951 4.273847 0.000019
##
## LogLikelihood : 712.8974
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.9103
## Bayes -3.7913
## Shibata -3.9121
## Hannan-Quinn -3.8630
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4544 5.003e-01
## Lag[2*(p+q)+(p+q)-1][11] 6.6572 1.388e-01
## Lag[4*(p+q)+(p+q)-1][19] 21.6385 7.611e-05
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.814 0.17803
## Lag[2*(p+q)+(p+q)-1][8] 6.348 0.20239
## Lag[4*(p+q)+(p+q)-1][14] 11.992 0.09275
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.09878 0.500 2.000 0.7533
## ARCH Lag[6] 1.58190 1.461 1.711 0.5897
## ARCH Lag[8] 5.02937 2.368 1.583 0.2457
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 4.0223
## Individual Statistics:
## mu 0.26291
## ar1 0.12667
## ar2 0.19302
## ma1 0.15434
## ma2 0.16529
## omega 0.06879
## alpha1 0.03742
## beta1 0.08302
## beta2 0.08332
## gamma1 0.03523
## shape 0.18096
##
## 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 0.2678 0.7890
## Negative Sign Bias 0.9865 0.3246
## Positive Sign Bias 1.1610 0.2464
## Joint Effect 2.3894 0.4956
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 53.42 4.040e-05
## 2 30 61.42 4.102e-04
## 3 40 81.45 7.989e-05
## 4 50 81.81 2.271e-03
##
##
## Elapsed time : 1.355784TSVNaft.model.list <- list(garch11n = TSVNaft11n,
garch11std = TSVNaft11std,
garch11sstd = TSVNaft11sstd,
garch11ged = TSVNaft11ged,
garch11sged = TSVNaft11sged,
garch12n = TSVNaft12n,
garch12std = TSVNaft12std,
garch12sstd = TSVNaft12sstd,
garch12sged = TSVNaft12sged,
garch21n = TSVNaft21n,
garch21std = TSVNaft21std,
garch21sstd = TSVNaft21sstd,
garch21ged = TSVNaft21ged,
garch21sged = TSVNaft21sged,
garch22n = TSVNaft22n,
garch22std = TSVNaft22std,
garch22sstd = TSVNaft22sstd,
garch22ged = TSVNaft22ged,
garch22sged = TSVNaft22sged)
TSVNaft.info.mat <- sapply(TSVNaft.model.list, infocriteria)
rownames(TSVNaft.info.mat) <- rownames(infocriteria(TSVNaft11n))
TSVNaft.info.mat## garch11n garch11std garch11sstd garch11ged garch11sged garch12n
## Akaike -2.765198 -3.420058 -3.417891 -3.663148 -3.613890 -2.759820
## Bayes -2.667845 -3.311888 -3.298903 -3.554978 -3.494902 -2.651649
## Shibata -2.766415 -3.421555 -3.419695 -3.664645 -3.615694 -2.761317
## Hannan-Quinn -2.726484 -3.377043 -3.370574 -3.620133 -3.566573 -2.716805
## garch12std garch12sstd garch12sged garch21n garch21std
## Akaike -3.417848 -3.634454 -3.626896 -2.759665 -3.525747
## Bayes -3.298860 -3.504649 -3.497091 -2.640678 -3.395942
## Shibata -3.419652 -3.636593 -3.629035 -2.761469 -3.527886
## Hannan-Quinn -3.370531 -3.582835 -3.575277 -2.712348 -3.474128
## garch21sstd garch21ged garch21sged garch22n garch22std
## Akaike -3.520362 -3.677414 -3.638286 -2.766677 -3.520167
## Bayes -3.379741 -3.547609 -3.497664 -2.636873 -3.379546
## Shibata -3.522865 -3.679553 -3.640788 -2.768817 -3.522670
## Hannan-Quinn -3.464443 -3.625795 -3.582366 -2.715059 -3.464248
## garch22sstd garch22ged garch22sged
## Akaike -3.514783 -3.566606 -3.596615
## Bayes -3.363345 -3.425984 -3.445176
## Shibata -3.517676 -3.569108 -3.599507
## Hannan-Quinn -3.454562 -3.510686 -3.536394TSVNaft.inds <- which(TSVNaft.info.mat == min(TSVNaft.info.mat), arr.ind = TRUE)
model.TSVNaft <- colnames(TSVNaft.info.mat)[TSVNaft.inds[,2]]
model.TSVNaft## [1] "garch21ged"TSVNaft21ged##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001981 0.000034 58.66451 0.00000
## ar1 0.351856 0.004439 79.27158 0.00000
## ar2 -0.039815 0.002014 -19.76676 0.00000
## ma1 -0.390770 0.004134 -94.53088 0.00000
## ma2 -0.011955 0.000533 -22.42283 0.00000
## omega 0.000009 0.000019 0.45853 0.64657
## alpha1 0.010322 0.013651 0.75615 0.44956
## alpha2 0.012142 0.015505 0.78312 0.43356
## beta1 0.966652 0.002340 413.10002 0.00000
## gamma1 0.677600 0.000977 693.81678 0.00000
## gamma2 -0.666050 0.003052 -218.21919 0.00000
## shape 0.452255 0.036868 12.26686 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.001981 0.000049 40.76615 0.00000
## ar1 0.351856 0.009077 38.76196 0.00000
## ar2 -0.039815 0.007275 -5.47312 0.00000
## ma1 -0.390770 0.004635 -84.30320 0.00000
## ma2 -0.011955 0.002157 -5.54341 0.00000
## omega 0.000009 0.000032 0.27480 0.78347
## alpha1 0.010322 0.016945 0.60916 0.54242
## alpha2 0.012142 0.008965 1.35440 0.17561
## beta1 0.966652 0.001693 570.97921 0.00000
## gamma1 0.677600 0.002592 261.40592 0.00000
## gamma2 -0.666050 0.001687 -394.92406 0.00000
## shape 0.452255 0.034925 12.94926 0.00000
##
## LogLikelihood : 672.0957
##
## Information Criteria
## ------------------------------------
##
## Akaike -3.6774
## Bayes -3.5476
## Shibata -3.6796
## Hannan-Quinn -3.6258
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.08338 7.728e-01
## Lag[2*(p+q)+(p+q)-1][11] 19.79652 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 26.83623 2.555e-07
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.744 0.1866
## Lag[2*(p+q)+(p+q)-1][8] 3.452 0.6029
## Lag[4*(p+q)+(p+q)-1][14] 6.558 0.5639
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.04466 0.500 2.000 0.8326
## ARCH Lag[6] 0.15780 1.461 1.711 0.9775
## ARCH Lag[8] 1.03095 2.368 1.583 0.9197
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 11.2263
## Individual Statistics:
## mu 0.04593
## ar1 1.28066
## ar2 0.46260
## ma1 1.12307
## ma2 0.39342
## omega 0.08223
## alpha1 0.07939
## alpha2 0.10180
## beta1 0.16796
## gamma1 0.18803
## gamma2 0.17000
## shape 0.41439
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.69 2.96 3.51
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.7035 0.4822
## Negative Sign Bias 0.3439 0.7312
## Positive Sign Bias 0.9092 0.3639
## Joint Effect 1.3749 0.7114
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 41.95 0.0018018
## 2 30 63.76 0.0002059
## 3 40 60.94 0.0138311
## 4 50 71.22 0.0207102
##
##
## Elapsed time : 1.798247TSXaft.res <- residuals(TSXaft12ged)/sigma(TSXaft12ged)
fitdist(distribution = 'ged' , TSXaft.res, control = list())$pars## mu sigma shape
## -4.503847e-05 9.405022e-01 3.718149e-01sa <- pdist(distribution = 'ged' , q = TSXaft.res, mu = -4.503847e-05, sigma = 9.405022e-01, shape = 3.718149e-01) TSVNaft.res <- residuals(TSVNaft21ged)/sigma(TSVNaft21ged)
fitdist(distribution = 'ged' , TSVNaft.res, control = list())$pars## Warning in .safefunx(tmpv, .solnp_fun, .env, ...):
## solnp-->warning: NaN detected in function call...check your function## mu sigma shape
## 0.0002696898 1.1622061936 0.4054556239va <- pdist(distribution = 'ged' , q = TSVNaft.res, mu = 0.0002696898 , sigma = 1.1622061936, shape = 0.4054556239) # Kiểm định Anderson-Darling
ad.test(sa, 'punif')##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: sa
## An = 2.0008, p-value = 0.09178ad.test(va, 'punif')##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: va
## An = 2.1564, p-value = 0.07552# Kiểm định Cramer-von Mises
cvm.test(sa, 'punif')##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: sa
## omega2 = 0.29182, p-value = 0.1425cvm.test(va, 'punif')##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: va
## omega2 = 0.33542, p-value = 0.1077# Kiểm định ks-test
ks.test(sa, 'punif')##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: sa
## D = 0.073892, p-value = 0.03967
## alternative hypothesis: two-sidedks.test(va, 'punif')##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: va
## D = 0.06693, p-value = 0.0802
## alternative hypothesis: two-sidedBiCopSelect(sa, va, familyset = NA, selectioncrit = 'AIC' , indeptest = FALSE , level = 0.05)## Bivariate copula: t (par = 0.01, par2 = 3.67, tau = 0.01)hihi <- BiCopEst(sa,va, family = 2, method = 'mle', se = T, max.df = 10)
summary(hihi)## Family
## ------
## No: 2
## Name: t
##
## Parameter(s)
## ------------
## par: 0.01 (SE = 0.06)
## par2: 3.67 (SE = 0.77)
## Dependence measures
## -------------------
## Kendall's tau: 0.01 (empirical = -0.01, p value = 0.87)
## Upper TD: 0.09
## Lower TD: 0.09
##
## Fit statistics
## --------------
## logLik: 15.51
## AIC: -27.01
## BIC: -19.24