MPNN2
2024-08-10
CẤU TRÚC PHỤ THUỘC GIỮA CHỈ SỐ THỊ TRƯỜNG CHỨNG KHOÁN VIỆT NAM ĐẾN TỶ GIÁ VÀNG XAU/USD: TIẾP CẬN BẰNG PHƯƠNG PHÁP COPULA
Các họ hàm cơ bản của Copula
Copula họ Elip
library(moments)
library(kableExtra)## Warning: package 'kableExtra' was built under R version 4.3.3library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:kableExtra':
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## group_rows## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(knitr)## Warning: package 'knitr' was built under R version 4.3.3library(copula)## Warning: package 'copula' was built under R version 4.3.3library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.3.3library(plotly)## Warning: package 'plotly' was built under R version 4.3.3##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
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## layoutlibrary(gridExtra)## Warning: package 'gridExtra' was built under R version 4.3.3##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
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## combinelibrary(VC2copula)## Warning: package 'VC2copula' was built under R version 4.3.3library(VineCopula)## Warning: package 'VineCopula' was built under R version 4.3.3##
## Attaching package: 'VineCopula'## The following objects are masked from 'package:VC2copula':
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## BB1Copula, BB6Copula, BB7Copula, BB8Copula, copulaFromFamilyIndex,
## joeBiCopula, r270BB1Copula, r270BB6Copula, r270BB7Copula,
## r270BB8Copula, r270ClaytonCopula, r270GumbelCopula,
## r270JoeBiCopula, r270TawnT1Copula, r270TawnT2Copula, r90BB1Copula,
## r90BB6Copula, r90BB7Copula, r90BB8Copula, r90ClaytonCopula,
## r90GumbelCopula, r90JoeBiCopula, r90TawnT1Copula, r90TawnT2Copula,
## surBB1Copula, surBB6Copula, surBB7Copula, surBB8Copula,
## surClaytonCopula, surGumbelCopula, surJoeBiCopula, surTawnT1Copula,
## surTawnT2Copula, tawnT1Copula, tawnT2Copula, vineCopula## The following object is masked from 'package:copula':
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## pobslibrary(gridGraphics)## Warning: package 'gridGraphics' was built under R version 4.3.3## Loading required package: gridlibrary(png)
library(quantmod)## Warning: package 'quantmod' was built under R version 4.3.3## Loading required package: xts## Warning: package 'xts' was built under R version 4.3.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 4.3.3##
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## first, last## Loading required package: TTR## Warning: package 'TTR' was built under R version 4.3.3## Registered S3 method overwritten by 'quantmod':
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## Attaching package: 'PerformanceAnalytics'## The following objects are masked from 'package:moments':
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## legendlibrary(tidyr)
library(tseries)## Warning: package 'tseries' was built under R version 4.3.3library(FinTS)## Warning: package 'FinTS' was built under R version 4.3.3library(ggcorrplot)## Warning: package 'ggcorrplot' was built under R version 4.3.3library(goftest)
library(VC2copula)
library(rugarch)## Warning: package 'rugarch' was built under R version 4.3.3## Loading required package: parallel##
## Attaching package: 'rugarch'## The following object is masked from 'package:stats':
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## sigmascatter_plot <- function(random_data, cl) {
ggplot(data.frame(random_data), aes(random_data[,1], random_data[,2])) +
geom_point(alpha = 0.5, col = cl) +
theme_minimal() +
labs(x = "u", y = "v")
}
persp_plot <- function(copula_obj, file_name, cl) {
png(file_name)
persp(copula_obj, dCopula,
xlab = 'u', ylab = 'v', col = cl, ltheta = 120,
ticktype = "detailed", cex.axis = 0.8)
dev.off()
rasterGrob(readPNG(file_name),interpolate = TRUE)
}
set.seed(123)
cop_nor <- normalCopula(param = 0.8, dim = 2)
random_nor <- rCopula(copula = cop_nor,n = 7600)
cop_std <- tCopula(param = 0.8, dim = 2, df = 1)
random_std <- rCopula(copula = cop_std,n = 7600)
#Vẽ biểu đồ
png('nors.png')
scatter_plot(random_nor, '#ADD8E6')
dev.off()## png
## 2nors <- rasterGrob(readPNG('nors.png'), interpolate = TRUE)
png('stds.png')
scatter_plot(random_std, '#F08080')
dev.off()## png
## 2stds <- rasterGrob(readPNG('stds.png'), interpolate = TRUE)
nor_per <- persp_plot(cop_nor, 'norp.png', '#ADD8E6')
std_per <- persp_plot(cop_std, 'stdp.png', '#F08080')
legend <- legendGrob(
labels = c("Gauss", "Student"), pch = 15,
gp = gpar(col = c('#ADD8E6', '#F08080'), fill = c('#ADD8E6', '#F08080'))
)
grid.arrange(nors, nor_per, stds, std_per, legend, ncol = 3,
layout_matrix = rbind(c(1, 2, 5), c(3, 4, 5)),
widths = c(2, 2, 1),
top = textGrob("Hình : Biểu đồ phân tán và phối cảnh PDF của Copula họ Elip",
gp = gpar(fontsize = 15, font = 2))
)
## Copula họ Archimedean
set.seed(123)
cop_clay <- claytonCopula(param = 4, dim = 2)
random_clay <- rCopula(copula = cop_clay,n = 7600)
cop_gum <- gumbelCopula(param = 5, dim = 2)
random_gum <- rCopula(copula = cop_gum,n = 7600)
png('clays.png')
scatter_plot(random_clay,'#90EE90')
dev.off()## png
## 2clays <- rasterGrob(readPNG('clays.png'), interpolate = TRUE)
png('gums.png')
scatter_plot(random_gum,'#FFA07A')
dev.off()## png
## 2gums <- rasterGrob(readPNG('gums.png'), interpolate = TRUE)
clayp <- persp_plot(cop_clay,'clayp.png','#90EE90')
gump <- persp_plot(cop_gum,'gump.png','#FFA07A')
legend <- legendGrob(
labels = c("Clayton", "Gumbel"), pch = 15,
gp = gpar(col = c('#90EE90', '#FFA07A'), fill = c('#90EE90', '#FFA07A'))
)
grid.arrange(clays, clayp, gums, gump, legend, ncol = 3,
layout_matrix = rbind(c(1, 2, 5), c(3, 4, 5)),
widths = c(2, 2, 1),
top = textGrob("Hình : Biểu đồ phân tán và PDF của Copula Clayton và Gumbel",
gp = gpar(fontsize = 15, font = 2))
)
set.seed(123)
cop_surgum <- VC2copula::surGumbelCopula(param = 5)
random_surgum <- rCopula(copula = cop_surgum,n = 7600)
cop_surclay <- VC2copula::surClaytonCopula(param = 4)
random_surclay <- rCopula(copula = cop_surclay,n = 7600)
png('surclays.png')
scatter_plot(random_surclay,'#FFB6C1')
dev.off()## png
## 2surclays <- rasterGrob(readPNG('surclays.png'), interpolate = TRUE)
png('surgums.png')
scatter_plot(random_surgum,'#E6E6FA')
dev.off()## png
## 2surgums <- rasterGrob(readPNG('surgums.png'), interpolate = TRUE)
surclayp <- persp_plot(cop_surclay, "surclayp.png","#FFB6C1")
surgump <- persp_plot(cop_surgum, "surgump.png","#E6E6FA")
legend <- legendGrob(labels = c("Survival Clayton","Survival Gumbel"), pch = 15,
gp = gpar(col = c('#FFB6C1','#E6E6FA'), fill = c('#FFB6C1','#E6E6FA' )))
grid.arrange(surclays, surclayp,surgums, surgump, legend, ncol = 3,
layout_matrix = rbind(c(1,2,5),c(3,4,5)),
widths = c(2,2,1),
top = textGrob("Hình : Biểu đồ phân tán và PDF của Copula Sur Clayton và Gumbel",
gp = gpar(fontsize = 15, font = 2))
)
set.seed(123)
cop_frank <- frankCopula(param = 9.2)
random_frank <- rCopula(copula = cop_frank,n = 7600)
cop_joe <- joeCopula(param = 3)
random_joe <- rCopula(copula = cop_joe,n = 7600)
png('franks.png')
scatter_plot(random_frank,'#FFFACD')
dev.off()## png
## 2franks <- rasterGrob(readPNG('franks.png'), interpolate = TRUE)
png('joes.png')
scatter_plot(random_joe,'#FF6347')
dev.off()## png
## 2joes <- rasterGrob(readPNG('joes.png'), interpolate = TRUE)
frankp <- persp_plot(cop_frank, "frankp.png","#FFFACD")
joep <- persp_plot(cop_joe, "joep.png","#FF6347")
legend <- legendGrob(labels = c("Franl","Joe"), pch = 15,
gp = gpar(col = c('#FFFACD','#FF6347'), fill = c('#FFFACD','#FF6347')))
grid.arrange(franks, frankp,joes, joep, legend, ncol = 3,
layout_matrix = rbind(c(1,2,5),c(3,4,5)),
widths = c(2,2,1),
top = textGrob("Hình : Biểu đồ phân tán và PDF của Copula Frank và Joe",
gp = gpar(fontsize = 15, font = 2))
)
set.seed(123)
cop_bb1 <- VC2copula::BB1Copula(param = c(2,1.7))
random_bb1 <- rCopula(copula = cop_bb1,n = 7600)
cop_bb6 <- VC2copula::BB6Copula(param = c(2,4.5))
random_bb6 <- rCopula(copula = cop_bb6,n = 7600)
png('bb1s.png')
scatter_plot(random_bb1,'#6A5ACD')
dev.off()## png
## 2bb1s <- rasterGrob(readPNG('bb1s.png'), interpolate = TRUE)
png('bb6s.png')
scatter_plot(random_bb6,'#DC143C')
dev.off()## png
## 2bb6s <- rasterGrob(readPNG('bb6s.png'), interpolate = TRUE)
bb1p <- persp_plot(cop_bb1, "bb1p.png","#6A5ACD")
bb6p <- persp_plot(cop_bb6, "bb6p.png","#DC143C")
legend <- legendGrob(labels = c("BB1","BB6"), pch = 15,
gp = gpar(col = c('#6A5ACD','#DC143C'), fill = c('#6A5ACD','#DC143C')))
grid.arrange(bb1s, bb1p,bb6s, bb6p, legend, ncol = 3,
layout_matrix = rbind(c(1,2,5),c(3,4,5)),
widths = c(2,2,1),
top = textGrob("Hình: Biểu đồ phân tán và PDF của Copula BB1 và BB6",
gp = gpar(fontsize = 15, font = 2))
)
set.seed(123)
cop_bb7 <- VC2copula::BB7Copula(param = c(2,4.5))
random_bb7 <- rCopula(copula = cop_bb7,n = 7600)
cop_bb8 <- VC2copula::BB8Copula(param = c(4,0.8))
random_bb8 <- rCopula(copula = cop_bb8,n = 7600)
png('bb7s.png')
scatter_plot(random_bb7,'#FFA07A')
dev.off()## png
## 2bb7s <- rasterGrob(readPNG('bb7s.png'), interpolate = TRUE)
png('bb8s.png')
scatter_plot(random_bb8,'#C0C0C0')
dev.off()## png
## 2bb8s <- rasterGrob(readPNG('bb8s.png'), interpolate = TRUE)
bb7p <- persp_plot(cop_bb7, "bb7p.png","#FFA07A")
bb8p <- persp_plot(cop_bb8, "bb8p.png","#C0C0C0")
legend <- legendGrob(labels = c("BB7","BB8"), pch = 15,
gp = gpar(col = c('#FFA07A','#C0C0C0'), fill = c('#FFA07A','#C0C0C0')))
grid.arrange(bb7s, bb7p,bb8s, bb8p, legend, ncol = 3,
layout_matrix = rbind(c(1,2,5),c(3,4,5)),
widths = c(2,2,1),
top = textGrob("Hình: Biểu đồ phân tán và PDF của Copula BB7 và BB8",
gp = gpar(fontsize = 15, font = 2))
)
Thống Kê Mô Tả dỮ LIỆU
library(lmtest)## Warning: package 'lmtest' was built under R version 4.3.3library(fGarch)## Warning: package 'fGarch' was built under R version 4.3.3## NOTE: Packages 'fBasics', 'timeDate', and 'timeSeries' are no longer
## attached to the search() path when 'fGarch' is attached.
##
## If needed attach them yourself in your R script by e.g.,
## require("timeSeries")##
## Attaching package: 'fGarch'## The following objects are masked from 'package:PerformanceAnalytics':
##
## ES, VaR## The following object is masked from 'package:TTR':
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## volatilitylibrary(rugarch)
library(tseries)
library(xlsx)## Warning: package 'xlsx' was built under R version 4.3.3library(quantmod)
library(PerformanceAnalytics)
library(ggplot2)
library(kableExtra)
library(tidyr)
data <- read.xlsx("D:/MHNN/datapractical5.xlsx", sheetIndex = 1, header = T)
data <- na.omit(data)
library(moments)
library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.3.3## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0 ✔ readr 2.1.5
## ✔ lubridate 1.9.3 ✔ stringr 1.5.1
## ✔ purrr 1.0.2 ✔ tibble 3.2.1## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ gridExtra::combine() masks dplyr::combine()
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsdatan <- as.data.frame(data)
rVNI <- datan %>% summarise(Min = min(VNI),
Max = max(VNI),
Mean = mean(VNI),
StDev = sd(VNI),
Skewness = skewness(VNI),
Kurtosis = kurtosis(VNI))
rXAU <- datan %>% summarise(Min = min(XAU.USD),
Max = max(XAU.USD),
Mean = mean(XAU.USD),
StDev = sd(XAU.USD),
Skewness = skewness(XAU.USD),
Kurtosis = kurtosis(XAU.USD))
print(rVNI)## Min Max Mean StDev Skewness Kurtosis
## 1 -0.0275133 0.04363962 -2.686766e-06 0.007796302 0.5756554 3.1855print(rXAU)## Min Max Mean StDev Skewness Kurtosis
## 1 -0.02561258 0.01866097 0.0001347535 0.003920565 -0.330554 3.430407Ma trận hệ số tương quan
library(PerformanceAnalytics)
library(Hmisc)## Warning: package 'Hmisc' was built under R version 4.3.3##
## Attaching package: 'Hmisc'## The following object is masked from 'package:quantmod':
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## Lag## The following object is masked from 'package:plotly':
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## subplot## The following objects are masked from 'package:dplyr':
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## format.pval, unitsres <- cor(data[,2:3])
round(res, 2)## VNI XAU.USD
## VNI 1.00 -0.05
## XAU.USD -0.05 1.00library(corrplot)## Warning: package 'corrplot' was built under R version 4.3.3## corrplot 0.92 loadedcorrplot(res, type = "upper", order = "hclust",
tl.col = "black", tl.srt = 45)
data2 <- data[,c(2,3)]
data1 <- data.frame(sapply(data2, as.numeric))
chart.Correlation(data1, histogram=TRUE, pch=19)## Warning in par(usr): argument 1 does not name a graphical parameter
pearson <- cor(data$XAU.USD,data$VNI, method="pearson")
spearman <- cor(data$XAU.USD,data$VNI, method="spearman")
kendall <- cor(data$XAU.USD,data$VNI, method="kendall")
print(pearson)## [1] -0.04830442print(spearman)## [1] -0.04166188print(kendall)## [1] -0.02801631library(ggcorrplot)
Note <- cor(data2)
ggcorrplot(Note, hc.order = TRUE,
outline.col = "pink",
ggtheme = ggplot2::theme_gray,
colors = c("#6D9EC1", "pink", "darkred"),
lab = TRUE, lab_col = 'pink',title = ' Trực quan hóa hệ số tương quan với phương pháp Pearson')
Biển đồ chuỗi tỷ suất theo ngày
library(quantmod)
library(PerformanceAnalytics)
library(ggplot2)
library(kableExtra)
library(tidyr)
# Giả sử dữ liệu của bạn đã được load vào data1
# Tạo một dataframe mới để vẽ đồ thị ghép
data_plot <- data %>%
pivot_longer(cols = c(VNI, XAU.USD), names_to = "VNI", values_to = "XAU.USD")
# Vẽ đồ thị ghép
ggplot(data_plot, aes(x = DATE, y = XAU.USD)) +
geom_line() +
facet_wrap(~ VNI, ncol = 2) + # Tạo các subplot theo biến Index
labs(title = "Biến động tỷ suất lợi nhuận của các chỉ số")
theme_minimal()## List of 136
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## - attr(*, "complete")= logi TRUE
## - attr(*, "validate")= logi TRUEKiểm định phân phối chuẩn: Jarque-Bera
library(tseries)
XAU.USD <- data$XAU.USD
VNI <- data$VNI
result1 <- jarque.bera.test(XAU.USD)
result2 <- jarque.bera.test(VNI)
print(result1)##
## Jarque Bera Test
##
## data: XAU.USD
## X-squared = 740.42, df = 2, p-value < 2.2e-16print(result2)##
## Jarque Bera Test
##
## data: VNI
## X-squared = 696.02, df = 2, p-value < 2.2e-16Kiểm định tính dừng: Augmented Dickey–Fuller
result3 <- adf.test(XAU.USD)## Warning in adf.test(XAU.USD): p-value smaller than printed p-valueresult4 <- adf.test(VNI)## Warning in adf.test(VNI): p-value smaller than printed p-valueprint(result3)##
## Augmented Dickey-Fuller Test
##
## data: XAU.USD
## Dickey-Fuller = -11.244, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationaryprint(result4)##
## Augmented Dickey-Fuller Test
##
## data: VNI
## Dickey-Fuller = -17.899, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationaryKiểm định tương quan chuỗi: Ljung-Box
result7 <- autoarfima(data2[, 2],ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")
print(result7)## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.199441 0.044998 4.4322 0.000009
## ar2 -0.947042 0.010145 -93.3499 0.000000
## ma1 -0.197572 0.055853 -3.5373 0.000404
## ma2 0.918403 0.016753 54.8201 0.000000
## sigma 0.003906 0.000072 53.9629 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.199441 0.051500 3.8727 0.000108
## ar2 -0.947042 0.011725 -80.7692 0.000000
## ma1 -0.197572 0.065616 -3.0110 0.002604
## ma2 0.918403 0.006531 140.6121 0.000000
## sigma 0.003906 0.000180 21.7264 0.000000
##
## LogLikelihood : 6007.8
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.2456
## Bayes -8.2275
## Shibata -8.2456
## Hannan-Quinn -8.2388
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8933 0.3446
## Lag[2*(p+q)+(p+q)-1][11] 6.4316 0.2319
## Lag[4*(p+q)+(p+q)-1][19] 12.5557 0.1423
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 6.745 9.401e-03
## Lag[2*(p+q)+(p+q)-1][2] 19.107 7.637e-06
## Lag[4*(p+q)+(p+q)-1][5] 41.793 1.421e-11
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 29.74 2 3.487e-07
## ARCH Lag[5] 55.58 5 9.896e-11
## ARCH Lag[10] 89.74 10 5.995e-15
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.5734
## Individual Statistics:
## ar1 0.07574
## ar2 0.19881
## ma1 0.08032
## ma2 0.26677
## sigma 1.00371
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.2575748
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 1 1 1 0 0 -8.245605 1
## 2 0 0 0 0 1 0 -8.243102 1
## 3 0 1 0 0 0 0 -8.243049 1
## 4 0 0 0 1 0 0 -8.242999 1
## 5 0 1 0 0 1 0 -8.242940 1
## 6 0 1 0 1 0 0 -8.242931 1
## 7 0 0 0 1 1 0 -8.242889 1
## 8 1 1 0 1 0 0 -8.242852 1
## 9 0 0 1 0 0 0 -8.242737 1
## 10 1 0 0 0 0 0 -8.242682 1
## 11 1 1 0 1 1 0 -8.242651 1
## 12 1 1 0 0 0 0 -8.242490 1
## 13 0 0 1 0 1 0 -8.242480 1
## 14 0 1 1 0 0 0 -8.242459 1
## 15 1 0 0 0 1 0 -8.242428 1
## 16 1 0 0 1 0 0 -8.242406 1
## 17 0 0 1 1 0 0 -8.242370 1
## 18 0 1 0 1 1 0 -8.242328 1
## 19 1 1 0 0 1 0 -8.242318 1
## 20 0 1 1 1 0 0 -8.242313 1
## 21 0 1 1 0 1 0 -8.242285 1
## 22 1 0 0 1 1 0 -8.242229 1
## 23 0 0 1 1 1 0 -8.242192 1
## 24 1 0 1 1 1 0 -8.242129 1
## 25 1 0 1 1 0 0 -8.241989 1
## 26 1 0 1 0 0 0 -8.241692 1
## 27 0 1 1 1 1 0 -8.241683 1
## 28 1 0 1 0 1 0 -8.241446 1
## 29 1 1 1 0 0 0 -8.241340 1
## 30 1 1 1 0 1 0 -8.241159 1
## 31 1 1 1 1 1 0 -8.240424 1result8 <- autoarfima(data[, 2],ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")
print(result8)## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.000000 NA NA NA
## ar2 0.041249 0.025472 1.6194e+00 0.10537
## ma1 -0.935097 0.000001 -6.5187e+05 0.00000
## ma2 -0.044486 0.000565 -7.8797e+01 0.00000
## sigma 0.005690 0.000105 5.3963e+01 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.000000 NA NA NA
## ar2 0.041249 0.037879 1.0889e+00 0.27618
## ma1 -0.935097 0.000002 -4.7778e+05 0.00000
## ma2 -0.044486 0.000831 -5.3559e+01 0.00000
## sigma 0.005690 0.000178 3.1910e+01 0.00000
##
## LogLikelihood : 5460.075
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.4946
## Bayes -7.4801
## Shibata -7.4946
## Hannan-Quinn -7.4892
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.0004785 0.9825
## Lag[2*(p+q)+(p+q)-1][11] 2.5580236 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 7.2559589 0.8841
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 55.62 8.815e-14
## Lag[2*(p+q)+(p+q)-1][2] 85.35 0.000e+00
## Lag[4*(p+q)+(p+q)-1][5] 144.74 0.000e+00
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 95.94 2 0
## ARCH Lag[5] 122.55 5 0
## ARCH Lag[10] 168.75 10 0
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.1062
## Individual Statistics:
## ar2 0.4003
## ma1 0.4951
## ma2 0.5211
## sigma 0.3162
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.09141994
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 0 1 1 1 0 0 -7.494608 1
## 2 1 1 1 0 0 0 -7.494605 1
## 3 1 0 1 1 0 0 -7.494588 1
## 4 1 0 1 0 0 0 -7.494509 1
## 5 0 0 1 1 0 0 -7.494362 1
## 6 0 1 1 0 0 0 -7.494008 1
## 7 0 0 1 0 0 0 -7.493919 1
## 8 0 1 1 1 1 0 -7.493427 1
## 9 1 1 1 0 1 0 -7.493424 1
## 10 1 1 0 1 0 0 -7.493378 1
## 11 1 0 1 1 1 0 -7.493344 1
## 12 1 0 1 0 1 0 -7.493322 1
## 13 1 1 1 1 0 0 -7.493235 1
## 14 0 0 1 1 1 0 -7.493173 1
## 15 1 0 0 1 0 0 -7.493149 1
## 16 0 1 1 0 1 0 -7.492811 1
## 17 0 0 1 0 1 0 -7.492715 1
## 18 1 1 0 1 1 0 -7.492189 1
## 19 1 1 1 1 1 0 -7.492053 1
## 20 1 0 0 1 1 0 -7.491945 1
## 21 1 1 0 0 0 0 -7.247547 1
## 22 1 1 0 0 1 0 -7.246174 1
## 23 1 0 0 0 0 0 -7.151703 1
## 24 1 0 0 0 1 0 -7.150330 1
## 25 0 1 0 1 0 0 -6.871026 1
## 26 0 0 0 1 0 0 -6.868593 1
## 27 0 1 0 0 0 0 -6.868581 1
## 28 0 0 0 0 1 0 -6.868274 1
## 29 0 0 0 1 1 0 -6.867220 1
## 30 0 1 0 0 1 0 -6.867208 1
## 31 0 1 0 1 1 0 -6.865819 1re_XAU <- result7$fit@fit$residuals
re_VNI <- result8$fit@fit$residuals
result5 <- Box.test(re_XAU, lag = 2, type = "Ljung-Box")
result6 <- Box.test(re_VNI, lag = 2, type = "Ljung-Box")
print(result5)##
## Box-Ljung test
##
## data: re_XAU
## X-squared = 0.89368, df = 2, p-value = 0.6396print(result6)##
## Box-Ljung test
##
## data: re_VNI
## X-squared = 0.00089726, df = 2, p-value = 0.9996result55 <- Box.test(re_XAU^2, lag = 2, type = "Ljung-Box")
result66 <- Box.test(re_VNI^2, lag = 2, type = "Ljung-Box")
print(result55)##
## Box-Ljung test
##
## data: re_XAU^2
## X-squared = 31.469, df = 2, p-value = 1.467e-07print(result66)##
## Box-Ljung test
##
## data: re_VNI^2
## X-squared = 115.09, df = 2, p-value < 2.2e-16Kiểm định hiệu ứng ARCH: ARCH-LM
library(lmtest)
library(fGarch)
library(rugarch)
library(tseries)
# Kiểm định hiệu ứng ARCH - LM
arch_spec <- ugarchspec(variance.model = list(model = "sGARCH"))
arch_XAU.USD <- ugarchfit(spec = arch_spec, data = data$XAU.USD)
arch_VNI <- ugarchfit(spec = arch_spec, data = data$VNI)
residuals <- residuals(arch_XAU.USD)
residuals1 <- residuals(arch_VNI)
n <- length(residuals)
n1 <- length(residuals1)
x <- 1:n
x1 <- 1:n1
# Tạo mô hình tuyến tính
arch_lm_model_XAU.USD <- lm(residuals^2 ~ x)
arch_lm_model_VNI <- lm(residuals1^2 ~ x1)
# Kiểm định hiệu ứng ARCH-LM
arch1 <- bptest(arch_lm_model_XAU.USD)
arch2 <- bptest(arch_lm_model_VNI)
# Hiển thị kết quả
arch1##
## studentized Breusch-Pagan test
##
## data: arch_lm_model_XAU.USD
## BP = 0.0015143, df = 1, p-value = 0.969arch2##
## studentized Breusch-Pagan test
##
## data: arch_lm_model_VNI
## BP = 0.37244, df = 1, p-value = 0.5417Đồ thị biến động hai chuỗi lợi suất
library(quantmod)
library(PerformanceAnalytics)
library(ggplot2)
library(kableExtra)
library(tidyr)
data_plot <- data %>%
pivot_longer(cols = c(VNI, XAU.USD), names_to = "VNI", values_to = "XAU.USD")
# Vẽ đồ thị ghép
ggplot(data_plot, aes(x = DATE, y = XAU.USD)) +
geom_line() +
facet_wrap(~ VNI, ncol = 2) + # Tạo các subplot theo biến Index
labs(title = "Biến động tỷ suất lợi nhuận của các chỉ số")
theme_minimal()## List of 136
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## ..$ lineend : chr "butt"
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## [list output truncated]
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**Mô hình ARMA cho XAU.USD
result7 <- autoarfima(data2[, 2],ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")
print(result7)## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.199441 0.044998 4.4322 0.000009
## ar2 -0.947042 0.010145 -93.3499 0.000000
## ma1 -0.197572 0.055853 -3.5373 0.000404
## ma2 0.918403 0.016753 54.8201 0.000000
## sigma 0.003906 0.000072 53.9629 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.199441 0.051500 3.8727 0.000108
## ar2 -0.947042 0.011725 -80.7692 0.000000
## ma1 -0.197572 0.065616 -3.0110 0.002604
## ma2 0.918403 0.006531 140.6121 0.000000
## sigma 0.003906 0.000180 21.7264 0.000000
##
## LogLikelihood : 6007.8
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.2456
## Bayes -8.2275
## Shibata -8.2456
## Hannan-Quinn -8.2388
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8933 0.3446
## Lag[2*(p+q)+(p+q)-1][11] 6.4316 0.2319
## Lag[4*(p+q)+(p+q)-1][19] 12.5557 0.1423
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 6.745 9.401e-03
## Lag[2*(p+q)+(p+q)-1][2] 19.107 7.637e-06
## Lag[4*(p+q)+(p+q)-1][5] 41.793 1.421e-11
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 29.74 2 3.487e-07
## ARCH Lag[5] 55.58 5 9.896e-11
## ARCH Lag[10] 89.74 10 5.995e-15
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.5734
## Individual Statistics:
## ar1 0.07574
## ar2 0.19881
## ma1 0.08032
## ma2 0.26677
## sigma 1.00371
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.2281008
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 1 1 1 1 0 0 -8.245605 1
## 2 0 0 0 0 1 0 -8.243102 1
## 3 0 1 0 0 0 0 -8.243049 1
## 4 0 0 0 1 0 0 -8.242999 1
## 5 0 1 0 0 1 0 -8.242940 1
## 6 0 1 0 1 0 0 -8.242931 1
## 7 0 0 0 1 1 0 -8.242889 1
## 8 1 1 0 1 0 0 -8.242852 1
## 9 0 0 1 0 0 0 -8.242737 1
## 10 1 0 0 0 0 0 -8.242682 1
## 11 1 1 0 1 1 0 -8.242651 1
## 12 1 1 0 0 0 0 -8.242490 1
## 13 0 0 1 0 1 0 -8.242480 1
## 14 0 1 1 0 0 0 -8.242459 1
## 15 1 0 0 0 1 0 -8.242428 1
## 16 1 0 0 1 0 0 -8.242406 1
## 17 0 0 1 1 0 0 -8.242370 1
## 18 0 1 0 1 1 0 -8.242328 1
## 19 1 1 0 0 1 0 -8.242318 1
## 20 0 1 1 1 0 0 -8.242313 1
## 21 0 1 1 0 1 0 -8.242285 1
## 22 1 0 0 1 1 0 -8.242229 1
## 23 0 0 1 1 1 0 -8.242192 1
## 24 1 0 1 1 1 0 -8.242129 1
## 25 1 0 1 1 0 0 -8.241989 1
## 26 1 0 1 0 0 0 -8.241692 1
## 27 0 1 1 1 1 0 -8.241683 1
## 28 1 0 1 0 1 0 -8.241446 1
## 29 1 1 1 0 0 0 -8.241340 1
## 30 1 1 1 0 1 0 -8.241159 1
## 31 1 1 1 1 1 0 -8.240424 1Mô hình ARMA cho VNI
result8 <- autoarfima(data[, 2],ar.max = 2, ma.max = 2, criterion = "AIC", method = "full")
print(result8)## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.000000 NA NA NA
## ar2 0.041249 0.025472 1.6194e+00 0.10537
## ma1 -0.935097 0.000001 -6.5187e+05 0.00000
## ma2 -0.044486 0.000565 -7.8797e+01 0.00000
## sigma 0.005690 0.000105 5.3963e+01 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## ar1 0.000000 NA NA NA
## ar2 0.041249 0.037879 1.0889e+00 0.27618
## ma1 -0.935097 0.000002 -4.7778e+05 0.00000
## ma2 -0.044486 0.000831 -5.3559e+01 0.00000
## sigma 0.005690 0.000178 3.1910e+01 0.00000
##
## LogLikelihood : 5460.075
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.4946
## Bayes -7.4801
## Shibata -7.4946
## Hannan-Quinn -7.4892
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.0004785 0.9825
## Lag[2*(p+q)+(p+q)-1][11] 2.5580236 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 7.2559589 0.8841
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 55.62 8.815e-14
## Lag[2*(p+q)+(p+q)-1][2] 85.35 0.000e+00
## Lag[4*(p+q)+(p+q)-1][5] 144.74 0.000e+00
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 95.94 2 0
## ARCH Lag[5] 122.55 5 0
## ARCH Lag[10] 168.75 10 0
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.1062
## Individual Statistics:
## ar2 0.4003
## ma1 0.4951
## ma2 0.5211
## sigma 0.3162
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.1008711
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 0 1 1 1 0 0 -7.494608 1
## 2 1 1 1 0 0 0 -7.494605 1
## 3 1 0 1 1 0 0 -7.494588 1
## 4 1 0 1 0 0 0 -7.494509 1
## 5 0 0 1 1 0 0 -7.494362 1
## 6 0 1 1 0 0 0 -7.494008 1
## 7 0 0 1 0 0 0 -7.493919 1
## 8 0 1 1 1 1 0 -7.493427 1
## 9 1 1 1 0 1 0 -7.493424 1
## 10 1 1 0 1 0 0 -7.493378 1
## 11 1 0 1 1 1 0 -7.493344 1
## 12 1 0 1 0 1 0 -7.493322 1
## 13 1 1 1 1 0 0 -7.493235 1
## 14 0 0 1 1 1 0 -7.493173 1
## 15 1 0 0 1 0 0 -7.493149 1
## 16 0 1 1 0 1 0 -7.492811 1
## 17 0 0 1 0 1 0 -7.492715 1
## 18 1 1 0 1 1 0 -7.492189 1
## 19 1 1 1 1 1 0 -7.492053 1
## 20 1 0 0 1 1 0 -7.491945 1
## 21 1 1 0 0 0 0 -7.247547 1
## 22 1 1 0 0 1 0 -7.246174 1
## 23 1 0 0 0 0 0 -7.151703 1
## 24 1 0 0 0 1 0 -7.150330 1
## 25 0 1 0 1 0 0 -6.871026 1
## 26 0 0 0 1 0 0 -6.868593 1
## 27 0 1 0 0 0 0 -6.868581 1
## 28 0 0 0 0 1 0 -6.868274 1
## 29 0 0 0 1 1 0 -6.867220 1
## 30 0 1 0 0 1 0 -6.867208 1
## 31 0 1 0 1 1 0 -6.865819 1ƯỚC LƯỢNG CÁC DẠNG MÔ HÌNH GJR-GARCH
Ước lượng cho chuỗi XAU.USD
Garch11
XAU.garch11n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
XAU.garch11n.fit <- ugarchfit(spec = XAU.garch11n.spec, data = data[, 3])
XAU.garch11t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
XAU.garch11t.fit <- ugarchfit(spec = XAU.garch11t.spec, data = data[, 3])
XAU.garch11st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
XAU.garch11st.fit <- ugarchfit(spec = XAU.garch11st.spec, data = data[, 3])
XAU.garch11g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
XAU.garch11g.fit <- ugarchfit(spec = XAU.garch11g.spec, data = data[, 3])
XAU.garch11sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
XAU.garch11sg.fit <- ugarchfit(spec = XAU.garch11sg.spec, data = data[, 3])
print(XAU.garch11n.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Convergence Problem:
## Solver Message:print(XAU.garch11t.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000181 0.000082 2.20901 0.027174
## ar1 0.196179 0.035543 5.51953 0.000000
## ar2 -0.951156 0.028707 -33.13358 0.000000
## ma1 -0.203561 0.046358 -4.39104 0.000011
## ma2 0.922402 0.036302 25.40912 0.000000
## omega 0.000000 0.000000 0.65282 0.513870
## alpha1 0.076762 0.012866 5.96610 0.000000
## beta1 0.932286 0.010272 90.76373 0.000000
## gamma1 -0.047757 0.016920 -2.82241 0.004766
## shape 4.652846 0.566421 8.21447 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000181 0.000082 2.196426 0.028061
## ar1 0.196179 0.043763 4.482746 0.000007
## ar2 -0.951156 0.032147 -29.587541 0.000000
## ma1 -0.203561 0.057396 -3.546607 0.000390
## ma2 0.922402 0.040028 23.043650 0.000000
## omega 0.000000 0.000005 0.060085 0.952088
## alpha1 0.076762 0.246489 0.311423 0.755479
## beta1 0.932286 0.158975 5.864361 0.000000
## gamma1 -0.047757 0.119235 -0.400524 0.688771
## shape 4.652846 3.639958 1.278269 0.201155
##
## LogLikelihood : 6133.19
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4110
## Bayes -8.3747
## Shibata -8.4111
## Hannan-Quinn -8.3974
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.028 0.1544
## Lag[2*(p+q)+(p+q)-1][11] 4.918 0.9700
## Lag[4*(p+q)+(p+q)-1][19] 7.688 0.8353
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2631 0.6080
## Lag[2*(p+q)+(p+q)-1][5] 4.5710 0.1909
## Lag[4*(p+q)+(p+q)-1][9] 5.9517 0.3038
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.3203 0.500 2.000 0.5714
## ARCH Lag[5] 2.1840 1.440 1.667 0.4320
## ARCH Lag[7] 2.7452 2.315 1.543 0.5629
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 422.4859
## Individual Statistics:
## mu 0.18209
## ar1 0.04960
## ar2 0.35585
## ma1 0.05596
## ma2 0.46660
## omega 131.44213
## alpha1 0.19290
## beta1 0.26442
## gamma1 0.22246
## shape 0.22720
##
## 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 1.603536 0.1090
## Negative Sign Bias 1.425741 0.1542
## Positive Sign Bias 0.008289 0.9934
## Joint Effect 3.700502 0.2957
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 19.69 0.4136
## 2 30 28.42 0.4954
## 3 40 33.29 0.7274
## 4 50 37.20 0.8916
##
##
## Elapsed time : 1.45211print(XAU.garch11st.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000095 0.000092 1.03961 0.298519
## ar1 0.189180 0.035770 5.28872 0.000000
## ar2 -0.952305 0.029817 -31.93807 0.000000
## ma1 -0.194287 0.047185 -4.11757 0.000038
## ma2 0.923479 0.037593 24.56487 0.000000
## omega 0.000000 0.000001 0.64905 0.516306
## alpha1 0.078112 0.013912 5.61458 0.000000
## beta1 0.928840 0.011488 80.85497 0.000000
## gamma1 -0.047055 0.017381 -2.70722 0.006785
## skew 0.938318 0.032972 28.45769 0.000000
## shape 4.647912 0.559284 8.31047 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000095 0.000098 0.973244 0.330432
## ar1 0.189180 0.045217 4.183799 0.000029
## ar2 -0.952305 0.037053 -25.701252 0.000000
## ma1 -0.194287 0.060740 -3.198664 0.001381
## ma2 0.923479 0.045159 20.449471 0.000000
## omega 0.000000 0.000006 0.058923 0.953014
## alpha1 0.078112 0.255923 0.305216 0.760201
## beta1 0.928840 0.173867 5.342231 0.000000
## gamma1 -0.047055 0.115545 -0.407241 0.683831
## skew 0.938318 0.033641 27.892254 0.000000
## shape 4.647912 3.417027 1.360221 0.173760
##
## LogLikelihood : 6134.849
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4119
## Bayes -8.3720
## Shibata -8.4120
## Hannan-Quinn -8.3970
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.702 0.1920
## Lag[2*(p+q)+(p+q)-1][11] 4.628 0.9927
## Lag[4*(p+q)+(p+q)-1][19] 7.402 0.8687
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3678 0.5442
## Lag[2*(p+q)+(p+q)-1][5] 4.7069 0.1781
## Lag[4*(p+q)+(p+q)-1][9] 6.0549 0.2919
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.3758 0.500 2.000 0.5399
## ARCH Lag[5] 2.2715 1.440 1.667 0.4143
## ARCH Lag[7] 2.7677 2.315 1.543 0.5585
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 419.6437
## Individual Statistics:
## mu 0.21467
## ar1 0.05563
## ar2 0.34110
## ma1 0.06844
## ma2 0.43970
## omega 126.56295
## alpha1 0.19473
## beta1 0.25834
## gamma1 0.21919
## skew 0.40620
## shape 0.21136
##
## 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 1.56316 0.1182
## Negative Sign Bias 1.47836 0.1395
## Positive Sign Bias 0.07202 0.9426
## Joint Effect 3.77608 0.2867
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 17.41 0.5623
## 2 30 23.15 0.7697
## 3 40 29.05 0.8773
## 4 50 35.00 0.9342
##
##
## Elapsed time : 1.965402print(XAU.garch11g.fit)##
## *---------------------------------*
## * 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 0.000165 0.000084 1.95787 0.050245
## ar1 0.206413 0.019123 10.79383 0.000000
## ar2 -0.952339 0.011621 -81.95221 0.000000
## ma1 -0.212286 0.024898 -8.52626 0.000000
## ma2 0.920332 0.014900 61.76779 0.000000
## omega 0.000000 0.000001 0.48257 0.629403
## alpha1 0.085363 0.019430 4.39333 0.000011
## beta1 0.921970 0.017639 52.26943 0.000000
## gamma1 -0.054730 0.015903 -3.44146 0.000579
## shape 1.235955 0.043980 28.10235 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000165 0.000091 1.819920 0.068771
## ar1 0.206413 0.015211 13.570042 0.000000
## ar2 -0.952339 0.006346 -150.059338 0.000000
## ma1 -0.212286 0.019294 -11.002696 0.000000
## ma2 0.920332 0.013967 65.891382 0.000000
## omega 0.000000 0.000010 0.032544 0.974038
## alpha1 0.085363 0.406846 0.209816 0.833811
## beta1 0.921970 0.310236 2.971838 0.002960
## gamma1 -0.054730 0.197261 -0.277451 0.781434
## shape 1.235955 0.628791 1.965606 0.049344
##
## LogLikelihood : 6134.853
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4133
## Bayes -8.3770
## Shibata -8.4134
## Hannan-Quinn -8.3997
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.776 0.1826
## Lag[2*(p+q)+(p+q)-1][11] 4.918 0.9701
## Lag[4*(p+q)+(p+q)-1][19] 7.736 0.8293
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4629 0.4963
## Lag[2*(p+q)+(p+q)-1][5] 4.0875 0.2434
## Lag[4*(p+q)+(p+q)-1][9] 5.1303 0.4105
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.5028 0.500 2.000 0.4783
## ARCH Lag[5] 1.8978 1.440 1.667 0.4943
## ARCH Lag[7] 2.2372 2.315 1.543 0.6672
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 407.6392
## Individual Statistics:
## mu 0.18811
## ar1 0.05270
## ar2 0.33316
## ma1 0.04896
## ma2 0.45659
## omega 113.10651
## alpha1 0.19921
## beta1 0.24886
## gamma1 0.21461
## shape 0.11955
##
## 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 1.5652 0.1178
## Negative Sign Bias 1.5273 0.1269
## Positive Sign Bias 0.2344 0.8147
## Joint Effect 4.1850 0.2422
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 24.88 0.1646
## 2 30 24.47 0.7056
## 3 40 31.91 0.7824
## 4 50 42.56 0.7302
##
##
## Elapsed time : 2.298662print(XAU.garch11sg.fit)##
## *---------------------------------*
## * 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 0.000113 0.000097 1.15859 0.246624
## ar1 0.192069 0.009983 19.23960 0.000000
## ar2 -0.955622 0.020650 -46.27678 0.000000
## ma1 -0.197211 0.013453 -14.65879 0.000000
## ma2 0.923142 0.026860 34.36811 0.000000
## omega 0.000000 0.000000 0.52014 0.602965
## alpha1 0.075977 0.010264 7.40208 0.000000
## beta1 0.935272 0.010395 89.97283 0.000000
## gamma1 -0.051365 0.014260 -3.60213 0.000316
## skew 0.940130 0.026509 35.46520 0.000000
## shape 1.239972 0.054491 22.75555 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000113 0.000179 0.630313 0.528490
## ar1 0.192069 0.005504 34.897577 0.000000
## ar2 -0.955622 0.020250 -47.192276 0.000000
## ma1 -0.197211 0.009436 -20.900237 0.000000
## ma2 0.923142 0.027260 33.864170 0.000000
## omega 0.000000 0.000005 0.042267 0.966286
## alpha1 0.075977 0.245173 0.309893 0.756642
## beta1 0.935272 0.177962 5.255451 0.000000
## gamma1 -0.051365 0.134421 -0.382118 0.702374
## skew 0.940130 0.037132 25.318900 0.000000
## shape 1.239972 0.314817 3.938710 0.000082
##
## LogLikelihood : 6136.139
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4137
## Bayes -8.3737
## Shibata -8.4138
## Hannan-Quinn -8.3988
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.942 0.1634
## Lag[2*(p+q)+(p+q)-1][11] 5.282 0.8866
## Lag[4*(p+q)+(p+q)-1][19] 8.157 0.7720
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.268 0.6047
## Lag[2*(p+q)+(p+q)-1][5] 4.519 0.1961
## Lag[4*(p+q)+(p+q)-1][9] 5.875 0.3129
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.340 0.500 2.000 0.5598
## ARCH Lag[5] 2.197 1.440 1.667 0.4293
## ARCH Lag[7] 2.727 2.315 1.543 0.5665
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 434.7946
## Individual Statistics:
## mu 0.11225
## ar1 0.12486
## ar2 0.33482
## ma1 0.13756
## ma2 0.42012
## omega 145.06067
## alpha1 0.19970
## beta1 0.19108
## gamma1 0.17149
## skew 0.37979
## shape 0.07843
##
## 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 1.6252 0.1043
## Negative Sign Bias 1.4696 0.1419
## Positive Sign Bias 0.1329 0.8943
## Joint Effect 4.1044 0.2504
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 20.57 0.3613
## 2 30 19.73 0.9012
## 3 40 40.04 0.4236
## 4 50 37.20 0.8916
##
##
## Elapsed time : 4.199541Garch12
XAU.garch12n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
XAU.garch12n.fit <- ugarchfit(spec = XAU.garch12n.spec, data = data[, 3])
XAU.garch12t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
XAU.garch12t.fit <- ugarchfit(spec = XAU.garch12t.spec, data = data[, 3])
XAU.garch12st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
XAU.garch12st.fit <- ugarchfit(spec = XAU.garch12st.spec, data = data[, 3])
XAU.garch12g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
XAU.garch12g.fit <- ugarchfit(spec = XAU.garch12g.spec, data = data[, 3])
XAU.garch12sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
XAU.garch12sg.fit <- ugarchfit(spec = XAU.garch12g.spec, data = data[, 3])
print(XAU.garch12n.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000097 0.000091 1.075938 0.281955
## ar1 0.196626 0.003595 54.688167 0.000000
## ar2 -0.978170 0.001401 -698.063657 0.000000
## ma1 -0.197599 0.009734 -20.300799 0.000000
## ma2 0.956424 0.005771 165.738775 0.000000
## omega 0.000000 0.000001 0.697407 0.485548
## alpha1 0.104596 0.023729 4.408021 0.000010
## beta1 0.906029 0.063195 14.337147 0.000000
## beta2 0.000002 0.056508 0.000032 0.999975
## gamma1 -0.067170 0.021027 -3.194411 0.001401
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000097 0.000106 0.917411 0.358927
## ar1 0.196626 0.006908 28.464427 0.000000
## ar2 -0.978170 0.006950 -140.752665 0.000000
## ma1 -0.197599 0.008635 -22.882324 0.000000
## ma2 0.956424 0.007337 130.351206 0.000000
## omega 0.000000 0.000010 0.041807 0.966652
## alpha1 0.104596 0.257965 0.405467 0.685134
## beta1 0.906029 0.441666 2.051390 0.040229
## beta2 0.000002 0.234344 0.000008 0.999994
## gamma1 -0.067170 0.141398 -0.475041 0.634758
##
## LogLikelihood : 6086.736
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.3472
## Bayes -8.3109
## Shibata -8.3473
## Hannan-Quinn -8.3336
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.102 0.2939
## Lag[2*(p+q)+(p+q)-1][11] 3.684 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 6.241 0.9601
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.9223 0.3369
## Lag[2*(p+q)+(p+q)-1][8] 4.4010 0.4408
## Lag[4*(p+q)+(p+q)-1][14] 5.1644 0.7489
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.8365 0.500 2.000 0.3604
## ARCH Lag[6] 0.9355 1.461 1.711 0.7663
## ARCH Lag[8] 1.0255 2.368 1.583 0.9205
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 393.9766
## Individual Statistics:
## mu 0.07500
## ar1 0.07214
## ar2 0.19102
## ma1 0.05417
## ma2 0.25390
## omega 75.34192
## alpha1 0.20321
## beta1 0.24575
## beta2 0.25036
## gamma1 0.21036
##
## 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 1.5424 0.12319
## Negative Sign Bias 1.6926 0.09074 *
## Positive Sign Bias 0.5171 0.60515
## Joint Effect 5.0931 0.16510
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 68.12 1.883e-07
## 2 30 86.16 1.405e-07
## 3 40 88.89 9.181e-06
## 4 50 102.17 1.300e-05
##
##
## Elapsed time : 1.132464print(XAU.garch12t.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000173 0.000082 2.112181 0.034671
## ar1 0.196901 0.036477 5.398020 0.000000
## ar2 -0.950858 0.029477 -32.257819 0.000000
## ma1 -0.204309 0.047609 -4.291355 0.000018
## ma2 0.922836 0.036890 25.015615 0.000000
## omega 0.000000 0.000000 0.581214 0.561096
## alpha1 0.075701 0.013307 5.688980 0.000000
## beta1 0.933826 0.033521 27.857987 0.000000
## beta2 0.000577 0.037001 0.015604 0.987550
## gamma1 -0.046582 0.016666 -2.794943 0.005191
## shape 4.594893 0.515930 8.906031 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000173 0.000082 2.114591 0.034465
## ar1 0.196901 0.045529 4.324756 0.000015
## ar2 -0.950858 0.029861 -31.843280 0.000000
## ma1 -0.204309 0.059818 -3.415500 0.000637
## ma2 0.922836 0.036408 25.347090 0.000000
## omega 0.000000 0.000006 0.049626 0.960420
## alpha1 0.075701 0.261904 0.289040 0.772551
## beta1 0.933826 0.063210 14.773297 0.000000
## beta2 0.000577 0.228256 0.002530 0.997982
## gamma1 -0.046582 0.123858 -0.376091 0.706849
## shape 4.594893 4.191023 1.096365 0.272919
##
## LogLikelihood : 6133.146
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4095
## Bayes -8.3696
## Shibata -8.4097
## Hannan-Quinn -8.3946
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.060 0.1513
## Lag[2*(p+q)+(p+q)-1][11] 4.902 0.9720
## Lag[4*(p+q)+(p+q)-1][19] 7.628 0.8426
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2607 0.6096
## Lag[2*(p+q)+(p+q)-1][8] 5.7172 0.2647
## Lag[4*(p+q)+(p+q)-1][14] 6.8874 0.5204
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 2.291 0.500 2.000 0.1301
## ARCH Lag[6] 2.607 1.461 1.711 0.3711
## ARCH Lag[8] 2.905 2.368 1.583 0.5614
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 459.181
## Individual Statistics:
## mu 0.20178
## ar1 0.04701
## ar2 0.32056
## ma1 0.05238
## ma2 0.42566
## omega 137.85652
## alpha1 0.17723
## beta1 0.23501
## beta2 0.23934
## gamma1 0.20674
## shape 0.19066
##
## 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 1.614749 0.1066
## Negative Sign Bias 1.449478 0.1474
## Positive Sign Bias 0.007429 0.9941
## Joint Effect 3.764980 0.2880
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 18.75 0.4728
## 2 30 29.00 0.4651
## 3 40 31.03 0.8146
## 4 50 37.34 0.8884
##
##
## Elapsed time : 1.57421print(XAU.garch12st.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000099 0.000092 1.080428 0.279951
## ar1 0.187992 0.035671 5.270095 0.000000
## ar2 -0.953452 0.029830 -31.963007 0.000000
## ma1 -0.192762 0.047154 -4.087927 0.000044
## ma2 0.924935 0.037699 24.534568 0.000000
## omega 0.000000 0.000001 0.563712 0.572950
## alpha1 0.076921 0.014375 5.350922 0.000000
## beta1 0.932703 0.044071 21.163627 0.000000
## beta2 0.000504 0.048688 0.010342 0.991748
## gamma1 -0.047367 0.016509 -2.869117 0.004116
## skew 0.937840 0.032984 28.433537 0.000000
## shape 4.618179 0.519043 8.897487 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000099 0.000099 0.998555 0.318010
## ar1 0.187992 0.045452 4.136090 0.000035
## ar2 -0.953452 0.032627 -29.222370 0.000000
## ma1 -0.192762 0.061365 -3.141236 0.001682
## ma2 0.924935 0.040109 23.060249 0.000000
## omega 0.000000 0.000006 0.046895 0.962597
## alpha1 0.076921 0.275626 0.279076 0.780186
## beta1 0.932703 0.162474 5.740622 0.000000
## beta2 0.000504 0.336793 0.001495 0.998807
## gamma1 -0.047367 0.129963 -0.364463 0.715513
## skew 0.937840 0.033511 27.986433 0.000000
## shape 4.618179 4.410094 1.047184 0.295015
##
## LogLikelihood : 6134.787
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4104
## Bayes -8.3669
## Shibata -8.4106
## Hannan-Quinn -8.3942
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.755 0.1852
## Lag[2*(p+q)+(p+q)-1][11] 4.704 0.9891
## Lag[4*(p+q)+(p+q)-1][19] 7.458 0.8625
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3196 0.5719
## Lag[2*(p+q)+(p+q)-1][8] 5.9098 0.2442
## Lag[4*(p+q)+(p+q)-1][14] 7.0791 0.4956
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 2.389 0.500 2.000 0.1222
## ARCH Lag[6] 2.690 1.461 1.711 0.3569
## ARCH Lag[8] 2.986 2.368 1.583 0.5461
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 458.3485
## Individual Statistics:
## mu 0.19684
## ar1 0.05556
## ar2 0.33472
## ma1 0.06858
## ma2 0.42620
## omega 138.78963
## alpha1 0.18141
## beta1 0.23959
## beta2 0.24344
## gamma1 0.20503
## skew 0.37962
## shape 0.19478
##
## 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 1.56001 0.1190
## Negative Sign Bias 1.46064 0.1443
## Positive Sign Bias 0.06758 0.9461
## Joint Effect 3.73767 0.2912
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 15.90 0.6642
## 2 30 23.44 0.7562
## 3 40 29.93 0.8513
## 4 50 45.99 0.5958
##
##
## Elapsed time : 2.006666print(XAU.garch12g.fit)##
## *---------------------------------*
## * 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 0.000165 0.000084 1.95787 0.050245
## ar1 0.206413 0.019123 10.79383 0.000000
## ar2 -0.952339 0.011621 -81.95221 0.000000
## ma1 -0.212286 0.024898 -8.52626 0.000000
## ma2 0.920332 0.014900 61.76779 0.000000
## omega 0.000000 0.000001 0.48257 0.629403
## alpha1 0.085363 0.019430 4.39333 0.000011
## beta1 0.921970 0.017639 52.26943 0.000000
## gamma1 -0.054730 0.015903 -3.44146 0.000579
## shape 1.235955 0.043980 28.10235 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000165 0.000091 1.819920 0.068771
## ar1 0.206413 0.015211 13.570042 0.000000
## ar2 -0.952339 0.006346 -150.059338 0.000000
## ma1 -0.212286 0.019294 -11.002696 0.000000
## ma2 0.920332 0.013967 65.891382 0.000000
## omega 0.000000 0.000010 0.032544 0.974038
## alpha1 0.085363 0.406846 0.209816 0.833811
## beta1 0.921970 0.310236 2.971838 0.002960
## gamma1 -0.054730 0.197261 -0.277451 0.781434
## shape 1.235955 0.628791 1.965606 0.049344
##
## LogLikelihood : 6134.853
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4133
## Bayes -8.3770
## Shibata -8.4134
## Hannan-Quinn -8.3997
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.776 0.1826
## Lag[2*(p+q)+(p+q)-1][11] 4.918 0.9701
## Lag[4*(p+q)+(p+q)-1][19] 7.736 0.8293
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4629 0.4963
## Lag[2*(p+q)+(p+q)-1][5] 4.0875 0.2434
## Lag[4*(p+q)+(p+q)-1][9] 5.1303 0.4105
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.5028 0.500 2.000 0.4783
## ARCH Lag[5] 1.8978 1.440 1.667 0.4943
## ARCH Lag[7] 2.2372 2.315 1.543 0.6672
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 407.6392
## Individual Statistics:
## mu 0.18811
## ar1 0.05270
## ar2 0.33316
## ma1 0.04896
## ma2 0.45659
## omega 113.10651
## alpha1 0.19921
## beta1 0.24886
## gamma1 0.21461
## shape 0.11955
##
## 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 1.5652 0.1178
## Negative Sign Bias 1.5273 0.1269
## Positive Sign Bias 0.2344 0.8147
## Joint Effect 4.1850 0.2422
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 24.88 0.1646
## 2 30 24.47 0.7056
## 3 40 31.91 0.7824
## 4 50 42.56 0.7302
##
##
## Elapsed time : 2.272967print(XAU.garch12sg.fit)##
## *---------------------------------*
## * 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 0.000165 0.000084 1.95787 0.050245
## ar1 0.206413 0.019123 10.79383 0.000000
## ar2 -0.952339 0.011621 -81.95221 0.000000
## ma1 -0.212286 0.024898 -8.52626 0.000000
## ma2 0.920332 0.014900 61.76779 0.000000
## omega 0.000000 0.000001 0.48257 0.629403
## alpha1 0.085363 0.019430 4.39333 0.000011
## beta1 0.921970 0.017639 52.26943 0.000000
## gamma1 -0.054730 0.015903 -3.44146 0.000579
## shape 1.235955 0.043980 28.10235 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000165 0.000091 1.819920 0.068771
## ar1 0.206413 0.015211 13.570042 0.000000
## ar2 -0.952339 0.006346 -150.059338 0.000000
## ma1 -0.212286 0.019294 -11.002696 0.000000
## ma2 0.920332 0.013967 65.891382 0.000000
## omega 0.000000 0.000010 0.032544 0.974038
## alpha1 0.085363 0.406846 0.209816 0.833811
## beta1 0.921970 0.310236 2.971838 0.002960
## gamma1 -0.054730 0.197261 -0.277451 0.781434
## shape 1.235955 0.628791 1.965606 0.049344
##
## LogLikelihood : 6134.853
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4133
## Bayes -8.3770
## Shibata -8.4134
## Hannan-Quinn -8.3997
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.776 0.1826
## Lag[2*(p+q)+(p+q)-1][11] 4.918 0.9701
## Lag[4*(p+q)+(p+q)-1][19] 7.736 0.8293
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4629 0.4963
## Lag[2*(p+q)+(p+q)-1][5] 4.0875 0.2434
## Lag[4*(p+q)+(p+q)-1][9] 5.1303 0.4105
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.5028 0.500 2.000 0.4783
## ARCH Lag[5] 1.8978 1.440 1.667 0.4943
## ARCH Lag[7] 2.2372 2.315 1.543 0.6672
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 407.6392
## Individual Statistics:
## mu 0.18811
## ar1 0.05270
## ar2 0.33316
## ma1 0.04896
## ma2 0.45659
## omega 113.10651
## alpha1 0.19921
## beta1 0.24886
## gamma1 0.21461
## shape 0.11955
##
## 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 1.5652 0.1178
## Negative Sign Bias 1.5273 0.1269
## Positive Sign Bias 0.2344 0.8147
## Joint Effect 4.1850 0.2422
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 24.88 0.1646
## 2 30 24.47 0.7056
## 3 40 31.91 0.7824
## 4 50 42.56 0.7302
##
##
## Elapsed time : 2.335893Garch21
XAU.garch21n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
XAU.garch21n.fit <- ugarchfit(spec = XAU.garch21n.spec, data = data[, 3])
XAU.garch21t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
XAU.garch21t.fit <- ugarchfit(spec = XAU.garch21t.spec, data = data[, 3])
XAU.garch21st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
XAU.garch21st.fit <- ugarchfit(spec = XAU.garch21st.spec, data = data[, 3])
XAU.garch21g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
XAU.garch21g.fit <- ugarchfit(spec = XAU.garch21g.spec, data = data[, 3])
XAU.garch21sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
XAU.garch21sg.fit <- ugarchfit(spec = XAU.garch21g.spec, data = data[, 3])
print(XAU.garch21n.fit)##
## *---------------------------------*
## * 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 0.000095 0.000091 1.04526 0.295905
## ar1 0.194290 0.000734 264.71381 0.000000
## ar2 -0.977991 0.004592 -212.97099 0.000000
## ma1 -0.192536 0.007244 -26.57887 0.000000
## ma2 0.956887 0.003359 284.85411 0.000000
## omega 0.000000 0.000001 0.88160 0.377991
## alpha1 0.026348 0.034616 0.76115 0.446569
## alpha2 0.095066 0.039683 2.39565 0.016591
## beta1 0.887843 0.017018 52.17070 0.000000
## gamma1 -0.004095 0.040178 -0.10192 0.918824
## gamma2 -0.072665 0.043781 -1.65972 0.096971
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000095 0.000094 1.014859 0.31017
## ar1 0.194290 0.006457 30.089025 0.00000
## ar2 -0.977991 0.006149 -159.049225 0.00000
## ma1 -0.192536 0.006607 -29.141241 0.00000
## ma2 0.956887 0.004405 217.205257 0.00000
## omega 0.000000 0.000008 0.066042 0.94734
## alpha1 0.026348 0.060681 0.434197 0.66414
## alpha2 0.095066 0.162583 0.584725 0.55873
## beta1 0.887843 0.165178 5.375059 0.00000
## gamma1 -0.004095 0.055251 -0.074111 0.94092
## gamma2 -0.072665 0.130224 -0.557997 0.57685
##
## LogLikelihood : 6089.188
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.3492
## Bayes -8.3092
## Shibata -8.3493
## Hannan-Quinn -8.3343
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.9435 0.3314
## Lag[2*(p+q)+(p+q)-1][11] 3.3845 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 5.8455 0.9764
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.001655 0.9675
## Lag[2*(p+q)+(p+q)-1][8] 2.470950 0.7810
## Lag[4*(p+q)+(p+q)-1][14] 3.232770 0.9417
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.7214 0.500 2.000 0.3957
## ARCH Lag[6] 0.9634 1.461 1.711 0.7583
## ARCH Lag[8] 1.0416 2.368 1.583 0.9181
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 263.9994
## Individual Statistics:
## mu 0.10241
## ar1 0.05535
## ar2 0.20711
## ma1 0.04942
## ma2 0.27187
## omega 56.66848
## alpha1 0.25217
## alpha2 0.21082
## beta1 0.29061
## gamma1 0.25104
## gamma2 0.20381
##
## 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 1.7001 0.08932 *
## Negative Sign Bias 1.3692 0.17114
## Positive Sign Bias 0.6151 0.53855
## Joint Effect 3.2668 0.35229
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 68.45 1.661e-07
## 2 30 77.30 2.860e-06
## 3 40 92.13 3.444e-06
## 4 50 94.96 9.091e-05
##
##
## Elapsed time : 1.703766print(XAU.garch21t.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000167 0.000082 2.04782 0.040578
## ar1 0.201456 0.036264 5.55520 0.000000
## ar2 -0.949094 0.030301 -31.32256 0.000000
## ma1 -0.210178 0.046937 -4.47787 0.000008
## ma2 0.921619 0.037446 24.61194 0.000000
## omega 0.000000 0.000000 0.70747 0.479271
## alpha1 0.014903 0.045334 0.32873 0.742360
## alpha2 0.067713 0.044705 1.51466 0.129859
## beta1 0.927263 0.010917 84.93648 0.000000
## gamma1 -0.010240 0.053513 -0.19136 0.848247
## gamma2 -0.041319 0.055380 -0.74611 0.455600
## shape 4.614070 0.559064 8.25320 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000167 0.000085 1.971247 0.048696
## ar1 0.201456 0.044877 4.489112 0.000007
## ar2 -0.949094 0.032083 -29.582291 0.000000
## ma1 -0.210178 0.058453 -3.595654 0.000324
## ma2 0.921619 0.038526 23.921724 0.000000
## omega 0.000000 0.000005 0.070237 0.944005
## alpha1 0.014903 0.066777 0.223171 0.823403
## alpha2 0.067713 0.208223 0.325193 0.745035
## beta1 0.927263 0.158685 5.843430 0.000000
## gamma1 -0.010240 0.063459 -0.161365 0.871806
## gamma2 -0.041319 0.141473 -0.292066 0.770236
## shape 4.614070 2.966241 1.555528 0.119820
##
## LogLikelihood : 6134.194
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4096
## Bayes -8.3661
## Shibata -8.4097
## Hannan-Quinn -8.3934
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.486 0.1149
## Lag[2*(p+q)+(p+q)-1][11] 5.072 0.9443
## Lag[4*(p+q)+(p+q)-1][19] 7.685 0.8356
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3262 0.5679
## Lag[2*(p+q)+(p+q)-1][8] 4.7800 0.3836
## Lag[4*(p+q)+(p+q)-1][14] 5.8478 0.6593
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 2.476 0.500 2.000 0.1156
## ARCH Lag[6] 2.685 1.461 1.711 0.3577
## ARCH Lag[8] 2.994 2.368 1.583 0.5445
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 415.9854
## Individual Statistics:
## mu 0.23204
## ar1 0.05755
## ar2 0.33832
## ma1 0.06187
## ma2 0.45292
## omega 123.53265
## alpha1 0.20552
## alpha2 0.17033
## beta1 0.26622
## gamma1 0.23431
## gamma2 0.18664
## shape 0.18964
##
## 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 1.6351 0.1023
## Negative Sign Bias 0.8510 0.3949
## Positive Sign Bias 0.9515 0.3415
## Joint Effect 2.6951 0.4411
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 20.68 0.3550
## 2 30 25.00 0.6781
## 3 40 30.54 0.8316
## 4 50 40.43 0.8034
##
##
## Elapsed time : 2.266276print(XAU.garch21st.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000091 0.000092 0.99666 0.318931
## ar1 0.190121 0.036040 5.27531 0.000000
## ar2 -0.953773 0.030061 -31.72822 0.000000
## ma1 -0.194557 0.047319 -4.11165 0.000039
## ma2 0.926167 0.038092 24.31418 0.000000
## omega 0.000000 0.000000 0.72663 0.467453
## alpha1 0.023245 0.048670 0.47760 0.632935
## alpha2 0.061544 0.047851 1.28617 0.198385
## beta1 0.924331 0.011344 81.48221 0.000000
## gamma1 -0.020827 0.055822 -0.37310 0.709073
## gamma2 -0.030968 0.057432 -0.53920 0.589747
## skew 0.938829 0.033118 28.34782 0.000000
## shape 4.617767 0.557100 8.28893 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000091 0.000099 0.922247 0.356400
## ar1 0.190121 0.046979 4.046912 0.000052
## ar2 -0.953773 0.037692 -25.304126 0.000000
## ma1 -0.194557 0.062715 -3.102265 0.001920
## ma2 0.926167 0.046148 20.069562 0.000000
## omega 0.000000 0.000004 0.074931 0.940269
## alpha1 0.023245 0.072337 0.321338 0.747954
## alpha2 0.061544 0.203650 0.302204 0.762496
## beta1 0.924331 0.158586 5.828588 0.000000
## gamma1 -0.020827 0.068425 -0.304384 0.760835
## gamma2 -0.030968 0.140017 -0.221172 0.824959
## skew 0.938829 0.033449 28.067552 0.000000
## shape 4.617767 2.611525 1.768227 0.077023
##
## LogLikelihood : 6135.821
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4105
## Bayes -8.3633
## Shibata -8.4106
## Hannan-Quinn -8.3929
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.981 0.1593
## Lag[2*(p+q)+(p+q)-1][11] 4.661 0.9913
## Lag[4*(p+q)+(p+q)-1][19] 7.283 0.8813
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2323 0.6298
## Lag[2*(p+q)+(p+q)-1][8] 4.5646 0.4155
## Lag[4*(p+q)+(p+q)-1][14] 5.5675 0.6966
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 2.268 0.500 2.000 0.1321
## ARCH Lag[6] 2.438 1.461 1.711 0.4016
## ARCH Lag[8] 2.697 2.368 1.583 0.6014
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 414.9671
## Individual Statistics:
## mu 0.24114
## ar1 0.05389
## ar2 0.33816
## ma1 0.06446
## ma2 0.41970
## omega 121.72962
## alpha1 0.20550
## alpha2 0.17425
## beta1 0.25537
## gamma1 0.22713
## gamma2 0.18356
## skew 0.39144
## shape 0.18194
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.5054 0.1324
## Negative Sign Bias 0.7912 0.4289
## Positive Sign Bias 0.7109 0.4772
## Joint Effect 2.2762 0.5171
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 22.43 0.2632
## 2 30 20.14 0.8885
## 3 40 37.90 0.5199
## 4 50 38.64 0.8559
##
##
## Elapsed time : 3.045832print(XAU.garch21g.fit)##
## *---------------------------------*
## * 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 0.000183 0.000077 2.38846 0.016919
## ar1 0.208046 0.014166 14.68586 0.000000
## ar2 -0.950826 0.011829 -80.37943 0.000000
## ma1 -0.213250 0.017967 -11.86908 0.000000
## ma2 0.919762 0.014828 62.02728 0.000000
## omega 0.000000 0.000001 0.41998 0.674501
## alpha1 0.018686 0.042115 0.44370 0.657261
## alpha2 0.075208 0.034954 2.15163 0.031426
## beta1 0.913390 0.025093 36.40035 0.000000
## gamma1 -0.006427 0.049297 -0.13037 0.896273
## gamma2 -0.054457 0.048398 -1.12518 0.260513
## shape 1.232940 0.029595 41.66072 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000183 0.000076 2.398490 0.016463
## ar1 0.208046 0.009096 22.873043 0.000000
## ar2 -0.950826 0.006411 -148.320489 0.000000
## ma1 -0.213250 0.014634 -14.571790 0.000000
## ma2 0.919762 0.013198 69.690407 0.000000
## omega 0.000000 0.000017 0.023634 0.981145
## alpha1 0.018686 0.119065 0.156942 0.875291
## alpha2 0.075208 0.538691 0.139612 0.888967
## beta1 0.913390 0.495664 1.842762 0.065364
## gamma1 -0.006427 0.064632 -0.099438 0.920790
## gamma2 -0.054457 0.361751 -0.150537 0.880341
## shape 1.232940 0.947024 1.301910 0.192947
##
## LogLikelihood : 6135.996
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4121
## Bayes -8.3685
## Shibata -8.4122
## Hannan-Quinn -8.3958
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.881 0.1702
## Lag[2*(p+q)+(p+q)-1][11] 4.750 0.9862
## Lag[4*(p+q)+(p+q)-1][19] 7.440 0.8645
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1141 0.7356
## Lag[2*(p+q)+(p+q)-1][8] 3.7583 0.5481
## Lag[4*(p+q)+(p+q)-1][14] 4.6823 0.8077
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 1.926 0.500 2.000 0.1652
## ARCH Lag[6] 2.096 1.461 1.711 0.4700
## ARCH Lag[8] 2.283 2.368 1.583 0.6842
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 389.2474
## Individual Statistics:
## mu 0.14830
## ar1 0.04840
## ar2 0.29217
## ma1 0.04777
## ma2 0.40633
## omega 99.13800
## alpha1 0.24415
## alpha2 0.20464
## beta1 0.31806
## gamma1 0.26240
## gamma2 0.21218
## shape 0.10029
##
## 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 1.5473 0.1220
## Negative Sign Bias 1.0232 0.3064
## Positive Sign Bias 0.7625 0.4459
## Joint Effect 2.4838 0.4782
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 26.03 0.1293
## 2 30 22.53 0.7976
## 3 40 37.85 0.5224
## 4 50 51.35 0.3818
##
##
## Elapsed time : 4.387095print(XAU.garch21sg.fit)##
## *---------------------------------*
## * 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 0.000183 0.000077 2.38846 0.016919
## ar1 0.208046 0.014166 14.68586 0.000000
## ar2 -0.950826 0.011829 -80.37943 0.000000
## ma1 -0.213250 0.017967 -11.86908 0.000000
## ma2 0.919762 0.014828 62.02728 0.000000
## omega 0.000000 0.000001 0.41998 0.674501
## alpha1 0.018686 0.042115 0.44370 0.657261
## alpha2 0.075208 0.034954 2.15163 0.031426
## beta1 0.913390 0.025093 36.40035 0.000000
## gamma1 -0.006427 0.049297 -0.13037 0.896273
## gamma2 -0.054457 0.048398 -1.12518 0.260513
## shape 1.232940 0.029595 41.66072 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000183 0.000076 2.398490 0.016463
## ar1 0.208046 0.009096 22.873043 0.000000
## ar2 -0.950826 0.006411 -148.320489 0.000000
## ma1 -0.213250 0.014634 -14.571790 0.000000
## ma2 0.919762 0.013198 69.690407 0.000000
## omega 0.000000 0.000017 0.023634 0.981145
## alpha1 0.018686 0.119065 0.156942 0.875291
## alpha2 0.075208 0.538691 0.139612 0.888967
## beta1 0.913390 0.495664 1.842762 0.065364
## gamma1 -0.006427 0.064632 -0.099438 0.920790
## gamma2 -0.054457 0.361751 -0.150537 0.880341
## shape 1.232940 0.947024 1.301910 0.192947
##
## LogLikelihood : 6135.996
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4121
## Bayes -8.3685
## Shibata -8.4122
## Hannan-Quinn -8.3958
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.881 0.1702
## Lag[2*(p+q)+(p+q)-1][11] 4.750 0.9862
## Lag[4*(p+q)+(p+q)-1][19] 7.440 0.8645
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1141 0.7356
## Lag[2*(p+q)+(p+q)-1][8] 3.7583 0.5481
## Lag[4*(p+q)+(p+q)-1][14] 4.6823 0.8077
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 1.926 0.500 2.000 0.1652
## ARCH Lag[6] 2.096 1.461 1.711 0.4700
## ARCH Lag[8] 2.283 2.368 1.583 0.6842
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 389.2474
## Individual Statistics:
## mu 0.14830
## ar1 0.04840
## ar2 0.29217
## ma1 0.04777
## ma2 0.40633
## omega 99.13800
## alpha1 0.24415
## alpha2 0.20464
## beta1 0.31806
## gamma1 0.26240
## gamma2 0.21218
## shape 0.10029
##
## 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 1.5473 0.1220
## Negative Sign Bias 1.0232 0.3064
## Positive Sign Bias 0.7625 0.4459
## Joint Effect 2.4838 0.4782
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 26.03 0.1293
## 2 30 22.53 0.7976
## 3 40 37.85 0.5224
## 4 50 51.35 0.3818
##
##
## Elapsed time : 4.38931Garch22
XAU.garch22n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
XAU.garch22n.fit <- ugarchfit(spec = XAU.garch22n.spec, data = data[, 3])
XAU.garch22t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
XAU.garch22t.fit <- ugarchfit(spec = XAU.garch22t.spec, data = data[, 3])
XAU.garch22st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
XAU.garch22st.fit <- ugarchfit(spec = XAU.garch22st.spec, data = data[, 3])
XAU.garch22g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
XAU.garch22g.fit <- ugarchfit(spec = XAU.garch22g.spec, data = data[, 3])
XAU.garch22sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
XAU.garch22sg.fit <- ugarchfit(spec = XAU.garch22g.spec, data = data[, 3])
print(XAU.garch22n.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000094 0.000091 1.03398 0.301147
## ar1 0.193973 0.029806 6.50792 0.000000
## ar2 -0.980198 0.012730 -77.00203 0.000000
## ma1 -0.192377 0.042508 -4.52568 0.000006
## ma2 0.959263 0.014046 68.29626 0.000000
## omega 0.000001 0.000001 1.23524 0.216740
## alpha1 0.006635 0.030282 0.21911 0.826566
## alpha2 0.173230 0.039258 4.41261 0.000010
## beta1 0.258787 0.118432 2.18511 0.028881
## beta2 0.569285 0.113065 5.03505 0.000000
## gamma1 0.013813 0.034388 0.40167 0.687924
## gamma2 -0.123536 0.042719 -2.89184 0.003830
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000094 0.000093 1.01380 0.310678
## ar1 0.193973 0.069148 2.80518 0.005029
## ar2 -0.980198 0.026357 -37.18971 0.000000
## ma1 -0.192377 0.099009 -1.94302 0.052014
## ma2 0.959263 0.029986 31.99089 0.000000
## omega 0.000001 0.000006 0.13350 0.893799
## alpha1 0.006635 0.059093 0.11228 0.910602
## alpha2 0.173230 0.115561 1.49904 0.133864
## beta1 0.258787 0.168256 1.53806 0.124034
## beta2 0.569285 0.136358 4.17493 0.000030
## gamma1 0.013813 0.050745 0.27220 0.785467
## gamma2 -0.123536 0.083713 -1.47570 0.140024
##
## LogLikelihood : 6092.022
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.3517
## Bayes -8.3081
## Shibata -8.3518
## Hannan-Quinn -8.3354
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.9911 0.3195
## Lag[2*(p+q)+(p+q)-1][11] 3.5403 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 6.0016 0.9707
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1941 0.6595
## Lag[2*(p+q)+(p+q)-1][11] 0.9830 0.9967
## Lag[4*(p+q)+(p+q)-1][19] 2.0166 0.9995
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.01693 0.500 2.000 0.8965
## ARCH Lag[7] 0.20351 1.473 1.746 0.9698
## ARCH Lag[9] 0.28817 2.402 1.619 0.9953
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 188.3737
## Individual Statistics:
## mu 0.09115
## ar1 0.07143
## ar2 0.18071
## ma1 0.07689
## ma2 0.23059
## omega 30.97011
## alpha1 0.26767
## alpha2 0.20724
## beta1 0.28937
## beta2 0.30827
## gamma1 0.28797
## gamma2 0.20117
##
## 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 1.5581 0.1194
## Negative Sign Bias 1.1530 0.2491
## Positive Sign Bias 0.8986 0.3690
## Joint Effect 2.6912 0.4417
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 65.95 4.275e-07
## 2 30 86.24 1.365e-07
## 3 40 91.69 3.939e-06
## 4 50 109.73 1.511e-06
##
##
## Elapsed time : 1.922106print(XAU.garch22t.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000176 0.000081 2.156841 0.031018
## ar1 0.202455 0.035486 5.705154 0.000000
## ar2 -0.951742 0.028452 -33.450635 0.000000
## ma1 -0.211764 0.045812 -4.622402 0.000004
## ma2 0.924806 0.035785 25.843474 0.000000
## omega 0.000001 0.000001 0.916168 0.359579
## alpha1 0.000001 0.030568 0.000022 0.999982
## alpha2 0.150151 0.030602 4.906582 0.000001
## beta1 0.161332 0.132896 1.213971 0.224759
## beta2 0.707192 0.142223 4.972431 0.000001
## gamma1 0.019074 0.037415 0.509800 0.610191
## gamma2 -0.114736 0.039834 -2.880359 0.003972
## shape 4.599626 0.516276 8.909234 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000176 0.000082 2.146989 0.031794
## ar1 0.202455 0.046693 4.335890 0.000015
## ar2 -0.951742 0.028976 -32.845985 0.000000
## ma1 -0.211764 0.060457 -3.502702 0.000461
## ma2 0.924806 0.036040 25.660520 0.000000
## omega 0.000001 0.000005 0.121373 0.903396
## alpha1 0.000001 0.135840 0.000005 0.999996
## alpha2 0.150151 0.228120 0.658211 0.510403
## beta1 0.161332 0.736423 0.219075 0.826592
## beta2 0.707192 0.517021 1.367820 0.171368
## gamma1 0.019074 0.043740 0.436081 0.662778
## gamma2 -0.114736 0.197778 -0.580127 0.561829
## shape 4.599626 2.751687 1.671566 0.094610
##
## LogLikelihood : 6136.927
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4120
## Bayes -8.3648
## Shibata -8.4121
## Hannan-Quinn -8.3944
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.387 0.1223
## Lag[2*(p+q)+(p+q)-1][11] 5.091 0.9404
## Lag[4*(p+q)+(p+q)-1][19] 7.747 0.8279
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3089 0.5784
## Lag[2*(p+q)+(p+q)-1][11] 2.8137 0.8898
## Lag[4*(p+q)+(p+q)-1][19] 4.1117 0.9751
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.1336 0.500 2.000 0.7147
## ARCH Lag[7] 1.0458 1.473 1.746 0.7445
## ARCH Lag[9] 1.1798 2.402 1.619 0.9052
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 354.5176
## Individual Statistics:
## mu 0.20754
## ar1 0.07258
## ar2 0.30597
## ma1 0.07527
## ma2 0.40421
## omega 68.46700
## alpha1 0.27582
## alpha2 0.17837
## beta1 0.27797
## beta2 0.30094
## gamma1 0.30853
## gamma2 0.17511
## shape 0.22029
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.598 0.1103
## Negative Sign Bias 1.067 0.2860
## Positive Sign Bias 1.132 0.2580
## Joint Effect 2.895 0.4082
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 20.26 0.3789
## 2 30 24.38 0.7097
## 3 40 33.01 0.7388
## 4 50 50.73 0.4052
##
##
## Elapsed time : 2.573189print(XAU.garch22st.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000102 0.000091 1.111092 0.266529
## ar1 0.193873 0.033961 5.708693 0.000000
## ar2 -0.953885 0.029018 -32.871866 0.000000
## ma1 -0.200492 0.044642 -4.491155 0.000007
## ma2 0.926319 0.036583 25.321364 0.000000
## omega 0.000001 0.000001 0.931240 0.351729
## alpha1 0.000045 0.029771 0.001513 0.998793
## alpha2 0.150230 0.029014 5.177872 0.000000
## beta1 0.164821 0.131052 1.257681 0.208507
## beta2 0.702377 0.140215 5.009299 0.000001
## gamma1 0.019032 0.036827 0.516784 0.605307
## gamma2 -0.114029 0.038547 -2.958150 0.003095
## skew 0.938658 0.033241 28.237656 0.000000
## shape 4.648304 0.537252 8.652000 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000102 0.000096 1.060064 0.289116
## ar1 0.193873 0.044006 4.405563 0.000011
## ar2 -0.953885 0.031875 -29.925416 0.000000
## ma1 -0.200492 0.058657 -3.418068 0.000631
## ma2 0.926319 0.038833 23.853716 0.000000
## omega 0.000001 0.000005 0.125588 0.900058
## alpha1 0.000045 0.125434 0.000359 0.999713
## alpha2 0.150230 0.226215 0.664103 0.506625
## beta1 0.164821 0.717689 0.229656 0.818359
## beta2 0.702377 0.503236 1.395720 0.162799
## gamma1 0.019032 0.052483 0.362624 0.716885
## gamma2 -0.114029 0.206331 -0.552652 0.580502
## skew 0.938658 0.031816 29.502535 0.000000
## shape 4.648304 2.636690 1.762932 0.077912
##
## LogLikelihood : 6138.512
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4128
## Bayes -8.3620
## Shibata -8.4130
## Hannan-Quinn -8.3938
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.090 0.1482
## Lag[2*(p+q)+(p+q)-1][11] 4.874 0.9753
## Lag[4*(p+q)+(p+q)-1][19] 7.547 0.8523
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2915 0.5893
## Lag[2*(p+q)+(p+q)-1][11] 2.7873 0.8927
## Lag[4*(p+q)+(p+q)-1][19] 4.0778 0.9761
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.1633 0.500 2.000 0.6861
## ARCH Lag[7] 1.0696 1.473 1.746 0.7379
## ARCH Lag[9] 1.2018 2.402 1.619 0.9018
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 356.7794
## Individual Statistics:
## mu 0.20391
## ar1 0.08672
## ar2 0.31705
## ma1 0.09877
## ma2 0.39837
## omega 69.76473
## alpha1 0.26571
## alpha2 0.18651
## beta1 0.27850
## beta2 0.30068
## gamma1 0.29208
## gamma2 0.18123
## skew 0.36676
## shape 0.22657
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 3.08 3.34 3.9
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.525 0.1275
## Negative Sign Bias 1.061 0.2891
## Positive Sign Bias 1.071 0.2841
## Joint Effect 2.674 0.4446
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 17.90 0.5291
## 2 30 17.87 0.9468
## 3 40 37.08 0.5579
## 4 50 40.43 0.8034
##
##
## Elapsed time : 3.51786print(XAU.garch22g.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000176 0.000089 1.964712 0.049448
## ar1 0.207003 0.011185 18.507388 0.000000
## ar2 -0.953014 0.011582 -82.281821 0.000000
## ma1 -0.212996 0.014477 -14.712881 0.000000
## ma2 0.922289 0.014694 62.765824 0.000000
## omega 0.000001 0.000002 0.340910 0.733171
## alpha1 0.000155 0.020936 0.007419 0.994080
## alpha2 0.153430 0.048280 3.177906 0.001483
## beta1 0.220285 0.033345 6.606197 0.000000
## beta2 0.638611 0.118717 5.379260 0.000000
## gamma1 0.015488 0.038456 0.402747 0.687134
## gamma2 -0.114706 0.016169 -7.094165 0.000000
## shape 1.236551 0.054940 22.507188 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000176 0.000136 1.288739 0.19749
## ar1 0.207003 0.011916 17.372548 0.00000
## ar2 -0.953014 0.005610 -169.875363 0.00000
## ma1 -0.212996 0.007621 -27.949488 0.00000
## ma2 0.922289 0.017379 53.068179 0.00000
## omega 0.000001 0.000039 0.016332 0.98697
## alpha1 0.000155 0.530460 0.000293 0.99977
## alpha2 0.153430 1.333935 0.115020 0.90843
## beta1 0.220285 2.872393 0.076690 0.93887
## beta2 0.638611 1.384399 0.461291 0.64459
## gamma1 0.015488 0.040636 0.381142 0.70310
## gamma2 -0.114706 0.934143 -0.122793 0.90227
## shape 1.236551 1.712930 0.721892 0.47036
##
## LogLikelihood : 6138.273
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4138
## Bayes -8.3667
## Shibata -8.4140
## Hannan-Quinn -8.3962
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.978 0.1596
## Lag[2*(p+q)+(p+q)-1][11] 4.940 0.9671
## Lag[4*(p+q)+(p+q)-1][19] 7.643 0.8408
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4038 0.5251
## Lag[2*(p+q)+(p+q)-1][11] 2.0484 0.9573
## Lag[4*(p+q)+(p+q)-1][19] 3.2080 0.9929
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.01649 0.500 2.000 0.8978
## ARCH Lag[7] 0.59250 1.473 1.746 0.8720
## ARCH Lag[9] 0.67022 2.402 1.619 0.9698
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 331.5984
## Individual Statistics:
## mu 0.15888
## ar1 0.08463
## ar2 0.27350
## ma1 0.07843
## ma2 0.37258
## omega 60.58513
## alpha1 0.27723
## alpha2 0.19546
## beta1 0.29713
## beta2 0.31509
## gamma1 0.30901
## gamma2 0.19094
## shape 0.09036
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.4359 0.1512
## Negative Sign Bias 0.9581 0.3382
## Positive Sign Bias 1.0120 0.3117
## Joint Effect 2.3314 0.5065
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 32.54 0.02712
## 2 30 32.21 0.31055
## 3 40 47.85 0.15653
## 4 50 45.99 0.59583
##
##
## Elapsed time : 4.519516print(XAU.garch22sg.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000176 0.000089 1.964712 0.049448
## ar1 0.207003 0.011185 18.507388 0.000000
## ar2 -0.953014 0.011582 -82.281821 0.000000
## ma1 -0.212996 0.014477 -14.712881 0.000000
## ma2 0.922289 0.014694 62.765824 0.000000
## omega 0.000001 0.000002 0.340910 0.733171
## alpha1 0.000155 0.020936 0.007419 0.994080
## alpha2 0.153430 0.048280 3.177906 0.001483
## beta1 0.220285 0.033345 6.606197 0.000000
## beta2 0.638611 0.118717 5.379260 0.000000
## gamma1 0.015488 0.038456 0.402747 0.687134
## gamma2 -0.114706 0.016169 -7.094165 0.000000
## shape 1.236551 0.054940 22.507188 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000176 0.000136 1.288739 0.19749
## ar1 0.207003 0.011916 17.372548 0.00000
## ar2 -0.953014 0.005610 -169.875363 0.00000
## ma1 -0.212996 0.007621 -27.949488 0.00000
## ma2 0.922289 0.017379 53.068179 0.00000
## omega 0.000001 0.000039 0.016332 0.98697
## alpha1 0.000155 0.530460 0.000293 0.99977
## alpha2 0.153430 1.333935 0.115020 0.90843
## beta1 0.220285 2.872393 0.076690 0.93887
## beta2 0.638611 1.384399 0.461291 0.64459
## gamma1 0.015488 0.040636 0.381142 0.70310
## gamma2 -0.114706 0.934143 -0.122793 0.90227
## shape 1.236551 1.712930 0.721892 0.47036
##
## LogLikelihood : 6138.273
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4138
## Bayes -8.3667
## Shibata -8.4140
## Hannan-Quinn -8.3962
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.978 0.1596
## Lag[2*(p+q)+(p+q)-1][11] 4.940 0.9671
## Lag[4*(p+q)+(p+q)-1][19] 7.643 0.8408
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4038 0.5251
## Lag[2*(p+q)+(p+q)-1][11] 2.0484 0.9573
## Lag[4*(p+q)+(p+q)-1][19] 3.2080 0.9929
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.01649 0.500 2.000 0.8978
## ARCH Lag[7] 0.59250 1.473 1.746 0.8720
## ARCH Lag[9] 0.67022 2.402 1.619 0.9698
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 331.5984
## Individual Statistics:
## mu 0.15888
## ar1 0.08463
## ar2 0.27350
## ma1 0.07843
## ma2 0.37258
## omega 60.58513
## alpha1 0.27723
## alpha2 0.19546
## beta1 0.29713
## beta2 0.31509
## gamma1 0.30901
## gamma2 0.19094
## shape 0.09036
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.4359 0.1512
## Negative Sign Bias 0.9581 0.3382
## Positive Sign Bias 1.0120 0.3117
## Joint Effect 2.3314 0.5065
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 32.54 0.02712
## 2 30 32.21 0.31055
## 3 40 47.85 0.15653
## 4 50 45.99 0.59583
##
##
## Elapsed time : 4.584688Ước lượng cho chuỗi VNI
Garch11
VNI.garch11n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
VNI.garch11n.fit <- ugarchfit(spec = VNI.garch11n.spec, data = data[, 2])
VNI.garch11t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
VNI.garch11t.fit <- ugarchfit(spec = VNI.garch11t.spec, data = data[, 2])
VNI.garch11st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
VNI.garch11st.fit <- ugarchfit(spec = VNI.garch11st.spec, data = data[, 2])
VNI.garch11g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
VNI.garch11g.fit <- ugarchfit(spec = VNI.garch11g.spec, data = data[, 2])
VNI.garch11sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
VNI.garch11sg.fit <- ugarchfit(spec = VNI.garch11sg.spec, data = data[, 2])
print(VNI.garch11n.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000003 0.000003 -1.0491 0.294152
## ar1 -0.343553 0.029695 -11.5696 0.000000
## ar2 0.069775 0.029536 2.3624 0.018158
## ma1 -0.566212 0.000294 -1923.6895 0.000000
## ma2 -0.397267 0.000104 -3832.2267 0.000000
## omega 0.000001 0.000000 3.3765 0.000734
## alpha1 0.012469 0.005628 2.2157 0.026715
## beta1 0.876144 0.009637 90.9170 0.000000
## gamma1 0.135127 0.020536 6.5799 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000003 0.000007 -0.46094 0.644842
## ar1 -0.343553 0.032244 -10.65483 0.000000
## ar2 0.069775 0.032073 2.17551 0.029592
## ma1 -0.566212 0.000576 -982.74020 0.000000
## ma2 -0.397267 0.000507 -782.98721 0.000000
## omega 0.000001 0.000002 0.51429 0.607050
## alpha1 0.012469 0.061467 0.20286 0.839242
## beta1 0.876144 0.010655 82.22620 0.000000
## gamma1 0.135127 0.066756 2.02421 0.042949
##
## LogLikelihood : 5623.181
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.7118
## Bayes -7.6791
## Shibata -7.7119
## Hannan-Quinn -7.6996
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1609 0.6883
## Lag[2*(p+q)+(p+q)-1][11] 1.6646 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 4.2644 0.9988
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.04302 0.8357
## Lag[2*(p+q)+(p+q)-1][5] 0.30110 0.9836
## Lag[4*(p+q)+(p+q)-1][9] 1.01114 0.9858
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.2515 0.500 2.000 0.6160
## ARCH Lag[5] 0.3841 1.440 1.667 0.9172
## ARCH Lag[7] 0.5929 2.315 1.543 0.9692
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 5.2131
## Individual Statistics:
## mu 0.18428
## ar1 0.05301
## ar2 0.39377
## ma1 0.16005
## ma2 0.21255
## omega 0.84062
## alpha1 0.18961
## beta1 0.09532
## gamma1 0.08173
##
## 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 1.3600 0.1740
## Negative Sign Bias 0.3198 0.7491
## Positive Sign Bias 0.8872 0.3751
## Joint Effect 6.0620 0.1086
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 125.8 8.892e-18
## 2 30 135.6 1.031e-15
## 3 40 177.6 1.388e-19
## 4 50 178.3 1.397e-16
##
##
## Elapsed time : 0.9788561print(VNI.garch11t.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Convergence Problem:
## Solver Message:print(VNI.garch11st.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Convergence Problem:
## Solver Message:print(VNI.garch11g.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Convergence Problem:
## Solver Message:print(VNI.garch11sg.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Convergence Problem:
## Solver Message:Garch12
VNI.garch12n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
VNI.garch12n.fit <- ugarchfit(spec = VNI.garch12n.spec, data = data[, 2])
VNI.garch12t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
VNI.garch12t.fit <- ugarchfit(spec = VNI.garch12t.spec, data = data[, 2])
VNI.garch12st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
VNI.garch12st.fit <- ugarchfit(spec = VNI.garch12st.spec, data = data[, 2])
VNI.garch12g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
VNI.garch12g.fit <- ugarchfit(spec = VNI.garch12g.spec, data = data[, 2])
VNI.garch12sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
VNI.garch12sg.fit <- ugarchfit(spec = VNI.garch12sg.spec, data = data[, 2])
print(VNI.garch12n.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Convergence Problem:
## Solver Message:print(VNI.garch12t.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Convergence Problem:
## Solver Message:print(VNI.garch12st.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Convergence Problem:
## Solver Message:print(VNI.garch12g.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Convergence Problem:
## Solver Message:print(VNI.garch12sg.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000004 0.000000 -13.90189 0.00000
## ar1 -0.517914 0.014260 -36.31814 0.00000
## ar2 0.025232 0.016865 1.49615 0.13461
## ma1 -0.454202 0.000778 -583.55143 0.00000
## ma2 -0.505516 0.000758 -667.07936 0.00000
## omega 0.000001 0.000006 0.24951 0.80297
## alpha1 0.034149 0.093371 0.36573 0.71457
## beta1 0.633997 0.048078 13.18679 0.00000
## beta2 0.190418 0.022175 8.58713 0.00000
## gamma1 0.171236 0.155098 1.10405 0.26957
## skew 0.858082 0.023235 36.92994 0.00000
## shape 1.125937 0.054339 20.72044 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000004 0.000096 -0.041922 0.966561
## ar1 -0.517914 0.788919 -0.656486 0.511512
## ar2 0.025232 0.671034 0.037602 0.970005
## ma1 -0.454202 0.016909 -26.860796 0.000000
## ma2 -0.505516 0.013964 -36.200489 0.000000
## omega 0.000001 0.000183 0.007917 0.993684
## alpha1 0.034149 3.024565 0.011290 0.990992
## beta1 0.633997 1.702291 0.372437 0.709567
## beta2 0.190418 0.070653 2.695136 0.007036
## gamma1 0.171236 5.036706 0.033998 0.972879
## skew 0.858082 0.051757 16.578967 0.000000
## shape 1.125937 0.220461 5.107189 0.000000
##
## LogLikelihood : 5737.164
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8642
## Bayes -7.8207
## Shibata -7.8644
## Hannan-Quinn -7.8480
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 3.087 0.07894
## Lag[2*(p+q)+(p+q)-1][11] 4.624 0.99286
## Lag[4*(p+q)+(p+q)-1][19] 6.766 0.92737
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.6962 0.4041
## Lag[2*(p+q)+(p+q)-1][8] 1.6441 0.9095
## Lag[4*(p+q)+(p+q)-1][14] 4.2894 0.8513
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.2391 0.500 2.000 0.6249
## ARCH Lag[6] 0.3726 1.461 1.711 0.9267
## ARCH Lag[8] 1.6701 2.368 1.583 0.8072
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 43.9813
## Individual Statistics:
## mu 0.12391
## ar1 0.11358
## ar2 0.11856
## ma1 0.21827
## ma2 0.21413
## omega 5.14888
## alpha1 0.21126
## beta1 0.14111
## beta2 0.14373
## gamma1 0.16412
## skew 0.08672
## shape 0.07903
##
## 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 1.9412 0.05243 *
## Negative Sign Bias 1.4411 0.14976
## Positive Sign Bias 0.8525 0.39409
## Joint Effect 8.0983 0.04402 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 21.28 0.3215
## 2 30 38.02 0.1218
## 3 40 48.51 0.1415
## 4 50 55.88 0.2322
##
##
## Elapsed time : 3.798047Garch21
VNI.garch21n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
VNI.garch21n.fit <- ugarchfit(spec = VNI.garch21n.spec, data = data[, 2])
VNI.garch21t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
VNI.garch21t.fit <- ugarchfit(spec = VNI.garch21t.spec, data = data[, 2])
VNI.garch21st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
VNI.garch21st.fit <- ugarchfit(spec = VNI.garch21st.spec, data = data[, 2])
VNI.garch21g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
VNI.garch21g.fit <- ugarchfit(spec = VNI.garch21g.spec, data = data[, 2])
VNI.garch21sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 1)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
VNI.garch21sg.fit <- ugarchfit(spec = VNI.garch21sg.spec, data = data[, 2])
print(VNI.garch21n.fit)##
## *---------------------------------*
## * 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 -0.000003 0.000003 -1.0630e+00 0.287798
## ar1 -0.438523 0.030369 -1.4440e+01 0.000000
## ar2 0.076226 0.029017 2.6269e+00 0.008616
## ma1 -0.472096 0.000231 -2.0406e+03 0.000000
## ma2 -0.495979 0.000226 -2.1928e+03 0.000000
## omega 0.000001 0.000001 1.5002e+00 0.133553
## alpha1 0.000001 0.046459 2.1000e-05 0.999983
## alpha2 0.022825 0.049307 4.6291e-01 0.643430
## beta1 0.887626 0.010145 8.7492e+01 0.000000
## gamma1 0.242035 0.071945 3.3642e+00 0.000768
## gamma2 -0.135452 0.069968 -1.9359e+00 0.052880
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000003 0.000012 -2.4610e-01 0.80560
## ar1 -0.438523 0.076561 -5.7278e+00 0.00000
## ar2 0.076226 0.064111 1.1890e+00 0.23445
## ma1 -0.472096 0.000528 -8.9372e+02 0.00000
## ma2 -0.495979 0.000492 -1.0082e+03 0.00000
## omega 0.000001 0.000009 1.0755e-01 0.91435
## alpha1 0.000001 0.346371 3.0000e-06 1.00000
## alpha2 0.022825 0.142570 1.6009e-01 0.87281
## beta1 0.887626 0.019372 4.5821e+01 0.00000
## gamma1 0.242035 0.353489 6.8471e-01 0.49353
## gamma2 -0.135452 0.140483 -9.6418e-01 0.33495
##
## LogLikelihood : 5626.752
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.7139
## Bayes -7.6740
## Shibata -7.7141
## Hannan-Quinn -7.6991
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.02245 0.8809
## Lag[2*(p+q)+(p+q)-1][11] 2.10744 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 4.61017 0.9974
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.800 0.3711
## Lag[2*(p+q)+(p+q)-1][8] 1.396 0.9389
## Lag[4*(p+q)+(p+q)-1][14] 4.054 0.8751
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.1022 0.500 2.000 0.7492
## ARCH Lag[6] 0.1547 1.461 1.711 0.9781
## ARCH Lag[8] 1.1388 2.368 1.583 0.9029
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 26.2358
## Individual Statistics:
## mu 0.18984
## ar1 0.08391
## ar2 0.46571
## ma1 0.20525
## ma2 0.30275
## omega 3.08485
## alpha1 0.14861
## alpha2 0.08547
## beta1 0.06126
## gamma1 0.05122
## gamma2 0.04176
##
## 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 1.8374 0.06635 *
## Negative Sign Bias 1.3399 0.18049
## Positive Sign Bias 0.5483 0.58357
## Joint Effect 6.3071 0.09759 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 122.8 3.328e-17
## 2 30 135.6 1.031e-15
## 3 40 150.8 4.575e-15
## 4 50 167.3 7.800e-15
##
##
## Elapsed time : 0.898603print(VNI.garch21t.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000004 0.000002 2.0179e+00 0.043601
## ar1 -0.288331 0.029760 -9.6886e+00 0.000000
## ar2 0.061634 0.026289 2.3445e+00 0.019053
## ma1 -0.651611 0.000112 -5.8012e+03 0.000000
## ma2 -0.324252 0.000257 -1.2619e+03 0.000000
## omega 0.000001 0.000001 8.7233e-01 0.383031
## alpha1 0.000018 0.104502 1.7500e-04 0.999860
## alpha2 0.037914 0.098746 3.8396e-01 0.701011
## beta1 0.843354 0.033078 2.5496e+01 0.000000
## gamma1 0.364868 0.131784 2.7687e+00 0.005628
## gamma2 -0.197878 0.115534 -1.7127e+00 0.086762
## shape 3.832555 0.421594 9.0906e+00 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000004 0.000002 2.0490e+00 0.040463
## ar1 -0.288331 0.058096 -4.9630e+00 0.000001
## ar2 0.061634 0.035814 1.7210e+00 0.085255
## ma1 -0.651611 0.000135 -4.8147e+03 0.000000
## ma2 -0.324252 0.000218 -1.4843e+03 0.000000
## omega 0.000001 0.000011 1.1456e-01 0.908795
## alpha1 0.000018 0.386232 4.7000e-05 0.999962
## alpha2 0.037914 0.360973 1.0503e-01 0.916349
## beta1 0.843354 0.194211 4.3425e+00 0.000014
## gamma1 0.364868 0.398551 9.1549e-01 0.359936
## gamma2 -0.197878 0.163966 -1.2068e+00 0.227500
## shape 3.832555 0.815057 4.7022e+00 0.000003
##
## LogLikelihood : 5731.316
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8562
## Bayes -7.8127
## Shibata -7.8563
## Hannan-Quinn -7.8400
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.5036 0.4779
## Lag[2*(p+q)+(p+q)-1][11] 1.9279 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 3.9456 0.9995
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.648 0.1992
## Lag[2*(p+q)+(p+q)-1][8] 2.521 0.7722
## Lag[4*(p+q)+(p+q)-1][14] 4.989 0.7708
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.1695 0.500 2.000 0.6806
## ARCH Lag[6] 0.4344 1.461 1.711 0.9101
## ARCH Lag[8] 1.4391 2.368 1.583 0.8509
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 68.694
## Individual Statistics:
## mu 0.21926
## ar1 0.05821
## ar2 0.30284
## ma1 0.37367
## ma2 0.41182
## omega 13.99148
## alpha1 0.20798
## alpha2 0.17853
## beta1 0.17149
## gamma1 0.17097
## gamma2 0.14779
## shape 0.23364
##
## 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 1.5379 0.12429
## Negative Sign Bias 2.0523 0.04032 **
## Positive Sign Bias 0.7894 0.43001
## Joint Effect 6.8109 0.07817 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 38.20 0.0055910
## 2 30 58.38 0.0009776
## 3 40 72.24 0.0009533
## 4 50 82.39 0.0019884
##
##
## Elapsed time : 1.274036print(VNI.garch21st.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000001 0.000003 -0.51472 0.606752
## ar1 -0.362262 0.028740 -12.60457 0.000000
## ar2 0.044761 0.026312 1.70120 0.088906
## ma1 -0.578157 0.000300 -1928.55203 0.000000
## ma2 -0.390991 0.000308 -1270.06883 0.000000
## omega 0.000001 0.000001 0.91168 0.361939
## alpha1 0.006296 0.043457 0.14487 0.884815
## alpha2 0.022793 0.045159 0.50473 0.613749
## beta1 0.868603 0.027155 31.98644 0.000000
## gamma1 0.346620 0.101967 3.39932 0.000676
## gamma2 -0.203859 0.094163 -2.16495 0.030392
## skew 0.836313 0.034724 24.08480 0.000000
## shape 4.209347 0.515075 8.17230 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000001 0.000006 -0.25006 0.802543
## ar1 -0.362262 0.034282 -10.56721 0.000000
## ar2 0.044761 0.038621 1.15899 0.246462
## ma1 -0.578157 0.000426 -1357.75075 0.000000
## ma2 -0.390991 0.000417 -938.33901 0.000000
## omega 0.000001 0.000009 0.11471 0.908674
## alpha1 0.006296 0.056090 0.11224 0.910633
## alpha2 0.022793 0.078918 0.28882 0.772722
## beta1 0.868603 0.164887 5.26787 0.000000
## gamma1 0.346620 0.133192 2.60240 0.009257
## gamma2 -0.203859 0.128610 -1.58509 0.112945
## skew 0.836313 0.117135 7.13973 0.000000
## shape 4.209347 1.360548 3.09386 0.001976
##
## LogLikelihood : 5743.455
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8715
## Bayes -7.8243
## Shibata -7.8717
## Hannan-Quinn -7.8539
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8657 0.3522
## Lag[2*(p+q)+(p+q)-1][11] 2.4867 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 4.5237 0.9979
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.783 0.1817
## Lag[2*(p+q)+(p+q)-1][8] 2.537 0.7693
## Lag[4*(p+q)+(p+q)-1][14] 4.988 0.7710
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.1669 0.500 2.000 0.6829
## ARCH Lag[6] 0.3117 1.461 1.711 0.9423
## ARCH Lag[8] 1.3056 2.368 1.583 0.8749
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 111.2287
## Individual Statistics:
## mu 0.16746
## ar1 0.06632
## ar2 0.25412
## ma1 0.23761
## ma2 0.26875
## omega 22.66056
## alpha1 0.17802
## alpha2 0.16753
## beta1 0.15757
## gamma1 0.15189
## gamma2 0.12873
## skew 0.13809
## shape 0.17779
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.6148 0.10658
## Negative Sign Bias 2.0461 0.04092 **
## Positive Sign Bias 0.8177 0.41366
## Joint Effect 7.0653 0.06984 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 26.23 0.12403
## 2 30 48.74 0.01230
## 3 40 61.91 0.01121
## 4 50 73.74 0.01269
##
##
## Elapsed time : 1.352411print(VNI.garch21g.fit)##
## *---------------------------------*
## * 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 0.000004 0.000002 2.0822e+00 0.037328
## ar1 -0.117005 0.011062 -1.0577e+01 0.000000
## ar2 0.044145 0.018706 2.3599e+00 0.018278
## ma1 -0.844635 0.000033 -2.5513e+04 0.000000
## ma2 -0.136335 0.000174 -7.8421e+02 0.000000
## omega 0.000001 0.000001 7.5081e-01 0.452768
## alpha1 0.000020 0.039792 5.0900e-04 0.999594
## alpha2 0.034149 0.042162 8.0994e-01 0.417973
## beta1 0.861113 0.029241 2.9449e+01 0.000000
## gamma1 0.291217 0.091506 3.1825e+00 0.001460
## gamma2 -0.168520 0.088070 -1.9135e+00 0.055687
## shape 1.059345 0.054555 1.9418e+01 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000004 0.000002 2.0567e+00 0.039713
## ar1 -0.117005 0.005811 -2.0136e+01 0.000000
## ar2 0.044145 0.015724 2.8075e+00 0.004993
## ma1 -0.844635 0.000033 -2.5402e+04 0.000000
## ma2 -0.136335 0.000272 -5.0037e+02 0.000000
## omega 0.000001 0.000014 7.6457e-02 0.939056
## alpha1 0.000020 0.085207 2.3800e-04 0.999810
## alpha2 0.034149 0.050300 6.7890e-01 0.497200
## beta1 0.861113 0.225414 3.8201e+00 0.000133
## gamma1 0.291217 0.142331 2.0461e+00 0.040751
## gamma2 -0.168520 0.189075 -8.9129e-01 0.372776
## shape 1.059345 0.236952 4.4707e+00 0.000008
##
## LogLikelihood : 5726.693
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8499
## Bayes -7.8063
## Shibata -7.8500
## Hannan-Quinn -7.8336
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.704 0.1917
## Lag[2*(p+q)+(p+q)-1][11] 3.073 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 5.083 0.9932
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.297 0.2547
## Lag[2*(p+q)+(p+q)-1][8] 1.864 0.8793
## Lag[4*(p+q)+(p+q)-1][14] 4.474 0.8314
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.07999 0.500 2.000 0.7773
## ARCH Lag[6] 0.19206 1.461 1.711 0.9704
## ARCH Lag[8] 1.12547 2.368 1.583 0.9051
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 70.1841
## Individual Statistics:
## mu 0.39787
## ar1 0.04728
## ar2 0.12981
## ma1 0.42155
## ma2 0.44564
## omega 11.90414
## alpha1 0.19001
## alpha2 0.13259
## beta1 0.10392
## gamma1 0.11802
## gamma2 0.10241
## shape 0.10727
##
## 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 1.593 0.11140
## Negative Sign Bias 1.718 0.08596 *
## Positive Sign Bias 0.685 0.49348
## Joint Effect 6.008 0.11122
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 44.44 0.0008206
## 2 30 58.30 0.0010005
## 3 40 68.73 0.0022997
## 4 50 86.45 0.0007705
##
##
## Elapsed time : 2.261734print(VNI.garch21sg.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000004 0.000003 -1.3370e+00 0.181234
## ar1 -0.500451 0.020979 -2.3855e+01 0.000000
## ar2 0.030263 0.020705 1.4617e+00 0.143837
## ma1 -0.459507 0.000481 -9.5601e+02 0.000000
## ma2 -0.503516 0.000483 -1.0423e+03 0.000000
## omega 0.000001 0.000001 6.4426e-01 0.519408
## alpha1 0.000085 0.017937 4.7360e-03 0.996221
## alpha2 0.026837 0.013031 2.0595e+00 0.039444
## beta1 0.884302 0.030094 2.9385e+01 0.000000
## gamma1 0.301102 0.042588 7.0701e+00 0.000000
## gamma2 -0.190324 0.041869 -4.5457e+00 0.000005
## skew 0.857944 0.025094 3.4189e+01 0.000000
## shape 1.131733 0.062591 1.8081e+01 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000004 0.000004 -1.038080 0.299233
## ar1 -0.500451 0.052844 -9.470304 0.000000
## ar2 0.030263 0.104212 0.290401 0.771510
## ma1 -0.459507 0.000886 -518.897267 0.000000
## ma2 -0.503516 0.001045 -481.736962 0.000000
## omega 0.000001 0.000016 0.054431 0.956591
## alpha1 0.000085 0.041290 0.002057 0.998358
## alpha2 0.026837 0.030796 0.871449 0.383509
## beta1 0.884302 0.303086 2.917665 0.003527
## gamma1 0.301102 0.148968 2.021249 0.043254
## gamma2 -0.190324 0.193973 -0.981188 0.326500
## skew 0.857944 0.118601 7.233878 0.000000
## shape 1.131733 0.358359 3.158100 0.001588
##
## LogLikelihood : 5739.215
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8657
## Bayes -7.8185
## Shibata -7.8658
## Hannan-Quinn -7.8481
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.454 0.1173
## Lag[2*(p+q)+(p+q)-1][11] 4.388 0.9983
## Lag[4*(p+q)+(p+q)-1][19] 6.494 0.9460
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.506 0.2197
## Lag[2*(p+q)+(p+q)-1][8] 2.143 0.8364
## Lag[4*(p+q)+(p+q)-1][14] 4.729 0.8023
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.1323 0.500 2.000 0.7160
## ARCH Lag[6] 0.2058 1.461 1.711 0.9674
## ARCH Lag[8] 1.2153 2.368 1.583 0.8903
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 112.6345
## Individual Statistics:
## mu 0.14620
## ar1 0.09825
## ar2 0.14401
## ma1 0.20605
## ma2 0.22400
## omega 21.80956
## alpha1 0.16540
## alpha2 0.14280
## beta1 0.10315
## gamma1 0.12750
## gamma2 0.10712
## skew 0.08246
## shape 0.08317
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 2.022 0.04332 **
## Negative Sign Bias 2.006 0.04505 **
## Positive Sign Bias 0.532 0.59478
## Joint Effect 7.663 0.05351 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 29.33 0.060973
## 2 30 43.26 0.043087
## 3 40 57.68 0.027323
## 4 50 80.54 0.003019
##
##
## Elapsed time : 5.160106Garch22
VNI.garch22n.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "norm")
VNI.garch22n.fit <- ugarchfit(spec = VNI.garch22n.spec, data = data[, 2])
VNI.garch22t.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
VNI.garch22t.fit <- ugarchfit(spec = VNI.garch22t.spec, data = data[, 2])
VNI.garch22st.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
VNI.garch22st.fit <- ugarchfit(spec = VNI.garch22st.spec, data = data[, 2])
VNI.garch22g.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
VNI.garch22g.fit <- ugarchfit(spec = VNI.garch22g.spec, data = data[, 2])
VNI.garch22sg.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(2, 2)), mean.model
= list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
VNI.garch22sg.fit <- ugarchfit(spec = VNI.garch22sg.spec, data = data[, 2])
print(VNI.garch22n.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000003 0.000003 -1.0037e+00 0.315533
## ar1 -0.408781 0.031152 -1.3122e+01 0.000000
## ar2 0.075331 0.029173 2.5822e+00 0.009817
## ma1 -0.501909 0.000225 -2.2343e+03 0.000000
## ma2 -0.466795 0.000209 -2.2287e+03 0.000000
## omega 0.000001 0.000000 2.1710e+00 0.029928
## alpha1 0.000000 0.053339 8.0000e-06 0.999994
## alpha2 0.022567 0.050810 4.4415e-01 0.656936
## beta1 0.888226 0.110348 8.0493e+00 0.000000
## beta2 0.000004 0.102950 3.8000e-05 0.999970
## gamma1 0.241648 0.084700 2.8530e+00 0.004331
## gamma2 -0.135329 0.081119 -1.6683e+00 0.095258
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000003 0.000004 -0.805507 0.420527
## ar1 -0.408781 0.032704 -12.499448 0.000000
## ar2 0.075331 0.035159 2.142563 0.032148
## ma1 -0.501909 0.000686 -731.514413 0.000000
## ma2 -0.466795 0.000643 -725.688028 0.000000
## omega 0.000001 0.000004 0.239107 0.811023
## alpha1 0.000000 0.095570 0.000004 0.999997
## alpha2 0.022567 0.063826 0.353572 0.723659
## beta1 0.888226 1.259510 0.705216 0.480676
## beta2 0.000004 1.163731 0.000003 0.999997
## gamma1 0.241648 0.192686 1.254101 0.209805
## gamma2 -0.135329 0.366232 -0.369519 0.711741
##
## LogLikelihood : 5626.748
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.7126
## Bayes -7.6690
## Shibata -7.7127
## Hannan-Quinn -7.6963
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.02263 0.8804
## Lag[2*(p+q)+(p+q)-1][11] 2.06229 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 4.56018 0.9977
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7965 0.3721
## Lag[2*(p+q)+(p+q)-1][11] 2.6336 0.9086
## Lag[4*(p+q)+(p+q)-1][19] 6.0758 0.8677
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.0002196 0.500 2.000 0.9882
## ARCH Lag[7] 0.2499049 1.473 1.746 0.9598
## ARCH Lag[9] 1.4182162 2.402 1.619 0.8663
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 76.0931
## Individual Statistics:
## mu 0.19732
## ar1 0.07445
## ar2 0.45796
## ma1 0.21145
## ma2 0.29975
## omega 3.17468
## alpha1 0.14854
## alpha2 0.08570
## beta1 0.06135
## beta2 0.06404
## gamma1 0.05162
## gamma2 0.04208
##
## 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 1.8390 0.06613 *
## Negative Sign Bias 1.3388 0.18086
## Positive Sign Bias 0.5479 0.58387
## Joint Effect 6.3105 0.09744 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 121.3 6.390e-17
## 2 30 135.0 1.301e-15
## 3 40 154.3 1.225e-15
## 4 50 165.9 1.281e-14
##
##
## Elapsed time : 1.887014print(VNI.garch22t.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000004 0.000002 2.0321e+00 0.042145
## ar1 -0.289930 0.027855 -1.0408e+01 0.000000
## ar2 0.061651 0.025879 2.3823e+00 0.017206
## ma1 -0.649935 0.000117 -5.5440e+03 0.000000
## ma2 -0.325887 0.000268 -1.2146e+03 0.000000
## omega 0.000001 0.000001 1.0001e+00 0.317261
## alpha1 0.000003 0.050522 6.4000e-05 0.999949
## alpha2 0.037860 0.051042 7.4175e-01 0.458241
## beta1 0.843289 0.272015 3.1002e+00 0.001934
## beta2 0.000002 0.213949 1.1000e-05 0.999991
## gamma1 0.363650 0.072899 4.9884e+00 0.000001
## gamma2 -0.197069 0.116893 -1.6859e+00 0.091817
## shape 3.843235 0.418923 9.1741e+00 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000004 0.000003 1.4854e+00 0.137445
## ar1 -0.289930 0.050454 -5.7464e+00 0.000000
## ar2 0.061651 0.032425 1.9013e+00 0.057258
## ma1 -0.649935 0.000229 -2.8401e+03 0.000000
## ma2 -0.325887 0.000380 -8.5763e+02 0.000000
## omega 0.000001 0.000008 1.6103e-01 0.872072
## alpha1 0.000003 0.051507 6.2000e-05 0.999950
## alpha2 0.037860 0.063238 5.9869e-01 0.549378
## beta1 0.843289 2.356155 3.5791e-01 0.720412
## beta2 0.000002 1.974747 1.0000e-06 0.999999
## gamma1 0.363650 0.858596 4.2354e-01 0.671901
## gamma2 -0.197069 1.303727 -1.5116e-01 0.879851
## shape 3.843235 0.613828 6.2611e+00 0.000000
##
## LogLikelihood : 5731.316
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8548
## Bayes -7.8077
## Shibata -7.8550
## Hannan-Quinn -7.8372
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.5009 0.4791
## Lag[2*(p+q)+(p+q)-1][11] 1.9261 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 3.9441 0.9995
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.646 0.1995
## Lag[2*(p+q)+(p+q)-1][11] 3.705 0.7759
## Lag[4*(p+q)+(p+q)-1][19] 6.730 0.8097
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.1367 0.500 2.000 0.7116
## ARCH Lag[7] 0.3326 1.473 1.746 0.9404
## ARCH Lag[9] 1.6622 2.402 1.619 0.8227
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 186.6699
## Individual Statistics:
## mu 0.21716
## ar1 0.05819
## ar2 0.30238
## ma1 0.37012
## ma2 0.40858
## omega 13.97019
## alpha1 0.20050
## alpha2 0.17177
## beta1 0.16387
## beta2 0.19469
## gamma1 0.16497
## gamma2 0.14284
## shape 0.23119
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.5378 0.12433
## Negative Sign Bias 2.0521 0.04034 **
## Positive Sign Bias 0.7901 0.42961
## Joint Effect 6.8126 0.07812 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 38.75 0.0047538
## 2 30 59.00 0.0008212
## 3 40 74.66 0.0005088
## 4 50 85.14 0.0010510
##
##
## Elapsed time : 2.545956print(VNI.garch22st.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000001 0.000003 -5.9526e-01 0.551671
## ar1 -0.377677 0.027972 -1.3502e+01 0.000000
## ar2 0.044959 0.026234 1.7138e+00 0.086572
## ma1 -0.562770 0.000309 -1.8205e+03 0.000000
## ma2 -0.405426 0.000299 -1.3552e+03 0.000000
## omega 0.000001 0.000001 1.3210e+00 0.186487
## alpha1 0.006566 0.043451 1.5112e-01 0.879883
## alpha2 0.022119 0.044346 4.9877e-01 0.617943
## beta1 0.869801 0.196227 4.4326e+00 0.000009
## beta2 0.000000 0.155622 1.0000e-06 0.999999
## gamma1 0.350075 0.076169 4.5960e+00 0.000004
## gamma2 -0.206884 0.068857 -3.0045e+00 0.002660
## skew 0.836431 0.029623 2.8236e+01 0.000000
## shape 4.200057 0.508228 8.2641e+00 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000001 0.000008 -0.18997 0.849329
## ar1 -0.377677 0.086494 -4.36651 0.000013
## ar2 0.044959 0.058093 0.77391 0.438986
## ma1 -0.562770 0.000696 -808.26377 0.000000
## ma2 -0.405426 0.000613 -660.91683 0.000000
## omega 0.000001 0.000004 0.24848 0.803760
## alpha1 0.006566 0.058646 0.11196 0.910853
## alpha2 0.022119 0.038356 0.57667 0.564164
## beta1 0.869801 1.712514 0.50791 0.611517
## beta2 0.000000 1.483403 0.00000 1.000000
## gamma1 0.350075 0.775664 0.45132 0.651757
## gamma2 -0.206884 1.015204 -0.20378 0.838521
## skew 0.836431 0.067289 12.43051 0.000000
## shape 4.200057 0.667315 6.29397 0.000000
##
## LogLikelihood : 5743.452
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8701
## Bayes -7.8193
## Shibata -7.8703
## Hannan-Quinn -7.8512
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8703 0.3509
## Lag[2*(p+q)+(p+q)-1][11] 2.4606 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 4.4948 0.9980
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.816 0.1778
## Lag[2*(p+q)+(p+q)-1][11] 3.727 0.7729
## Lag[4*(p+q)+(p+q)-1][19] 6.757 0.8071
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.03449 0.500 2.000 0.8527
## ARCH Lag[7] 0.19690 1.473 1.746 0.9712
## ARCH Lag[9] 1.52543 2.402 1.619 0.8475
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 232.3586
## Individual Statistics:
## mu 0.16195
## ar1 0.06821
## ar2 0.24459
## ma1 0.22454
## ma2 0.25622
## omega 23.49541
## alpha1 0.17642
## alpha2 0.16582
## beta1 0.15278
## beta2 0.18078
## gamma1 0.15511
## gamma2 0.13097
## skew 0.13757
## shape 0.17304
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 3.08 3.34 3.9
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.606 0.10844
## Negative Sign Bias 2.061 0.03948 **
## Positive Sign Bias 0.828 0.40781
## Joint Effect 7.103 0.06868 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 26.39 0.119681
## 2 30 48.86 0.011941
## 3 40 59.60 0.018394
## 4 50 75.11 0.009614
##
##
## Elapsed time : 3.772026print(VNI.garch22g.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000004 0.000002 2.0485e+00 0.040513
## ar1 -0.106922 0.010589 -1.0098e+01 0.000000
## ar2 0.044289 0.012059 3.6727e+00 0.000240
## ma1 -0.854273 0.000034 -2.5257e+04 0.000000
## ma2 -0.126726 0.000179 -7.0959e+02 0.000000
## omega 0.000001 0.000001 1.1422e+00 0.253381
## alpha1 0.000010 0.053781 1.8700e-04 0.999851
## alpha2 0.033474 0.053299 6.2804e-01 0.529976
## beta1 0.862620 0.182785 4.7193e+00 0.000002
## beta2 0.000025 0.143558 1.7400e-04 0.999861
## gamma1 0.289947 0.092180 3.1454e+00 0.001658
## gamma2 -0.167992 0.045380 -3.7019e+00 0.000214
## shape 1.060805 0.049088 2.1610e+01 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000004 0.000002 1.9790e+00 0.047813
## ar1 -0.106922 0.007260 -1.4727e+01 0.000000
## ar2 0.044289 0.006660 6.6497e+00 0.000000
## ma1 -0.854273 0.000038 -2.2387e+04 0.000000
## ma2 -0.126726 0.000585 -2.1659e+02 0.000000
## omega 0.000001 0.000006 1.8929e-01 0.849867
## alpha1 0.000010 0.048600 2.0700e-04 0.999835
## alpha2 0.033474 0.053447 6.2631e-01 0.531111
## beta1 0.862620 1.915460 4.5035e-01 0.652461
## beta2 0.000025 1.664240 1.5000e-05 0.999988
## gamma1 0.289947 0.511952 5.6636e-01 0.571153
## gamma2 -0.167992 0.791394 -2.1227e-01 0.831894
## shape 1.060805 0.070733 1.4997e+01 0.000000
##
## LogLikelihood : 5726.69
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8485
## Bayes -7.8013
## Shibata -7.8486
## Hannan-Quinn -7.8309
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.665 0.1969
## Lag[2*(p+q)+(p+q)-1][11] 3.014 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 5.026 0.9939
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.295 0.2551
## Lag[2*(p+q)+(p+q)-1][11] 3.079 0.8592
## Lag[4*(p+q)+(p+q)-1][19] 6.331 0.8463
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.04129 0.500 2.000 0.8390
## ARCH Lag[7] 0.15578 1.473 1.746 0.9793
## ARCH Lag[9] 1.38852 2.402 1.619 0.8714
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 189.1906
## Individual Statistics:
## mu 0.3748
## ar1 0.0468
## ar2 0.1337
## ma1 0.3634
## ma2 0.4181
## omega 12.3674
## alpha1 0.1851
## alpha2 0.1296
## beta1 0.1016
## beta2 0.1164
## gamma1 0.1159
## gamma2 0.1013
## shape 0.1110
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.6127 0.10704
## Negative Sign Bias 1.7235 0.08501 *
## Positive Sign Bias 0.6783 0.49768
## Joint Effect 6.0734 0.10809
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 44.82 0.0007253
## 2 30 59.04 0.0008116
## 3 40 65.87 0.0045613
## 4 50 84.25 0.0012961
##
##
## Elapsed time : 3.447312print(VNI.garch22sg.fit)##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000004 0.000003 -1.2776e+00 0.201377
## ar1 -0.498908 0.034163 -1.4604e+01 0.000000
## ar2 0.030443 0.063383 4.8030e-01 0.631017
## ma1 -0.461358 0.000492 -9.3852e+02 0.000000
## ma2 -0.501490 0.000472 -1.0630e+03 0.000000
## omega 0.000001 0.000002 5.5131e-01 0.581423
## alpha1 0.000029 0.033456 8.8000e-04 0.999298
## alpha2 0.027233 0.028775 9.4642e-01 0.343935
## beta1 0.882605 0.019626 4.4971e+01 0.000000
## beta2 0.000025 0.019652 1.2680e-03 0.998989
## gamma1 0.298213 0.062927 4.7390e+00 0.000002
## gamma2 -0.186028 0.068699 -2.7079e+00 0.006771
## skew 0.857728 0.026291 3.2624e+01 0.000000
## shape 1.131658 0.062019 1.8247e+01 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000004 0.000007 -0.557997 0.576846
## ar1 -0.498908 0.305542 -1.632861 0.102498
## ar2 0.030443 0.615032 0.049498 0.960522
## ma1 -0.461358 0.002185 -211.141055 0.000000
## ma2 -0.501490 0.001024 -489.947384 0.000000
## omega 0.000001 0.000022 0.039429 0.968548
## alpha1 0.000029 0.163191 0.000180 0.999856
## alpha2 0.027233 0.041167 0.661535 0.508269
## beta1 0.882605 0.227950 3.871933 0.000108
## beta2 0.000025 0.097866 0.000255 0.999797
## gamma1 0.298213 0.314022 0.949657 0.342286
## gamma2 -0.186028 0.476136 -0.390703 0.696017
## skew 0.857728 0.170479 5.031284 0.000000
## shape 1.131658 0.358837 3.153685 0.001612
##
## LogLikelihood : 5739.223
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8643
## Bayes -7.8135
## Shibata -7.8645
## Hannan-Quinn -7.8454
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.490 0.1146
## Lag[2*(p+q)+(p+q)-1][11] 4.401 0.9981
## Lag[4*(p+q)+(p+q)-1][19] 6.509 0.9451
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.469 0.2255
## Lag[2*(p+q)+(p+q)-1][11] 3.344 0.8256
## Lag[4*(p+q)+(p+q)-1][19] 6.587 0.8232
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.003942 0.500 2.000 0.9499
## ARCH Lag[7] 0.158651 1.473 1.746 0.9788
## ARCH Lag[9] 1.490623 2.402 1.619 0.8537
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 218.9166
## Individual Statistics:
## mu 0.14575
## ar1 0.10120
## ar2 0.14267
## ma1 0.20366
## ma2 0.21995
## omega 20.86131
## alpha1 0.17306
## alpha2 0.15078
## beta1 0.10864
## beta2 0.12344
## gamma1 0.13347
## gamma2 0.11320
## skew 0.08195
## shape 0.08388
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 3.08 3.34 3.9
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 2.0225 0.04330 **
## Negative Sign Bias 1.9881 0.04699 **
## Positive Sign Bias 0.5307 0.59568
## Joint Effect 7.6327 0.05425 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 29.58 0.057436
## 2 30 43.63 0.039781
## 3 40 58.67 0.022337
## 4 50 76.90 0.006638
##
##
## Elapsed time : 5.174909LỰA CHỌN MO HINH GJR-GARCH
Lựa chọn mô hình biên phù hợp nhất cho chuỗi XAU.USD
XAU.model.list5 <- list(
garch11t = XAU.garch11t.fit,
garch11st = XAU.garch11st.fit,
garch11g = XAU.garch11g.fit,
garch11sg = XAU.garch11sg.fit,
garch12n = XAU.garch12n.fit,
garch12t = XAU.garch12t.fit,
garch12st = XAU.garch12st.fit,
garch12g = XAU.garch12g.fit,
garch12sg = XAU.garch12sg.fit,
garch21n = XAU.garch21n.fit,
garch21t = XAU.garch21t.fit,
garch21st = XAU.garch21st.fit,
garch21g = XAU.garch21g.fit,
garch21sg = XAU.garch21sg.fit,
garch22n = XAU.garch22n.fit,
garch22t = XAU.garch22t.fit,
garch22st = XAU.garch22st.fit,
garch22g = XAU.garch22g.fit,
garch22sg = XAU.garch22sg.fit
)
XAU.model.list6 <- list(
garch11t = XAU.garch11n.fit,
garch11t = XAU.garch11t.fit,
garch11st = XAU.garch11st.fit,
garch11g = XAU.garch11g.fit,
garch12n = XAU.garch12n.fit,
garch12t = XAU.garch12t.fit,
garch12st = XAU.garch12st.fit,
garch12g = XAU.garch12g.fit,
garch12sg = XAU.garch12sg.fit,
garch21n = XAU.garch21n.fit,
garch21t = XAU.garch21t.fit,
garch21st = XAU.garch21st.fit,
garch21g = XAU.garch21g.fit,
garch21sg = XAU.garch21sg.fit,
garch22n = XAU.garch22n.fit,
garch22t = XAU.garch22t.fit,
garch22st = XAU.garch22st.fit,
garch22g = XAU.garch22g.fit,
garch22sg = XAU.garch22sg.fit
)
results14 <- lapply(XAU.model.list5, function(model) {
tryCatch({
print(infocriteria(model))
}, error = function(e) {
message("Lỗi khi xử lý mô hình: ", e$message)
return(NULL) # Hoặc giá trị mặc định khác
})
})##
## Akaike -8.410975
## Bayes -8.374687
## Shibata -8.411068
## Hannan-Quinn -8.397436
##
## Akaike -8.411881
## Bayes -8.371965
## Shibata -8.411994
## Hannan-Quinn -8.396989
##
## Akaike -8.413259
## Bayes -8.376972
## Shibata -8.413353
## Hannan-Quinn -8.399721
##
## Akaike -8.413652
## Bayes -8.373736
## Shibata -8.413765
## Hannan-Quinn -8.398760
##
## Akaike -8.347164
## Bayes -8.310877
## Shibata -8.347258
## Hannan-Quinn -8.333626
##
## Akaike -8.409542
## Bayes -8.369626
## Shibata -8.409655
## Hannan-Quinn -8.394649
##
## Akaike -8.410422
## Bayes -8.366877
## Shibata -8.410557
## Hannan-Quinn -8.394176
##
## Akaike -8.413259
## Bayes -8.376972
## Shibata -8.413353
## Hannan-Quinn -8.399721
##
## Akaike -8.413259
## Bayes -8.376972
## Shibata -8.413353
## Hannan-Quinn -8.399721
##
## Akaike -8.349159
## Bayes -8.309243
## Shibata -8.349273
## Hannan-Quinn -8.334267
##
## Akaike -8.409607
## Bayes -8.366062
## Shibata -8.409741
## Hannan-Quinn -8.393361
##
## Akaike -8.410468
## Bayes -8.363295
## Shibata -8.410626
## Hannan-Quinn -8.392868
##
## Akaike -8.412083
## Bayes -8.368538
## Shibata -8.412217
## Hannan-Quinn -8.395837
##
## Akaike -8.412083
## Bayes -8.368538
## Shibata -8.412217
## Hannan-Quinn -8.395837
##
## Akaike -8.351678
## Bayes -8.308134
## Shibata -8.351813
## Hannan-Quinn -8.335432
##
## Akaike -8.411987
## Bayes -8.364813
## Shibata -8.412145
## Hannan-Quinn -8.394387
##
## Akaike -8.412791
## Bayes -8.361988
## Shibata -8.412973
## Hannan-Quinn -8.393837
##
## Akaike -8.413837
## Bayes -8.366663
## Shibata -8.413995
## Hannan-Quinn -8.396237
##
## Akaike -8.413837
## Bayes -8.366663
## Shibata -8.413995
## Hannan-Quinn -8.396237print(results14)## $garch11t
##
## Akaike -8.410975
## Bayes -8.374687
## Shibata -8.411068
## Hannan-Quinn -8.397436
##
## $garch11st
##
## Akaike -8.411881
## Bayes -8.371965
## Shibata -8.411994
## Hannan-Quinn -8.396989
##
## $garch11g
##
## Akaike -8.413259
## Bayes -8.376972
## Shibata -8.413353
## Hannan-Quinn -8.399721
##
## $garch11sg
##
## Akaike -8.413652
## Bayes -8.373736
## Shibata -8.413765
## Hannan-Quinn -8.398760
##
## $garch12n
##
## Akaike -8.347164
## Bayes -8.310877
## Shibata -8.347258
## Hannan-Quinn -8.333626
##
## $garch12t
##
## Akaike -8.409542
## Bayes -8.369626
## Shibata -8.409655
## Hannan-Quinn -8.394649
##
## $garch12st
##
## Akaike -8.410422
## Bayes -8.366877
## Shibata -8.410557
## Hannan-Quinn -8.394176
##
## $garch12g
##
## Akaike -8.413259
## Bayes -8.376972
## Shibata -8.413353
## Hannan-Quinn -8.399721
##
## $garch12sg
##
## Akaike -8.413259
## Bayes -8.376972
## Shibata -8.413353
## Hannan-Quinn -8.399721
##
## $garch21n
##
## Akaike -8.349159
## Bayes -8.309243
## Shibata -8.349273
## Hannan-Quinn -8.334267
##
## $garch21t
##
## Akaike -8.409607
## Bayes -8.366062
## Shibata -8.409741
## Hannan-Quinn -8.393361
##
## $garch21st
##
## Akaike -8.410468
## Bayes -8.363295
## Shibata -8.410626
## Hannan-Quinn -8.392868
##
## $garch21g
##
## Akaike -8.412083
## Bayes -8.368538
## Shibata -8.412217
## Hannan-Quinn -8.395837
##
## $garch21sg
##
## Akaike -8.412083
## Bayes -8.368538
## Shibata -8.412217
## Hannan-Quinn -8.395837
##
## $garch22n
##
## Akaike -8.351678
## Bayes -8.308134
## Shibata -8.351813
## Hannan-Quinn -8.335432
##
## $garch22t
##
## Akaike -8.411987
## Bayes -8.364813
## Shibata -8.412145
## Hannan-Quinn -8.394387
##
## $garch22st
##
## Akaike -8.412791
## Bayes -8.361988
## Shibata -8.412973
## Hannan-Quinn -8.393837
##
## $garch22g
##
## Akaike -8.413837
## Bayes -8.366663
## Shibata -8.413995
## Hannan-Quinn -8.396237
##
## $garch22sg
##
## Akaike -8.413837
## Bayes -8.366663
## Shibata -8.413995
## Hannan-Quinn -8.396237XAU.info.mat <- sapply(XAU.model.list5, infocriteria)
XAU.info.mat## garch11t garch11st garch11g garch11sg garch12n garch12t garch12st
## [1,] -8.410975 -8.411881 -8.413259 -8.413652 -8.347164 -8.409542 -8.410422
## [2,] -8.374687 -8.371965 -8.376972 -8.373736 -8.310877 -8.369626 -8.366877
## [3,] -8.411068 -8.411994 -8.413353 -8.413765 -8.347258 -8.409655 -8.410557
## [4,] -8.397436 -8.396989 -8.399721 -8.398760 -8.333626 -8.394649 -8.394176
## garch12g garch12sg garch21n garch21t garch21st garch21g garch21sg
## [1,] -8.413259 -8.413259 -8.349159 -8.409607 -8.410468 -8.412083 -8.412083
## [2,] -8.376972 -8.376972 -8.309243 -8.366062 -8.363295 -8.368538 -8.368538
## [3,] -8.413353 -8.413353 -8.349273 -8.409741 -8.410626 -8.412217 -8.412217
## [4,] -8.399721 -8.399721 -8.334267 -8.393361 -8.392868 -8.395837 -8.395837
## garch22n garch22t garch22st garch22g garch22sg
## [1,] -8.351678 -8.411987 -8.412791 -8.413837 -8.413837
## [2,] -8.308134 -8.364813 -8.361988 -8.366663 -8.366663
## [3,] -8.351813 -8.412145 -8.412973 -8.413995 -8.413995
## [4,] -8.335432 -8.394387 -8.393837 -8.396237 -8.396237XAU.inds <- which(XAU.info.mat == min(XAU.info.mat), arr.ind=TRUE)
model.XAU <- colnames(XAU.info.mat)[XAU.inds[,2]]
model.XAU## [1] "garch22g" "garch22sg"Lựa chọn mô hình biên phù hợp nhất cho chuỗi VNI
VNI.model.list <- list(
garch11n = VNI.garch11n.fit,
garch11t = VNI.garch11t.fit,
garch11st = VNI.garch11st.fit,
garch11g = VNI.garch11g.fit,
garch11sg = VNI.garch11sg.fit,
garch12n = VNI.garch12n.fit,
garch12t = VNI.garch12t.fit,
garch12st =VNI.garch12st.fit,
garch12g = VNI.garch12g.fit,
garch21n = VNI.garch21n.fit,
garch21t = VNI.garch21t.fit,
garch21st = VNI.garch21st.fit,
garch21g = VNI.garch21g.fit,
garch21sg = VNI.garch21sg.fit,
garch22n = VNI.garch22n.fit,
garch22t = VNI.garch22t.fit,
garch22st = VNI.garch22st.fit,
garch22g = VNI.garch22g.fit,
garch22sg = VNI.garch22sg.fit
)
VNI.model.list1 <- list(
garch11n = VNI.garch11n.fit,
garch21n = VNI.garch21n.fit,
garch21t = VNI.garch21t.fit,
garch21st = VNI.garch21st.fit,
garch21g = VNI.garch21g.fit,
garch21sg = VNI.garch21sg.fit,
garch22n = VNI.garch22n.fit,
garch22t = VNI.garch22t.fit,
garch22st = VNI.garch22st.fit,
garch22g = VNI.garch22g.fit,
garch22sg = VNI.garch22sg.fit
)
VNI.model.list3 <- list(
garch11n = VNI.garch11n.fit,
garch11t = VNI.garch11t.fit,
garch11st = VNI.garch11st.fit,
garch11g = VNI.garch11g.fit,
garch11sg = VNI.garch11sg.fit,
garch12g = VNI.garch12g.fit,
garch12sg = VNI.garch12sg.fit,
garch21n = VNI.garch21n.fit,
garch21t = VNI.garch21t.fit,
garch21st = VNI.garch21st.fit,
garch21g = VNI.garch21g.fit,
garch21sg = VNI.garch21sg.fit,
garch22n = VNI.garch22n.fit,
garch22t = VNI.garch22t.fit,
garch22st = VNI.garch22st.fit,
garch22g = VNI.garch22g.fit,
garch22sg = VNI.garch22sg.fit
)
results15 <- lapply(VNI.model.list, function(model) {
tryCatch({
print(infocriteria(model))
}, error = function(e) {
message("Lỗi khi xử lý mô hình: ", e$message)
return(NULL) # Hoặc giá trị mặc định khác
})
})##
## Akaike -7.711787
## Bayes -7.679128
## Shibata -7.711862
## Hannan-Quinn -7.699602## Warning in log(log(nObs)): NaNs produced## Lỗi khi xử lý mô hình: replacement has length zero## Warning in log(log(nObs)): NaNs produced## Lỗi khi xử lý mô hình: replacement has length zero## Warning in log(log(nObs)): NaNs produced## Lỗi khi xử lý mô hình: replacement has length zero## Warning in log(log(nObs)): NaNs produced## Lỗi khi xử lý mô hình: replacement has length zero## Warning in log(log(nObs)): NaNs produced## Lỗi khi xử lý mô hình: replacement has length zero## Warning in log(log(nObs)): NaNs produced## Lỗi khi xử lý mô hình: replacement has length zero## Warning in log(log(nObs)): NaNs produced## Lỗi khi xử lý mô hình: replacement has length zero## Warning in log(log(nObs)): NaNs produced## Lỗi khi xử lý mô hình: replacement has length zero##
## Akaike -7.713945
## Bayes -7.674029
## Shibata -7.714058
## Hannan-Quinn -7.699053
##
## Akaike -7.856204
## Bayes -7.812659
## Shibata -7.856338
## Hannan-Quinn -7.839957
##
## Akaike -7.871504
## Bayes -7.824330
## Shibata -7.871661
## Hannan-Quinn -7.853904
##
## Akaike -7.849853
## Bayes -7.806308
## Shibata -7.849987
## Hannan-Quinn -7.833607
##
## Akaike -7.865680
## Bayes -7.818506
## Shibata -7.865837
## Hannan-Quinn -7.848080
##
## Akaike -7.712566
## Bayes -7.669021
## Shibata -7.712700
## Hannan-Quinn -7.696320
##
## Akaike -7.854829
## Bayes -7.807655
## Shibata -7.854987
## Hannan-Quinn -7.837229
##
## Akaike -7.870126
## Bayes -7.819323
## Shibata -7.870308
## Hannan-Quinn -7.851172
##
## Akaike -7.848475
## Bayes -7.801301
## Shibata -7.848633
## Hannan-Quinn -7.830875
##
## Akaike -7.864317
## Bayes -7.813514
## Shibata -7.864499
## Hannan-Quinn -7.845363print(results15)## $garch11n
##
## Akaike -7.711787
## Bayes -7.679128
## Shibata -7.711862
## Hannan-Quinn -7.699602
##
## $garch11t
## NULL
##
## $garch11st
## NULL
##
## $garch11g
## NULL
##
## $garch11sg
## NULL
##
## $garch12n
## NULL
##
## $garch12t
## NULL
##
## $garch12st
## NULL
##
## $garch12g
## NULL
##
## $garch21n
##
## Akaike -7.713945
## Bayes -7.674029
## Shibata -7.714058
## Hannan-Quinn -7.699053
##
## $garch21t
##
## Akaike -7.856204
## Bayes -7.812659
## Shibata -7.856338
## Hannan-Quinn -7.839957
##
## $garch21st
##
## Akaike -7.871504
## Bayes -7.824330
## Shibata -7.871661
## Hannan-Quinn -7.853904
##
## $garch21g
##
## Akaike -7.849853
## Bayes -7.806308
## Shibata -7.849987
## Hannan-Quinn -7.833607
##
## $garch21sg
##
## Akaike -7.865680
## Bayes -7.818506
## Shibata -7.865837
## Hannan-Quinn -7.848080
##
## $garch22n
##
## Akaike -7.712566
## Bayes -7.669021
## Shibata -7.712700
## Hannan-Quinn -7.696320
##
## $garch22t
##
## Akaike -7.854829
## Bayes -7.807655
## Shibata -7.854987
## Hannan-Quinn -7.837229
##
## $garch22st
##
## Akaike -7.870126
## Bayes -7.819323
## Shibata -7.870308
## Hannan-Quinn -7.851172
##
## $garch22g
##
## Akaike -7.848475
## Bayes -7.801301
## Shibata -7.848633
## Hannan-Quinn -7.830875
##
## $garch22sg
##
## Akaike -7.864317
## Bayes -7.813514
## Shibata -7.864499
## Hannan-Quinn -7.845363VNI.info.mat <- sapply(VNI.model.list1, infocriteria)
VNI.info.mat## garch11n garch21n garch21t garch21st garch21g garch21sg garch22n
## [1,] -7.711787 -7.713945 -7.856204 -7.871504 -7.849853 -7.865680 -7.712566
## [2,] -7.679128 -7.674029 -7.812659 -7.824330 -7.806308 -7.818506 -7.669021
## [3,] -7.711862 -7.714058 -7.856338 -7.871661 -7.849987 -7.865837 -7.712700
## [4,] -7.699602 -7.699053 -7.839957 -7.853904 -7.833607 -7.848080 -7.696320
## garch22t garch22st garch22g garch22sg
## [1,] -7.854829 -7.870126 -7.848475 -7.864317
## [2,] -7.807655 -7.819323 -7.801301 -7.813514
## [3,] -7.854987 -7.870308 -7.848633 -7.864499
## [4,] -7.837229 -7.851172 -7.830875 -7.845363VNI.inds <- which(VNI.info.mat == min(VNI.info.mat), arr.ind=TRUE)
model.VNI <- colnames(VNI.info.mat)[VNI.inds[,2]]
model.VNI## [1] "garch21st"Trích xuất chuỗi phần dư u của chuỗi XAU.USD
XAU.res <- residuals(XAU.garch22sg.fit)/sigma(XAU.garch22sg.fit)
fitdist(distribution = "sged", XAU.res, control = list())## $pars
## mu sigma skew shape
## -0.0151294 0.9966367 0.9469294 1.2428468
##
## $convergence
## [1] 0
##
## $values
## [1] 2065.913 2015.530 2015.530
##
## $lagrange
## [1] 0
##
## $hessian
## [,1] [,2] [,3] [,4]
## [1,] 1978.3268 322.14833 -681.81296 -52.13820
## [2,] 322.1483 1866.93662 -83.69796 176.35211
## [3,] -681.8130 -83.69796 1127.91352 71.36227
## [4,] -52.1382 176.35211 71.36227 281.80683
##
## $ineqx0
## NULL
##
## $nfuneval
## [1] 98
##
## $outer.iter
## [1] 2
##
## $elapsed
## Time difference of 0.287292 secs
##
## $vscale
## [1] 1 1 1 1 1uXAU <- pdist(distribution = "sged", q = XAU.res, mu = -0.0151294 , sigma = 0.9966367 ,skew = 0.9469294 ,shape = 1.2428468 )Trích xuất chuỗi phần dư u của chuỗi VNI
VNI.res <- residuals(VNI.garch21st.fit)/sigma(VNI.garch21st.fit)
fitdist(distribution = "sstd", VNI.res, control = list())## $pars
## mu sigma skew shape
## -0.01023424 1.00199113 0.83094357 4.21974648
##
## $convergence
## [1] 0
##
## $values
## [1] 2118.742 1940.301 1940.301
##
## $lagrange
## [1] 0
##
## $hessian
## [,1] [,2] [,3] [,4]
## [1,] 2085.69796 442.2572 -618.26810 24.79439
## [2,] 442.25716 1902.6492 160.10368 126.22200
## [3,] -618.26810 160.1037 1367.89391 21.24677
## [4,] 24.79439 126.2220 21.24677 13.09180
##
## $ineqx0
## NULL
##
## $nfuneval
## [1] 94
##
## $outer.iter
## [1] 2
##
## $elapsed
## Time difference of 0.136323 secs
##
## $vscale
## [1] 1 1 1 1 1uVNI = pdist("sstd",VNI.res, mu =-0.01023424 , sigma = 1.00199113 , skew = 0.83094357 , shape = 4.21974648 )Các kiểm định sự phù hợp của mô hình biên
Kiểm định Anderson-Darling
library(kSamples)## Warning: package 'kSamples' was built under R version 4.3.3## Loading required package: SuppDists## Warning: package 'SuppDists' was built under R version 4.3.3##
## Attaching package: 'kSamples'## The following object is masked from 'package:goftest':
##
## ad.testlibrary(nortest)##
## Attaching package: 'nortest'## The following object is masked from 'package:kSamples':
##
## ad.test## The following objects are masked from 'package:goftest':
##
## ad.test, cvm.test#test with Anderson-Darling
library(goftest)
ad_VNI <- ad.test(uVNI)
ad_XAU <- ad.test(uXAU)
#Kiểm định Cramer-von Mises
cvm_VNI <- cvm.test(uVNI)## Warning in cvm.test(uVNI): p-value is smaller than 7.37e-10, cannot be computed
## more accuratelycvm_XAU <- cvm.test(uXAU)## Warning in cvm.test(uXAU): p-value is smaller than 7.37e-10, cannot be computed
## more accurately# Kiem dinh ks-test
ks_VNI <- ks.test(uVNI, "punif")
ks_XAU <- ks.test(uXAU, "punif")
#Trình bày kết quả
test <- data.frame(test = c('P_value VNI' ,'P_value XAU'),
AD = c(ad_VNI$p.value, ad_XAU$p.value),
CVM = c(cvm_VNI$p.value, cvm_XAU$p.value),
KS = c(ks_VNI$p.value,ks_XAU$p.value))
library(tidyverse)
library(kableExtra)
library(knitr)
print(test)## test AD CVM KS
## 1 P_value VNI 3.7e-24 7.37e-10 0.2817218
## 2 P_value XAU 3.7e-24 7.37e-10 0.9361819ƯỚC LƯỢNG THAM SỐ MÔ HÌNH COPULA
library(copula)
library(VineCopula)
# Assuming uXAU and uVNI are already uniform margins
# Copula selection
selectedCopula <- BiCopSelect(uXAU, uVNI, familyset = 1:9, selectioncrit="AIC", indeptest = FALSE, level = 0.05)
gau <- BiCopEst(uXAU,uVNI,family = 1, method = "mle", se = T, max.df = 10)
stu <- BiCopEst(uXAU,uVNI,family = 2, method = "mle", se = T, max.df = 10)
# Copula estimation
copulaFit <- BiCopEst(uXAU, uVNI, family = selectedCopula$family, method = "mle", se = T, max.df = 10)
# Summary of the fitted copula
summary(copulaFit)## Family
## ------
## No: 34
## Name: Rotated Gumbel 270 degrees
##
## Parameter(s)
## ------------
## par: -1.04 (SE = 0.02)
##
## Dependence measures
## -------------------
## Kendall's tau: -0.04 (empirical = -0.03, p value = 0.07)
## Upper TD: 0
## Lower TD: 0
##
## Fit statistics
## --------------
## logLik: 5.28
## AIC: -8.55
## BIC: -3.27Kết quả mô hình ARMA(2,2)-GJR-Garch(2,2)-Sged của biến XAU
library(tidyverse)
XAU.garch22sg.fit ##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,2)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000176 0.000089 1.964712 0.049448
## ar1 0.207003 0.011185 18.507388 0.000000
## ar2 -0.953014 0.011582 -82.281821 0.000000
## ma1 -0.212996 0.014477 -14.712881 0.000000
## ma2 0.922289 0.014694 62.765824 0.000000
## omega 0.000001 0.000002 0.340910 0.733171
## alpha1 0.000155 0.020936 0.007419 0.994080
## alpha2 0.153430 0.048280 3.177906 0.001483
## beta1 0.220285 0.033345 6.606197 0.000000
## beta2 0.638611 0.118717 5.379260 0.000000
## gamma1 0.015488 0.038456 0.402747 0.687134
## gamma2 -0.114706 0.016169 -7.094165 0.000000
## shape 1.236551 0.054940 22.507188 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000176 0.000136 1.288739 0.19749
## ar1 0.207003 0.011916 17.372548 0.00000
## ar2 -0.953014 0.005610 -169.875363 0.00000
## ma1 -0.212996 0.007621 -27.949488 0.00000
## ma2 0.922289 0.017379 53.068179 0.00000
## omega 0.000001 0.000039 0.016332 0.98697
## alpha1 0.000155 0.530460 0.000293 0.99977
## alpha2 0.153430 1.333935 0.115020 0.90843
## beta1 0.220285 2.872393 0.076690 0.93887
## beta2 0.638611 1.384399 0.461291 0.64459
## gamma1 0.015488 0.040636 0.381142 0.70310
## gamma2 -0.114706 0.934143 -0.122793 0.90227
## shape 1.236551 1.712930 0.721892 0.47036
##
## LogLikelihood : 6138.273
##
## Information Criteria
## ------------------------------------
##
## Akaike -8.4138
## Bayes -8.3667
## Shibata -8.4140
## Hannan-Quinn -8.3962
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.978 0.1596
## Lag[2*(p+q)+(p+q)-1][11] 4.940 0.9671
## Lag[4*(p+q)+(p+q)-1][19] 7.643 0.8408
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.4038 0.5251
## Lag[2*(p+q)+(p+q)-1][11] 2.0484 0.9573
## Lag[4*(p+q)+(p+q)-1][19] 3.2080 0.9929
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 0.01649 0.500 2.000 0.8978
## ARCH Lag[7] 0.59250 1.473 1.746 0.8720
## ARCH Lag[9] 0.67022 2.402 1.619 0.9698
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 331.5984
## Individual Statistics:
## mu 0.15888
## ar1 0.08463
## ar2 0.27350
## ma1 0.07843
## ma2 0.37258
## omega 60.58513
## alpha1 0.27723
## alpha2 0.19546
## beta1 0.29713
## beta2 0.31509
## gamma1 0.30901
## gamma2 0.19094
## shape 0.09036
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.4359 0.1512
## Negative Sign Bias 0.9581 0.3382
## Positive Sign Bias 1.0120 0.3117
## Joint Effect 2.3314 0.5065
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 32.54 0.02712
## 2 30 32.21 0.31055
## 3 40 47.85 0.15653
## 4 50 45.99 0.59583
##
##
## Elapsed time : 4.584688library(knitr)
library(kableExtra)
#Trình bày kết quả
extract_garch_results <- function(fit) {
coef <- coef(fit)
se <- fit@fit$se.coef
pvalues <- 2 * (1 - pnorm(abs(fit@fit$tval))) # tính giá trị p từ giá trị t
results <- cbind(coef, se, pvalues)
colnames(results) <- c("Estimate", "Std. Error", "Pr(>|z|)")
return(results)
}
fit1 <- extract_garch_results(XAU.garch22sg.fit)
print(fit1)## Estimate Std. Error Pr(>|z|)
## mu 1.755142e-04 8.933332e-05 4.944762e-02
## ar1 2.070034e-01 1.118490e-02 0.000000e+00
## ar2 -9.530136e-01 1.158231e-02 0.000000e+00
## ma1 -2.129959e-01 1.447683e-02 0.000000e+00
## ma2 9.222895e-01 1.469413e-02 0.000000e+00
## omega 6.312975e-07 1.851799e-06 7.331710e-01
## alpha1 1.553254e-04 2.093577e-02 9.940804e-01
## alpha2 1.534296e-01 4.828010e-02 1.483426e-03
## beta1 2.202849e-01 3.334519e-02 3.943201e-11
## beta2 6.386107e-01 1.187172e-01 7.479253e-08
## gamma1 1.548803e-02 3.845598e-02 6.871344e-01
## gamma2 -1.147063e-01 1.616911e-02 1.301403e-12
## shape 1.236551e+00 5.494025e-02 0.000000e+00Kết quả mô hình ARMA(2,2)-GJR-Garch(2,1)-Skewed Student của biến VNI
library(tidyverse)
VNI.garch21st.fit##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(2,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000001 0.000003 -0.51472 0.606752
## ar1 -0.362262 0.028740 -12.60457 0.000000
## ar2 0.044761 0.026312 1.70120 0.088906
## ma1 -0.578157 0.000300 -1928.55203 0.000000
## ma2 -0.390991 0.000308 -1270.06883 0.000000
## omega 0.000001 0.000001 0.91168 0.361939
## alpha1 0.006296 0.043457 0.14487 0.884815
## alpha2 0.022793 0.045159 0.50473 0.613749
## beta1 0.868603 0.027155 31.98644 0.000000
## gamma1 0.346620 0.101967 3.39932 0.000676
## gamma2 -0.203859 0.094163 -2.16495 0.030392
## skew 0.836313 0.034724 24.08480 0.000000
## shape 4.209347 0.515075 8.17230 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000001 0.000006 -0.25006 0.802543
## ar1 -0.362262 0.034282 -10.56721 0.000000
## ar2 0.044761 0.038621 1.15899 0.246462
## ma1 -0.578157 0.000426 -1357.75075 0.000000
## ma2 -0.390991 0.000417 -938.33901 0.000000
## omega 0.000001 0.000009 0.11471 0.908674
## alpha1 0.006296 0.056090 0.11224 0.910633
## alpha2 0.022793 0.078918 0.28882 0.772722
## beta1 0.868603 0.164887 5.26787 0.000000
## gamma1 0.346620 0.133192 2.60240 0.009257
## gamma2 -0.203859 0.128610 -1.58509 0.112945
## skew 0.836313 0.117135 7.13973 0.000000
## shape 4.209347 1.360548 3.09386 0.001976
##
## LogLikelihood : 5743.455
##
## Information Criteria
## ------------------------------------
##
## Akaike -7.8715
## Bayes -7.8243
## Shibata -7.8717
## Hannan-Quinn -7.8539
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8657 0.3522
## Lag[2*(p+q)+(p+q)-1][11] 2.4867 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 4.5237 0.9979
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.783 0.1817
## Lag[2*(p+q)+(p+q)-1][8] 2.537 0.7693
## Lag[4*(p+q)+(p+q)-1][14] 4.988 0.7710
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 0.1669 0.500 2.000 0.6829
## ARCH Lag[6] 0.3117 1.461 1.711 0.9423
## ARCH Lag[8] 1.3056 2.368 1.583 0.8749
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 111.2287
## Individual Statistics:
## mu 0.16746
## ar1 0.06632
## ar2 0.25412
## ma1 0.23761
## ma2 0.26875
## omega 22.66056
## alpha1 0.17802
## alpha2 0.16753
## beta1 0.15757
## gamma1 0.15189
## gamma2 0.12873
## skew 0.13809
## shape 0.17779
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.89 3.15 3.69
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.6148 0.10658
## Negative Sign Bias 2.0461 0.04092 **
## Positive Sign Bias 0.8177 0.41366
## Joint Effect 7.0653 0.06984 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 26.23 0.12403
## 2 30 48.74 0.01230
## 3 40 61.91 0.01121
## 4 50 73.74 0.01269
##
##
## Elapsed time : 1.352411library(knitr)
library(kableExtra)
#Trình bày kết quả
extract_garch_results <- function(fit) {
coef <- coef(fit)
se <- fit@fit$se.coef
pvalues <- 2 * (1 - pnorm(abs(fit@fit$tval))) # tính giá trị p từ giá trị t
results <- cbind(coef, se, pvalues)
colnames(results) <- c("Estimate", "Std. Error", "Pr(>|z|)")
return(results)
}
fit3 <- extract_garch_results(VNI.garch21st.fit)
print(fit3)## Estimate Std. Error Pr(>|z|)
## mu -1.440339e-06 2.798324e-06 6.067523e-01
## ar1 -3.622618e-01 2.874050e-02 0.000000e+00
## ar2 4.476143e-02 2.631170e-02 8.890561e-02
## ma1 -5.781570e-01 2.997881e-04 0.000000e+00
## ma2 -3.909914e-01 3.078506e-04 0.000000e+00
## omega 1.032747e-06 1.132800e-06 3.619391e-01
## alpha1 6.295525e-03 4.345706e-02 8.848153e-01
## alpha2 2.279288e-02 4.515859e-02 6.137488e-01
## beta1 8.686032e-01 2.715535e-02 0.000000e+00
## gamma1 3.466197e-01 1.019675e-01 6.755452e-04
## gamma2 -2.038590e-01 9.416346e-02 3.039166e-02
## skew 8.363128e-01 3.472368e-02 0.000000e+00
## shape 4.209347e+00 5.150751e-01 2.220446e-16library(copula)
library(VineCopula)
library(tidyverse)
library(kableExtra)
#Lựa chọn và ước lượng
opt_cop <- BiCopSelect(uXAU,uVNI,selectioncrit = "AIC",method = "mle")
est_opt_cop <- BiCopEst(uXAU,uXAU,family = opt_cop$family,method = "mle",max.df = 30)
#Trình bày kết quả
est_opt_cop_dt <- data.frame(mqh = c('VNI-XAU'),
Copula = est_opt_cop$familyname,
Thamso = est_opt_cop$par,
Thamso2 = est_opt_cop$par2,
duoiduoi = est_opt_cop$taildep$lower,
duoitren = est_opt_cop$taildep$upper,
tau = est_opt_cop$tau,
aic = est_opt_cop$AIC,
bic = est_opt_cop$BIC)
print(est_opt_cop_dt)## mqh Copula Thamso Thamso2 duoiduoi duoitren
## 1 VNI-XAU Rotated Gumbel 270 degrees -1.000155 0 0 0
## tau aic bic
## 1 -0.0001546443 2.527038 7.810487VẼ COPULA
library(VC2copula)
copula <- VC2copula::r270GumbelCopula(param = est_opt_cop$par)
# Sử dụng hàm persp để vẽ đồ thị 3D
persp(copula, dCopula, xlab = "u", ylab = "v", col = "lightgreen",
main = "Đồ thị PDF của mô hình r270GumbelCopula")