library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ ggplot2 3.4.2 ✔ tibble 3.2.1
## ✔ lubridate 1.9.2 ✔ tidyr 1.3.0
## ✔ purrr 1.0.1
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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'
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## The following object is masked from 'package:purrr':
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## 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)data1 <- read_excel('C:/Users/Thanh Lan/Documents/data.xlsx')
SGX <- ts(data1$SGX)
VNI <- ts(data1$VNI)autoarfima(SGX, 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 8.39610 0.217640 38.5779 0.000000
## ar1 0.36230 0.099668 3.6351 0.000278
## ar2 0.62158 0.101224 6.1407 0.000000
## ma1 -0.17601 0.083789 -2.1006 0.035672
## ma2 -0.70333 0.080850 -8.6992 0.000000
## sigma 0.95587 0.021133 45.2320 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 8.39610 0.403169 20.8252 0.000000
## ar1 0.36230 0.127025 2.8522 0.004342
## ar2 0.62158 0.117146 5.3061 0.000000
## ma1 -0.17601 0.114555 -1.5365 0.124422
## ma2 -0.70333 0.089977 -7.8167 0.000000
## sigma 0.95587 0.035565 26.8764 0.000000
##
## LogLikelihood : -1377.929
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.7596
## Bayes 2.7890
## Shibata 2.7595
## Hannan-Quinn 2.7707
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 5.535 0.01864
## Lag[2*(p+q)+(p+q)-1][11] 50.099 0.00000
## Lag[4*(p+q)+(p+q)-1][19] 62.169 0.00000
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.829 1.763e-01
## Lag[2*(p+q)+(p+q)-1][2] 9.684 2.317e-03
## Lag[4*(p+q)+(p+q)-1][5] 49.607 8.205e-14
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 17.07 2 0.000197
## ARCH Lag[5] 93.58 5 0.000000
## ARCH Lag[10] 116.09 10 0.000000
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 24.6936
## Individual Statistics:
## mu 1.158
## ar1 5.374
## ar2 5.478
## ma1 4.486
## ma2 5.075
## sigma 8.944
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.110553
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 1 1 1 1 0 2.759580 1
## 2 1 1 0 1 1 0 2.762269 1
## 3 1 0 1 1 1 0 2.782004 1
## 4 0 1 1 1 1 0 2.782286 1
## 5 0 1 0 1 1 0 2.819140 1
## 6 1 1 1 0 1 0 2.945636 1
## 7 1 0 1 0 1 0 2.947436 1
## 8 0 0 1 0 1 0 2.947875 1
## 9 1 0 0 1 1 0 2.948337 1
## 10 0 0 1 1 1 0 2.948859 1
## 11 0 1 1 0 1 0 2.950354 1
## 12 1 0 0 0 1 0 2.952667 1
## 13 1 1 0 0 1 0 2.955422 1
## 14 0 1 0 0 1 0 3.031075 1
## 15 0 0 0 1 1 0 3.034308 1
## 16 0 0 0 0 1 0 3.038043 1
## 17 1 0 1 1 0 0 3.074446 1
## 18 1 0 1 0 0 0 3.077150 1
## 19 1 1 0 1 0 0 3.089679 1
## 20 1 1 1 1 0 0 3.090444 1
## 21 0 1 1 1 0 0 3.135866 1
## 22 0 1 0 1 0 0 3.277547 1
## 23 1 1 0 0 0 0 3.318641 1
## 24 1 0 0 1 0 0 3.341739 1
## 25 1 0 0 0 0 0 3.414841 1
## 26 0 1 1 0 0 0 3.561762 1
## 27 0 1 0 0 0 0 3.671486 1
## 28 0 0 1 1 0 0 5.299032 1
## 29 0 0 1 0 0 0 6.025187 1
## 30 0 0 0 1 0 0 6.144198 1
## 31 1 1 1 0 0 0 NA 0autoarfima(VNI, 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 1067.84393 36.769312 29.0417 0.000000
## ar1 0.41026 0.081371 5.0418 0.000000
## ar2 0.57410 0.080181 7.1600 0.000000
## ma1 -0.23411 0.070331 -3.3287 0.000872
## ma2 -0.64951 0.063788 -10.1823 0.000000
## sigma 177.87816 3.972033 44.7826 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1067.84393 37.817783 28.2366 0e+00
## ar1 0.41026 0.055441 7.3999 0e+00
## ar2 0.57410 0.056684 10.1281 0e+00
## ma1 -0.23411 0.051844 -4.5157 6e-06
## ma2 -0.64951 0.050201 -12.9381 0e+00
## sigma 177.87816 5.673102 31.3547 0e+00
##
## LogLikelihood : -6619.806
##
## Information Criteria
## ------------------------------------
##
## Akaike 13.212
## Bayes 13.241
## Shibata 13.212
## Hannan-Quinn 13.223
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 5.185 0.02278
## Lag[2*(p+q)+(p+q)-1][11] 33.608 0.00000
## Lag[4*(p+q)+(p+q)-1][19] 45.447 0.00000
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7747 3.788e-01
## Lag[2*(p+q)+(p+q)-1][2] 1.0065 4.961e-01
## Lag[4*(p+q)+(p+q)-1][5] 21.8838 5.861e-06
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 1.186 2 5.526e-01
## ARCH Lag[5] 58.116 5 2.977e-11
## ARCH Lag[10] 86.505 10 2.631e-14
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 11.9009
## Individual Statistics:
## mu 0.1983
## ar1 2.0868
## ar2 1.4282
## ma1 4.9852
## ma2 3.5469
## sigma 7.2946
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.08170295
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 1 1 1 1 0 13.21198 1
## 2 1 1 0 1 1 0 13.22486 1
## 3 0 1 1 1 1 0 13.22728 1
## 4 0 1 0 1 1 0 13.26008 1
## 5 1 1 1 0 1 0 13.35782 1
## 6 1 0 1 0 1 0 13.35832 1
## 7 1 0 1 1 1 0 13.35918 1
## 8 0 0 1 0 1 0 13.36044 1
## 9 0 0 1 1 1 0 13.36098 1
## 10 1 0 0 1 1 0 13.36225 1
## 11 0 1 1 0 1 0 13.36255 1
## 12 1 0 0 0 1 0 13.36414 1
## 13 1 1 0 0 1 0 13.36623 1
## 14 0 0 0 1 1 0 13.42126 1
## 15 0 0 0 0 1 0 13.42131 1
## 16 0 1 0 0 1 0 13.42334 1
## 17 1 0 1 1 0 0 13.43562 1
## 18 1 0 1 0 0 0 13.43597 1
## 19 1 1 0 1 0 0 13.43893 1
## 20 1 1 1 1 0 0 13.44069 1
## 21 0 1 1 1 0 0 13.46510 1
## 22 0 1 0 1 0 0 13.58601 1
## 23 1 1 0 0 0 0 13.71900 1
## 24 1 0 0 1 0 0 13.78596 1
## 25 1 0 0 0 0 0 13.84300 1
## 26 0 1 1 0 0 0 13.92197 1
## 27 0 1 0 0 0 0 14.06833 1
## 28 0 0 1 1 0 0 15.24073 1
## 29 0 0 1 0 0 0 15.80210 1
## 30 0 0 0 1 0 0 15.91548 1
## 31 1 1 1 0 0 0 150.89782 1# PHÂN PHỐI CHUẨN
sgx11n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
sgx11n <- ugarchfit(spec = sgx11n.spec, SGX)
# PHÂN PHỐI STUDENT
sgx11std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
sgx11std <- ugarchfit(sgx11std.spec, SGX)
# PHÂN PHỐI ĐỐI XỨNG
sgx11sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
sgx11sstd <- ugarchfit(sgx11sstd.spec, SGX)
# PHÂN PHỐI PHÂN PHỐI Generalized Error Distribution
sgx11ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
sgx11ged <- ugarchfit(sgx11ged.spec, SGX)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
sgx11sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
sgx11sged <- ugarchfit(sgx11sged.spec, SGX)# PHÂN PHỐI CHUẨN
sgx12n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
sgx12n <- ugarchfit(spec = sgx12n.spec, SGX)
# PHÂN PHỐI STUDENT
sgx12std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
sgx12std <- ugarchfit(sgx12std.spec, SGX)
# PHÂN PHỐI ĐỐI XỨNG
sgx12sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
sgx12sstd <- ugarchfit(sgx12sstd.spec, SGX)
# PHÂN PHỐI PHÂN PHỐI Generalized Error Distribution
sgx12ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
sgx12ged <- ugarchfit(sgx12ged.spec, SGX)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
sgx12sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
sgx12sged <- ugarchfit(sgx12sged.spec, SGX)# PHÂN PHỐI CHUẨN
sgx21n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
sgx21n <- ugarchfit(spec = sgx21n.spec, SGX)
# PHÂN PHỐI STUDENT
sgx21std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
sgx21std <- ugarchfit(sgx21std.spec, SGX)
# PHÂN PHỐI ĐỐI XỨNG
sgx21sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
sgx21sstd <- ugarchfit(sgx21sstd.spec, SGX)
# PHÂN PHỐI PHÂN PHỐI Generalized Error Distribution
sgx21ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
sgx21ged <- ugarchfit(sgx21ged.spec, SGX)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
sgx21sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
sgx21sged <- ugarchfit(sgx21sged.spec, SGX)# PHÂN PHỐI CHUẨN
sgx22n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
sgx22n <- ugarchfit(spec = sgx22n.spec, SGX)
# PHÂN PHỐI STUDENT
sgx22std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
sgx22std <- ugarchfit(sgx22std.spec, SGX)
# PHÂN PHỐI ĐỐI XỨNG
sgx22sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
sgx22sstd <- ugarchfit(sgx22sstd.spec, SGX)
# PHÂN PHỐI PHÂN PHỐI Generalized Error Distribution
sgx22ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
sgx22ged <- ugarchfit(sgx22ged.spec, SGX)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
sgx22sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
sgx22sged <- ugarchfit(sgx22sged.spec, SGX)# PHÂN PHỐI CHUẨN
vni11n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
vni11n <- ugarchfit(spec = vni11n.spec, VNI)
# PHÂN PHỐI STUDENT
vni11std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
vni11std <- ugarchfit(vni11std.spec, VNI)
# PHÂN PHỐI ĐỐI XỨNG
vni11sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
vni11sstd <- ugarchfit(vni11sstd.spec, VNI)
# PHÂN PHỐI PHÂN PHỐI Generalized Error Distribution
vni11ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
vni11ged <- ugarchfit(vni11ged.spec, VNI)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
vni11sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
vni11sged <- ugarchfit(vni11sged.spec, VNI)# PHÂN PHỐI CHUẨN
vni12n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
vni12n <- ugarchfit(spec = vni12n.spec, VNI)
# PHÂN PHỐI STUDENT
vni12std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
vni12std <- ugarchfit(vni12std.spec, VNI)
# PHÂN PHỐI ĐỐI XỨNG
vni12sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
vni12sstd <- ugarchfit(vni12sstd.spec, VNI)
# PHÂN PHỐI PHÂN PHỐI Generalized Error Distribution
vni12ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1,2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
vni12ged <- ugarchfit(vni12ged.spec, VNI)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
vni12sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(1,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
vni12sged <- ugarchfit(vni12sged.spec, VNI)# PHÂN PHỐI CHUẨN
vni21n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
vni21n <- ugarchfit(spec = vni21n.spec, VNI)
# PHÂN PHỐI STUDENT
vni21std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
vni21std <- ugarchfit(vni21std.spec, VNI)
# PHÂN PHỐI ĐỐI XỨNG
vni21sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
vni21sstd <- ugarchfit(vni21sstd.spec, VNI)
# PHÂN PHỐI PHÂN PHỐI Generalized Error Distribution
vni21ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
vni21ged <- ugarchfit(vni21ged.spec, VNI)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
vni21sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,1)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
vni21sged <- ugarchfit(vni21sged.spec, VNI)# PHÂN PHỐI CHUẨN
vni22n.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'norm')
vni22n <- ugarchfit(spec = vni22n.spec, VNI)
# PHÂN PHỐI STUDENT
vni22std.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'std')
vni22std <- ugarchfit(vni22std.spec, VNI)
# PHÂN PHỐI ĐỐI XỨNG
vni22sstd.spec <- ugarchspec(variance.model = list( model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sstd')
vni22sstd <- ugarchfit(vni22sstd.spec, VNI)
# PHÂN PHỐI PHÂN PHỐI Generalized Error Distribution
vni22ged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2,2)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
vni22ged <- ugarchfit(vni22ged.spec, VNI)
# PHÂN PHỐI Generalized Error Distribution đối xứng (sged)
vni22sged.spec <- ugarchspec(variance.model = list(model = 'gjrGARCH', garchOrder = c(2,2)), mean.model = list(armaOrder = c(2,2), include.mean = TRUE), distribution.model = 'sged')
vni22sged <- ugarchfit(vni22sged.spec, VNI)sgx.model.list <- list(garch11n = sgx11n,
garch11std = sgx11std,
garch11sstd = sgx11sstd,
garch11ged = sgx11ged,
garch11sged = sgx11sged,
garch12n = sgx12n,
garch12std = sgx12std,
garch12sstd = sgx12sstd,
garch12ged = sgx12ged,
garch12sged = sgx12sged,
garch21n = sgx21n,
garch21std = sgx21std,
garch21sstd = sgx21sstd,
garch21ged = sgx21ged,
garch21sged = sgx21sged,
garch22n = sgx22n,
garch22std = sgx22std,
garch22sstd = sgx22sstd,
garch22ged = sgx22ged,
garch22sged = sgx22sged)
sgx.info.mat <- sapply(sgx.model.list, infocriteria)
rownames(sgx.info.mat) <- rownames(infocriteria(sgx11n))
sgx.info.mat## garch11n garch11std garch11sstd garch11ged garch11sged garch12n
## Akaike 2.526233 2.528161 2.529850 2.528179 2.529741 2.528227
## Bayes 2.570298 2.577122 2.583707 2.577140 2.583597 2.577188
## Shibata 2.526074 2.527965 2.529613 2.527983 2.529504 2.528031
## Hannan-Quinn 2.542978 2.546767 2.550317 2.546785 2.550207 2.546833
## garch12std garch12sstd garch12ged garch12sged garch21n garch21std
## Akaike 2.530165 2.531844 2.530173 2.531735 2.512831 2.519675
## Bayes 2.584022 2.590597 2.584030 2.590487 2.566688 2.578428
## Shibata 2.529928 2.531562 2.529936 2.531453 2.512594 2.519393
## Hannan-Quinn 2.550632 2.554171 2.550639 2.554062 2.533298 2.542002
## garch21sstd garch21ged garch21sged garch22n garch22std garch22sstd
## Akaike 2.521248 2.519586 2.520872 2.519587 2.521734 2.517290
## Bayes 2.584897 2.578339 2.584520 2.578340 2.585383 2.585835
## Shibata 2.520918 2.519304 2.520541 2.519305 2.521403 2.516908
## Hannan-Quinn 2.545436 2.541913 2.545059 2.541914 2.545921 2.543338
## garch22ged garch22sged
## Akaike 2.521580 2.522865
## Bayes 2.585229 2.591410
## Shibata 2.521250 2.522483
## Hannan-Quinn 2.545768 2.548913sgx.inds <- which(sgx.info.mat == min(sgx.info.mat), arr.ind = TRUE)
model.sgx <- colnames(sgx.info.mat)[sgx.inds[,2]]
model.sgx## [1] "garch21n"sgx21n##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 7.409277 0.135438 5.4706e+01 0.00000
## ar1 0.457257 0.010445 4.3776e+01 0.00000
## ar2 0.540432 0.004878 1.1080e+02 0.00000
## ma1 -0.242441 0.040632 -5.9668e+00 0.00000
## ma2 -0.623333 0.078023 -7.9890e+00 0.00000
## omega 0.007952 0.000298 2.6687e+01 0.00000
## alpha1 0.090683 0.002847 3.1856e+01 0.00000
## alpha2 0.000000 0.011334 1.7000e-05 0.99999
## beta1 0.882426 0.000050 1.7488e+04 0.00000
## gamma1 -0.209070 0.018021 -1.1601e+01 0.00000
## gamma2 0.259791 0.021214 1.2246e+01 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 7.409277 0.482333 15.361336 0.000000
## ar1 0.457257 0.043226 10.578202 0.000000
## ar2 0.540432 0.023382 23.113535 0.000000
## ma1 -0.242441 0.180528 -1.342955 0.179286
## ma2 -0.623333 0.314488 -1.982055 0.047473
## omega 0.007952 0.003611 2.202075 0.027660
## alpha1 0.090683 0.033331 2.720655 0.006515
## alpha2 0.000000 0.038743 0.000005 0.999996
## beta1 0.882426 0.000117 7511.282693 0.000000
## gamma1 -0.209070 0.020212 -10.343891 0.000000
## gamma2 0.259791 0.036047 7.207023 0.000000
##
## LogLikelihood : -1249.185
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.5128
## Bayes 2.5667
## Shibata 2.5126
## Hannan-Quinn 2.5333
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.904 3.417e-01
## Lag[2*(p+q)+(p+q)-1][11] 24.385 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 33.963 4.131e-11
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.559 0.21184
## Lag[2*(p+q)+(p+q)-1][8] 10.729 0.02372
## Lag[4*(p+q)+(p+q)-1][14] 15.664 0.01834
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 8.739 0.500 2.000 0.003115
## ARCH Lag[6] 9.248 1.461 1.711 0.011920
## ARCH Lag[8] 12.296 2.368 1.583 0.006816
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 6.8514
## Individual Statistics:
## mu 0.03081
## ar1 0.29252
## ar2 0.25877
## ma1 3.46303
## ma2 3.63152
## omega 0.28628
## alpha1 0.06594
## alpha2 0.16258
## beta1 0.35314
## gamma1 0.12787
## gamma2 0.23233
##
## 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 1.6171 0.1062
## Negative Sign Bias 0.7976 0.4253
## Positive Sign Bias 0.2712 0.7863
## Joint Effect 3.2480 0.3549
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 93.65 7.434e-12
## 2 30 85.11 2.023e-07
## 3 40 112.89 4.125e-09
## 4 50 124.27 1.813e-08
##
##
## Elapsed time : 0.5167799vni.model.list <- list(garch11n = vni11n,
garch11std = vni11std,
garch11sstd = vni11sstd,
garch11ged = vni11ged,
garch11sged = vni11sged,
garch12n = vni12n,
garch12std = vni12std,
garch12sstd = vni12sstd,
garch12ged = vni12ged,
garch12sged = vni12sged,
garch21n = vni21n,
garch21std = vni21std,
garch21sstd = vni21sstd,
garch21ged = vni21ged,
garch21sged = vni21sged,
garch22n = vni22n,
garch22std = vni22std,
garch22sstd = vni22sstd,
garch22ged = vni22ged,
garch22sged = vni22sged)
vni.info.mat <- sapply(vni.model.list, infocriteria)
rownames(vni.info.mat) <- rownames(infocriteria(vni11n))
vni.info.mat## garch11n garch11std garch11sstd garch11ged garch11sged garch12n
## Akaike 13.02755 13.01303 12.94429 13.02502 12.93589 13.02846
## Bayes 13.07162 13.06199 12.99815 13.07398 12.98974 13.07743
## Shibata 13.02739 13.01283 12.94405 13.02483 12.93565 13.02827
## Hannan-Quinn 13.04430 13.03164 12.96476 13.04363 12.95635 13.04707
## garch12std garch12sstd garch12ged garch12sged garch21n garch21std
## Akaike 13.01454 12.94555 13.02614 12.93788 13.02936 13.01585
## Bayes 13.06840 13.00430 13.08000 12.99663 13.08321 13.07460
## Shibata 13.01431 12.94527 13.02590 12.93760 13.02912 13.01557
## Hannan-Quinn 13.03501 12.96788 13.04661 12.96021 13.04982 13.03818
## garch21sstd garch21ged garch21sged garch22n garch22std garch22sstd
## Akaike 12.94778 13.02720 12.93938 13.03135 13.01425 12.94554
## Bayes 13.01143 13.08595 13.00303 13.09010 13.07790 13.01409
## Shibata 12.94745 13.02692 12.93905 13.03107 13.01392 12.94516
## Hannan-Quinn 12.97197 13.04952 12.96357 13.05368 13.03843 12.97159
## garch22ged garch22sged
## Akaike 13.02580 12.93650
## Bayes 13.08945 13.00505
## Shibata 13.02547 12.93612
## Hannan-Quinn 13.04998 12.96255vni.inds <- which(vni.info.mat == min(vni.info.mat), arr.ind = TRUE)
model.vni <- colnames(vni.info.mat)[vni.inds[,2]]
model.vni## [1] "garch11sged"vni11sged##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1056.618112 28.346113 37.2756 0.000000
## ar1 0.483453 0.006557 73.7353 0.000000
## ar2 0.494958 0.006391 77.4428 0.000000
## ma1 -0.327051 0.019355 -16.8975 0.000000
## ma2 -0.537719 0.016398 -32.7921 0.000000
## omega 187.559395 77.345887 2.4249 0.015311
## alpha1 0.099859 0.013429 7.4362 0.000000
## beta1 0.918762 0.010053 91.3899 0.000000
## gamma1 -0.033359 0.019245 -1.7334 0.083018
## skew 1.509278 0.054210 27.8412 0.000000
## shape 1.165975 0.090351 12.9049 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1056.618112 47.737836 22.1338 0.000000
## ar1 0.483453 0.004539 106.5169 0.000000
## ar2 0.494958 0.004143 119.4810 0.000000
## ma1 -0.327051 0.025636 -12.7574 0.000000
## ma2 -0.537719 0.011916 -45.1262 0.000000
## omega 187.559395 145.396434 1.2900 0.197055
## alpha1 0.099859 0.010265 9.7277 0.000000
## beta1 0.918762 0.007234 127.0147 0.000000
## gamma1 -0.033359 0.012068 -2.7644 0.005704
## skew 1.509278 0.080204 18.8180 0.000000
## shape 1.165975 0.180441 6.4618 0.000000
##
## LogLikelihood : -6476.347
##
## Information Criteria
## ------------------------------------
##
## Akaike 12.936
## Bayes 12.990
## Shibata 12.936
## Hannan-Quinn 12.956
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1979 6.564e-01
## Lag[2*(p+q)+(p+q)-1][11] 25.4648 0.000e+00
## Lag[4*(p+q)+(p+q)-1][19] 36.8230 1.003e-12
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.144 0.70434
## Lag[2*(p+q)+(p+q)-1][5] 4.502 0.19778
## Lag[4*(p+q)+(p+q)-1][9] 10.073 0.04839
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 1.671 0.500 2.000 0.19608
## ARCH Lag[5] 3.166 1.440 1.667 0.26661
## ARCH Lag[7] 8.770 2.315 1.543 0.03526
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 9.7862
## Individual Statistics:
## mu 0.07939
## ar1 0.44657
## ar2 0.31978
## ma1 2.24638
## ma2 1.51758
## omega 0.06789
## alpha1 0.08952
## beta1 0.25788
## gamma1 0.11160
## skew 1.81608
## shape 0.33855
##
## 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 2.049 0.040706 **
## Negative Sign Bias 0.214 0.830614
## Positive Sign Bias 2.860 0.004322 ***
## Joint Effect 8.720 0.033262 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 48.55 2.139e-04
## 2 30 81.88 6.137e-07
## 3 40 105.47 4.945e-08
## 4 50 119.68 7.587e-08
##
##
## Elapsed time : 3.323833sgx.res <- residuals(sgx21n)/sigma(sgx21n)
fitdist(distribution = 'norm' , sgx.res, control = list())$pars## mu sigma
## 0.04993222 0.99128476s <- pdist(distribution = 'norm' , q = sgx.res, mu = 0.04993222 , sigma = 0.99128476)vni.res <- residuals(vni11sged)/sigma(vni11sged)
fitdist(distribution = 'sged' , vni.res, control = list())$pars## mu sigma skew shape
## 0.0001526608 0.9957763523 1.5076768019 1.1732611271v <- pdist(distribution = 'sged' , q = vni.res, mu = 0.0001526608 , sigma = 0.9957763523, skew = 1.5076768019, shape = 1.1732611271)# Kiểm định Anderson-Darling
ad.test(s, 'punif')##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: s
## An = 2.0949, p-value = 0.08151ad.test(v, 'punif')##
## Anderson-Darling test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: v
## An = 2.0199, p-value = 0.08957# Kiểm định Cramer-von Mises
cvm.test(s, 'punif')##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: s
## omega2 = 0.23188, p-value = 0.2134cvm.test(v, 'punif')##
## Cramer-von Mises test of goodness-of-fit
## Null hypothesis: uniform distribution
## Parameters assumed to be fixed
##
## data: v
## omega2 = 0.2657, p-value = 0.1694# Kiểm định ks-test
ks.test(s, 'punif')##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: s
## D = 0.95922, p-value < 2.2e-16
## alternative hypothesis: two-sidedks.test(v, 'punif')##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: v
## D = 0.034205, p-value = 0.1911
## alternative hypothesis: two-sidedBiCopSelect(s, v, familyset = 1:9, selectioncrit = 'AIC', indeptest = FALSE, level = 0.05)## Bivariate copula: Frank (par = 3.26, tau = 0.33)Stu <- BiCopEst(s, v, family = 5, method = 'mle', se = T, max.df = 10)
summary(Stu)## Family
## ------
## No: 5
## Name: Frank
##
## Parameter(s)
## ------------
## par: 3.26 (SE = 0.21)
##
## Dependence measures
## -------------------
## Kendall's tau: 0.33 (empirical = 0.33, p value < 0.01)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 130.26
## AIC: -258.53
## BIC: -253.62