Copula

library(rugarch)
library(rmgarch)
library("openxlsx")
library("writexl")
library(readxl)
library(tidyverse)
library(ggExtra)
library(ggplot2)
library("EnvStats")
library(zoo)
library(ConnectednessApproach)
library(VineCopula)
library(knitr)

CẢ GIAI ĐOẠN

1. NHẬP DATA

DATA <- read_xlsx("C://Users//84896//Desktop//CN3-Copula.xlsx", sheet="DATA")
SP500 <- DATA$y
VNI <- DATA$x1
MERVAL <- DATA$x2
CROBEX <- DATA$x3
MASI <- DATA$x4
MSM30 <- DATA$x5

2. MA TRẬN HỆ SỐ TƯƠNG QUAN

cor(cbind(SP500, VNI, MERVAL, CROBEX, MASI, MSM30), method="pearson")

##            SP500       VNI    MERVAL    CROBEX      MASI     MSM30
## SP500  1.0000000 0.2383986 0.3847411 0.3401699 0.1761739 0.1782534
## VNI    0.2383986 1.0000000 0.1299821 0.2093248 0.1066150 0.2090848
## MERVAL 0.3847411 0.1299821 1.0000000 0.2246492 0.1516347 0.1155129
## CROBEX 0.3401699 0.2093248 0.2246492 1.0000000 0.2382602 0.2149749
## MASI   0.1761739 0.1066150 0.1516347 0.2382602 1.0000000 0.1713024
## MSM30  0.1782534 0.2090848 0.1155129 0.2149749 0.1713024 1.0000000

3. THIẾT LẬP MÔ HÌNH ARMA(p,q)-GARCH(r,m)

model.a10.g11.n<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "norm")
model.a10.g12.n<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "norm")
model.a10.g21.n<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "norm")
model.a10.g22.n<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "norm")
model.a11.g11.n<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "norm")
model.a11.g12.n<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "norm")
model.a11.g21.n<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "norm")
model.a11.g22.n<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "norm")
model.a21.g11.n<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "norm")
model.a21.g12.n<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "norm")
model.a21.g21.n<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "norm")
model.a21.g22.n<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "norm")
model.a12.g11.n<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "norm")
model.a12.g12.n<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "norm")
model.a12.g21.n<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "norm")
model.a12.g22.n<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "norm")
model.a22.g11.n<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "norm")
model.a22.g12.n<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "norm")
model.a22.g21.n<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "norm")
model.a22.g22.n<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "norm")
model.a20.g11.n<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "norm")
model.a20.g12.n<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "norm")
model.a20.g21.n<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "norm")
model.a20.g22.n<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "norm")
model.a02.g11.n<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "norm")
model.a02.g12.n<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "norm")
model.a02.g21.n<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "norm")
model.a02.g22.n<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "norm")
model.a10.g11.s<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "std")
model.a10.g12.s<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "std")
model.a10.g21.s<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "std")
model.a10.g22.s<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "std")
model.a11.g11.s<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "std")
model.a11.g12.s<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "std")
model.a11.g21.s<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "std")
model.a11.g22.s<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "std")
model.a21.g11.s<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "std")
model.a21.g12.s<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "std")
model.a21.g21.s<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "std")
model.a21.g22.s<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "std")
model.a12.g11.s<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "std")
model.a12.g12.s<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "std")
model.a12.g21.s<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "std")
model.a12.g22.s<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "std")
model.a22.g11.s<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "std")
model.a22.g12.s<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "std")
model.a22.g21.s<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "std")
model.a22.g22.s<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "std")
model.a20.g11.s<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "std")
model.a20.g12.s<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "std")
model.a20.g21.s<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "std")
model.a20.g22.s<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "std")
model.a02.g11.s<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "std")
model.a02.g12.s<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "std")
model.a02.g21.s<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "std")
model.a02.g22.s<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "std")
model.a10.g11.ss<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sstd")
model.a10.g12.ss<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sstd")
model.a10.g21.ss<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sstd")
model.a10.g22.ss<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sstd")
model.a11.g11.ss<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sstd")
model.a11.g12.ss<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sstd")
model.a11.g21.ss<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sstd")
model.a11.g22.ss<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sstd")
model.a21.g11.ss<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sstd")
model.a21.g12.ss<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sstd")
model.a21.g21.ss<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sstd")
model.a21.g22.ss<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sstd")
model.a12.g11.ss<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sstd")
model.a12.g12.ss<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sstd")
model.a12.g21.ss<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sstd")
model.a12.g22.ss<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sstd")
model.a22.g11.ss<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sstd")
model.a22.g12.ss<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sstd")
model.a22.g21.ss<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sstd")
model.a22.g22.ss<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sstd")
model.a20.g11.ss<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sstd")
model.a20.g12.ss<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sstd")
model.a20.g21.ss<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sstd")
model.a20.g22.ss<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sstd")
model.a02.g11.ss<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sstd")
model.a02.g12.ss<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sstd")
model.a02.g21.ss<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sstd")
model.a02.g22.ss<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sstd")
model.a10.g11.g<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "ged")
model.a10.g12.g<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "ged")
model.a10.g21.g<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "ged")
model.a10.g22.g<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "ged")
model.a11.g11.g<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "ged")
model.a11.g12.g<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "ged")
model.a11.g21.g<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "ged")
model.a11.g22.g<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "ged")
model.a21.g11.g<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "ged")
model.a21.g12.g<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "ged")
model.a21.g21.g<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "ged")
model.a21.g22.g<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "ged")
model.a12.g11.g<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "ged")
model.a12.g12.g<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "ged")
model.a12.g21.g<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "ged")
model.a12.g22.g<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "ged")
model.a22.g11.g<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "ged")
model.a22.g12.g<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "ged")
model.a22.g21.g<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "ged")
model.a22.g22.g<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "ged")
model.a20.g11.g<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "ged")
model.a20.g12.g<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "ged")
model.a20.g21.g<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "ged")
model.a20.g22.g<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "ged")
model.a02.g11.g<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "ged")
model.a02.g12.g<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "ged")
model.a02.g21.g<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "ged")
model.a02.g22.g<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "ged")
model.a10.g11.sg<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sged")
model.a10.g12.sg<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sged")
model.a10.g21.sg<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sged")
model.a10.g22.sg<-ugarchspec(mean.model = list(armaOrder = c(1,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sged")
model.a11.g11.sg<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sged")
model.a11.g12.sg<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sged")
model.a11.g21.sg<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sged")
model.a11.g22.sg<-ugarchspec(mean.model = list(armaOrder = c(1,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sged")
model.a21.g11.sg<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sged")
model.a21.g12.sg<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sged")
model.a21.g21.sg<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sged")
model.a21.g22.sg<-ugarchspec(mean.model = list(armaOrder = c(2,1)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sged")
model.a12.g11.sg<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sged")
model.a12.g12.sg<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sged")
model.a12.g21.sg<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sged")
model.a12.g22.sg<-ugarchspec(mean.model = list(armaOrder = c(1,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sged")
model.a22.g11.sg<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sged")
model.a22.g12.sg<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sged")
model.a22.g21.sg<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sged")
model.a22.g22.sg<-ugarchspec(mean.model = list(armaOrder = c(2,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sged")
model.a20.g11.sg<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sged")
model.a20.g12.sg<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sged")
model.a20.g21.sg<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sged")
model.a20.g22.sg<-ugarchspec(mean.model = list(armaOrder = c(2,0)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sged")
model.a02.g11.sg<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,1), model="gjrGARCH"), distribution.model = "sged")
model.a02.g12.sg<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(1,2), model="gjrGARCH"), distribution.model = "sged")
model.a02.g21.sg<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,1), model="gjrGARCH"), distribution.model = "sged")
model.a02.g22.sg<-ugarchspec(mean.model = list(armaOrder = c(0,2)),variance.model= list(garchOrder=c(2,2), model="gjrGARCH"), distribution.model = "sged")

4. MÔ HÌNH ARMA(p,q)-GARCH(r,m) của từng mô hình

4.1 VNI - GJR-GARCH - AIC

garch1.n<-ugarchfit(data=VNI,spec=model.a10.g11.n) #1
garch2.n<-ugarchfit(data=VNI,spec=model.a10.g12.n) #2
garch3.n<-ugarchfit(data=VNI,spec=model.a10.g21.n) #3
garch4.n<-ugarchfit(data=VNI,spec=model.a10.g22.n) #4
garch5.n<-ugarchfit(data=VNI,spec=model.a11.g11.n) #5
garch6.n<-ugarchfit(data=VNI,spec=model.a11.g12.n) #6
garch7.n<-ugarchfit(data=VNI,spec=model.a11.g21.n) #7
garch8.n<-ugarchfit(data=VNI,spec=model.a11.g22.n) #8
garch9.n<-ugarchfit(data=VNI,spec=model.a21.g11.n) #9
garch10.n<-ugarchfit(data=VNI,spec=model.a21.g12.n) #10
garch11.n<-ugarchfit(data=VNI,spec=model.a21.g21.n) #11
garch12.n<-ugarchfit(data=VNI,spec=model.a21.g22.n) #12
garch13.n<-ugarchfit(data=VNI,spec=model.a12.g11.n) #13
garch14.n<-ugarchfit(data=VNI,spec=model.a12.g12.n) #14
garch15.n<-ugarchfit(data=VNI,spec=model.a12.g21.n) #15
garch16.n<-ugarchfit(data=VNI,spec=model.a12.g22.n) #16
garch17.n<-ugarchfit(data=VNI,spec=model.a22.g11.n) #17
garch18.n<-ugarchfit(data=VNI,spec=model.a22.g12.n) #18
garch19.n<-ugarchfit(data=VNI,spec=model.a22.g21.n) #19
garch20.n<-ugarchfit(data=VNI,spec=model.a22.g22.n) #20
garch21.n<-ugarchfit(data=VNI,spec=model.a20.g11.n) #21
garch22.n<-ugarchfit(data=VNI,spec=model.a20.g12.n) #22
garch23.n<-ugarchfit(data=VNI,spec=model.a20.g21.n) #23
garch24.n<-ugarchfit(data=VNI,spec=model.a20.g22.n) #24
garch25.n<-ugarchfit(data=VNI,spec=model.a02.g11.n) #25
garch26.n<-ugarchfit(data=VNI,spec=model.a02.g12.n) #26
garch27.n<-ugarchfit(data=VNI,spec=model.a02.g21.n) #27
garch28.n<-ugarchfit(data=VNI,spec=model.a02.g22.n) #28
garch1.s<-ugarchfit(data=VNI,spec=model.a10.g11.s) #29
garch2.s<-ugarchfit(data=VNI,spec=model.a10.g12.s) #30
garch3.s<-ugarchfit(data=VNI,spec=model.a10.g21.s) #31
garch4.s<-ugarchfit(data=VNI,spec=model.a10.g22.s) #32
garch5.s<-ugarchfit(data=VNI,spec=model.a11.g11.s) #33
garch6.s<-ugarchfit(data=VNI,spec=model.a11.g12.s) #34
garch7.s<-ugarchfit(data=VNI,spec=model.a11.g21.s) #35
garch8.s<-ugarchfit(data=VNI,spec=model.a11.g22.s) #36
garch9.s<-ugarchfit(data=VNI,spec=model.a21.g11.s) #37
garch10.s<-ugarchfit(data=VNI,spec=model.a21.g12.s) #38
garch11.s<-ugarchfit(data=VNI,spec=model.a21.g21.s) #39
garch12.s<-ugarchfit(data=VNI,spec=model.a21.g22.s) #40
garch13.s<-ugarchfit(data=VNI,spec=model.a12.g11.s) #41
garch14.s<-ugarchfit(data=VNI,spec=model.a12.g12.s) #42
garch15.s<-ugarchfit(data=VNI,spec=model.a12.g21.s) #43
garch16.s<-ugarchfit(data=VNI,spec=model.a12.g22.s) #44
garch17.s<-ugarchfit(data=VNI,spec=model.a22.g11.s) #45
garch18.s<-ugarchfit(data=VNI,spec=model.a22.g12.s) #46
garch19.s<-ugarchfit(data=VNI,spec=model.a22.g21.s) #47
garch20.s<-ugarchfit(data=VNI,spec=model.a22.g22.s) #48
garch21.s<-ugarchfit(data=VNI,spec=model.a20.g11.s) #49
garch22.s<-ugarchfit(data=VNI,spec=model.a20.g12.s) #50
garch23.s<-ugarchfit(data=VNI,spec=model.a20.g21.s) #51
garch24.s<-ugarchfit(data=VNI,spec=model.a20.g22.s) #52
garch25.s<-ugarchfit(data=VNI,spec=model.a02.g11.s) #53
garch26.s<-ugarchfit(data=VNI,spec=model.a02.g12.s) #54
garch27.s<-ugarchfit(data=VNI,spec=model.a02.g21.s) #55
garch28.s<-ugarchfit(data=VNI,spec=model.a02.g22.s) #56
garch1.ss<-ugarchfit(data=VNI,spec=model.a10.g11.ss) #57
garch2.ss<-ugarchfit(data=VNI,spec=model.a10.g12.ss) #58
garch3.ss<-ugarchfit(data=VNI,spec=model.a10.g21.ss) #59
garch4.ss<-ugarchfit(data=VNI,spec=model.a10.g22.ss) #60
garch5.ss<-ugarchfit(data=VNI,spec=model.a11.g11.ss) #61
garch6.ss<-ugarchfit(data=VNI,spec=model.a11.g12.ss) #62
garch7.ss<-ugarchfit(data=VNI,spec=model.a11.g21.ss) #63
garch8.ss<-ugarchfit(data=VNI,spec=model.a11.g22.ss) #64
garch9.ss<-ugarchfit(data=VNI,spec=model.a21.g11.ss) #65
garch10.ss<-ugarchfit(data=VNI,spec=model.a21.g12.ss) #66
garch11.ss<-ugarchfit(data=VNI,spec=model.a21.g21.ss) #67
garch12.ss<-ugarchfit(data=VNI,spec=model.a21.g22.ss) #68
garch13.ss<-ugarchfit(data=VNI,spec=model.a12.g11.ss) #69
garch14.ss<-ugarchfit(data=VNI,spec=model.a12.g12.ss) #70
garch15.ss<-ugarchfit(data=VNI,spec=model.a12.g21.ss) #71
garch16.ss<-ugarchfit(data=VNI,spec=model.a12.g22.ss) #72
garch17.ss<-ugarchfit(data=VNI,spec=model.a22.g11.ss) #73
garch18.ss<-ugarchfit(data=VNI,spec=model.a22.g12.ss) #74
garch19.ss<-ugarchfit(data=VNI,spec=model.a22.g21.ss) #75
garch20.ss<-ugarchfit(data=VNI,spec=model.a22.g22.ss) #76
garch21.ss<-ugarchfit(data=VNI,spec=model.a20.g11.ss) #77
garch22.ss<-ugarchfit(data=VNI,spec=model.a20.g12.ss) #78
garch23.ss<-ugarchfit(data=VNI,spec=model.a20.g21.ss) #79
garch24.ss<-ugarchfit(data=VNI,spec=model.a20.g22.ss) #80
garch25.ss<-ugarchfit(data=VNI,spec=model.a02.g11.ss) #81
garch26.ss<-ugarchfit(data=VNI,spec=model.a02.g12.ss) #82
garch27.ss<-ugarchfit(data=VNI,spec=model.a02.g21.ss) #83
garch28.ss<-ugarchfit(data=VNI,spec=model.a02.g22.ss) #84
garch1.g<-ugarchfit(data=VNI,spec=model.a10.g11.g) #85
garch2.g<-ugarchfit(data=VNI,spec=model.a10.g12.g) #86
garch3.g<-ugarchfit(data=VNI,spec=model.a10.g21.g) #87
garch4.g<-ugarchfit(data=VNI,spec=model.a10.g22.g) #88
garch5.g<-ugarchfit(data=VNI,spec=model.a11.g11.g) #89
garch6.g<-ugarchfit(data=VNI,spec=model.a11.g12.g) #90
garch7.g<-ugarchfit(data=VNI,spec=model.a11.g21.g) #91
garch8.g<-ugarchfit(data=VNI,spec=model.a11.g22.g) #92
garch9.g<-ugarchfit(data=VNI,spec=model.a21.g11.g) #93
garch10.g<-ugarchfit(data=VNI,spec=model.a21.g12.g) #94
garch11.g<-ugarchfit(data=VNI,spec=model.a21.g21.g) #95
garch12.g<-ugarchfit(data=VNI,spec=model.a21.g22.g) #96
garch13.g<-ugarchfit(data=VNI,spec=model.a12.g11.g) #97
garch14.g<-ugarchfit(data=VNI,spec=model.a12.g12.g) #98
garch15.g<-ugarchfit(data=VNI,spec=model.a12.g21.g) #99
garch16.g<-ugarchfit(data=VNI,spec=model.a12.g22.g) #100
garch17.g<-ugarchfit(data=VNI,spec=model.a22.g11.g) #101
garch18.g<-ugarchfit(data=VNI,spec=model.a22.g12.g) #102
garch19.g<-ugarchfit(data=VNI,spec=model.a22.g21.g) #103
garch20.g<-ugarchfit(data=VNI,spec=model.a22.g22.g) #104
garch21.g<-ugarchfit(data=VNI,spec=model.a20.g11.g) #105
garch22.g<-ugarchfit(data=VNI,spec=model.a20.g12.g) #106
garch23.g<-ugarchfit(data=VNI,spec=model.a20.g21.g) #107
garch24.g<-ugarchfit(data=VNI,spec=model.a20.g22.g) #108
garch25.g<-ugarchfit(data=VNI,spec=model.a02.g11.g) #109
garch26.g<-ugarchfit(data=VNI,spec=model.a02.g12.g) #110
garch27.g<-ugarchfit(data=VNI,spec=model.a02.g21.g) #111
garch28.g<-ugarchfit(data=VNI,spec=model.a02.g22.g) #112
garch1.sg<-ugarchfit(data=VNI,spec=model.a10.g11.sg) #113
garch2.sg<-ugarchfit(data=VNI,spec=model.a10.g12.sg) #114
garch3.sg<-ugarchfit(data=VNI,spec=model.a10.g21.sg) #115
garch4.sg<-ugarchfit(data=VNI,spec=model.a10.g22.sg) #116
garch5.sg<-ugarchfit(data=VNI,spec=model.a11.g11.sg) #117
garch6.sg<-ugarchfit(data=VNI,spec=model.a11.g12.sg) #118
garch7.sg<-ugarchfit(data=VNI,spec=model.a11.g21.sg) #119
garch8.sg<-ugarchfit(data=VNI,spec=model.a11.g22.sg) #120
garch9.sg<-ugarchfit(data=VNI,spec=model.a21.g11.sg) #121
garch10.sg<-ugarchfit(data=VNI,spec=model.a21.g12.sg) #122
garch11.sg<-ugarchfit(data=VNI,spec=model.a21.g21.sg) #123
garch12.sg<-ugarchfit(data=VNI,spec=model.a21.g22.sg) #124
garch13.sg<-ugarchfit(data=VNI,spec=model.a12.g11.sg) #125
garch14.sg<-ugarchfit(data=VNI,spec=model.a12.g12.sg) #126
garch15.sg<-ugarchfit(data=VNI,spec=model.a12.g21.sg) #127
garch16.sg<-ugarchfit(data=VNI,spec=model.a12.g22.sg) #128
garch17.sg<-ugarchfit(data=VNI,spec=model.a22.g11.sg) #129
garch18.sg<-ugarchfit(data=VNI,spec=model.a22.g12.sg) #130
garch19.sg<-ugarchfit(data=VNI,spec=model.a22.g21.sg) #131
garch20.sg<-ugarchfit(data=VNI,spec=model.a22.g22.sg) #132
garch21.sg<-ugarchfit(data=VNI,spec=model.a20.g11.sg) #133
garch22.sg<-ugarchfit(data=VNI,spec=model.a20.g12.sg) #134
garch23.sg<-ugarchfit(data=VNI,spec=model.a20.g21.sg) #135
garch24.sg<-ugarchfit(data=VNI,spec=model.a20.g22.sg) #136
garch25.sg<-ugarchfit(data=VNI,spec=model.a02.g11.sg) #137
garch26.sg<-ugarchfit(data=VNI,spec=model.a02.g12.sg) #138
garch27.sg<-ugarchfit(data=VNI,spec=model.a02.g21.sg) #139
garch28.sg<-ugarchfit(data=VNI,spec=model.a02.g22.sg) #140

model.aic.list <- list(garch1.n, garch1.s, garch1.ss, garch1.g, garch1.sg, garch2.n, garch2.s, garch2.ss, garch2.g, garch2.sg, garch3.n, garch3.s, garch3.ss, garch3.g, garch3.sg, garch4.n, garch4.s, garch4.ss, garch4.g, garch4.sg, garch5.n, garch5.s, garch5.ss, garch5.g, garch5.sg, garch6.n, garch6.s, garch6.ss, garch6.g, garch6.sg, garch7.n, garch7.s, garch7.ss, garch7.g, garch7.sg, garch8.n, garch8.s, garch8.ss, garch8.g, garch8.sg, garch9.n, garch9.s, garch9.ss, garch9.g, garch9.sg, garch10.n, garch10.s, garch10.ss, garch10.g, garch10.sg, garch11.n, garch11.s, garch11.ss, garch11.g, garch11.sg, garch12.n, garch12.s, garch12.ss, garch12.g, garch12.sg, garch13.n, garch13.s, garch13.ss, garch13.g, garch13.sg, garch14.n, garch14.s, garch14.ss, garch14.g, garch14.sg, garch15.n, garch15.s, garch15.ss, garch15.g, garch15.sg, garch16.n, garch16.s, garch16.ss, garch16.g, garch16.sg, garch17.n, garch17.s, garch17.ss, garch17.g, garch17.sg, garch18.n, garch18.s, garch18.ss, garch18.g, garch18.sg, garch19.n, garch19.s, garch19.ss, garch19.g, garch19.sg, garch20.n, garch20.s, garch20.ss, garch20.g, garch20.sg, garch21.n, garch21.s, garch21.ss, garch21.g, garch21.sg, garch22.n, garch22.s, garch22.ss, garch22.g, garch22.sg, garch23.n, garch23.s, garch23.ss, garch23.g, garch23.sg, garch24.n, garch24.s, garch24.ss, garch24.g, garch24.sg, garch25.n, garch25.s, garch25.ss, garch25.g, garch25.sg, garch26.n, garch26.s, garch26.ss, garch26.g, garch26.sg, garch27.n, garch27.s, garch27.ss, garch27.g, garch27.sg, garch28.n, garch28.s, garch28.ss, garch28.g, garch28.sg)
model.aic <- sapply(model.aic.list, infocriteria)[-4,][-3,]
min(model.aic[1,])

## [1] 3.28044

model.aic 

##          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
## [1,] 3.468580 3.290951 3.285436 3.291638 3.283325 3.469512 3.292054 3.286521
## [2,] 3.487914 3.313507 3.311214 3.314194 3.309103 3.492067 3.317832 3.315521
##          [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16]
## [1,] 3.292697 3.284335 3.461580 3.289263 3.283341 3.289612 3.280755 3.462767
## [2,] 3.318475 3.313336 3.487358 3.318264 3.315563 3.318612 3.312978 3.491767
##         [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24]
## [1,] 3.290450 3.284528 3.290799 3.281946 3.468326 3.291953 3.286126 3.292764
## [2,] 3.322673 3.319973 3.323021 3.317391 3.490882 3.317731 3.315126 3.318542
##         [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32]
## [1,] 3.284522 3.469250 3.293054 3.287206 3.293822 3.285181 3.461707 3.290432
## [2,] 3.313522 3.495028 3.322054 3.319428 3.322822 3.317404 3.490708 3.322655
##         [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40]
## [1,] 3.284423 3.290814 3.281906 3.462894 3.291619 3.285610 3.291975 3.283116
## [2,] 3.319868 3.323037 3.317350 3.495117 3.327064 3.324277 3.327420 3.321784
##         [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48]
## [1,] 3.468008 3.292296 3.286809 3.292567 3.284953 3.469195 3.293483 3.287996
## [2,] 3.493786 3.321296 3.319032 3.321567 3.317176 3.498195 3.325705 3.323441
##         [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56]
## [1,] 3.293755 3.286133 3.460887 3.290427 3.284635 3.290500 3.282448 3.462074
## [2,] 3.325977 3.321578 3.493110 3.325872 3.323303 3.325945 3.321115 3.497519
##         [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64]
## [1,] 3.291614 3.285822 3.291683 3.283635 3.468142 3.292268 3.286791 3.292518
## [2,] 3.330281 3.327712 3.330350 3.325524 3.493920 3.321268 3.319014 3.321519
##         [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72]
## [1,] 3.284937 3.469329 3.293455 3.287978 3.293705 3.286125 3.460988 3.290388
## [2,] 3.317160 3.498329 3.325678 3.323423 3.325928 3.321570 3.493211 3.325833
##         [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80]
## [1,] 3.284612 3.290437 3.282435 3.462175 3.291575 3.285799 3.291624 3.283622
## [2,] 3.323279 3.325882 3.321102 3.497620 3.330242 3.327688 3.330291 3.325512
##         [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88]
## [1,] 3.468555 3.290931 3.284798 3.286825 3.282610 3.469742 3.291147 3.285985
## [2,] 3.497555 3.323153 3.320243 3.319048 3.318055 3.501965 3.326592 3.324652
##         [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96]
## [1,] 3.288016 3.283797 3.461685 3.289538 3.282904 3.290137 3.280440 3.462872
## [2,] 3.323461 3.322465 3.497130 3.328206 3.324793 3.328804 3.322329 3.501539
##         [,97]    [,98]   [,99]   [,100]   [,101]   [,102]   [,103]   [,104]
## [1,] 3.290725 3.284091 3.29018 3.281616 3.467450 3.291831 3.286350 3.292396
## [2,] 3.332615 3.329203 3.33207 3.326728 3.490006 3.317609 3.315351 3.318174
##        [,105]   [,106]   [,107]   [,108]   [,109]   [,110]   [,111]   [,112]
## [1,] 3.284232 3.468637 3.293018 3.287537 3.293584 3.285419 3.460511 3.290135
## [2,] 3.313232 3.494415 3.322019 3.319760 3.322585 3.317642 3.489511 3.322358
##        [,113]   [,114]   [,115]   [,116]   [,117]   [,118]   [,119]   [,120]
## [1,] 3.284321 3.290447 3.281937 3.461698 3.291322 3.285508 3.291635 3.283122
## [2,] 3.319766 3.322669 3.317382 3.493921 3.326767 3.324175 3.327080 3.321790
##        [,121]   [,122]   [,123]   [,124]   [,125]   [,126]   [,127]   [,128]
## [1,] 3.467500 3.291812 3.286339 3.292395 3.284234 3.468687 3.292999 3.287526
## [2,] 3.490056 3.317590 3.315339 3.318173 3.313235 3.494465 3.321999 3.319748
##        [,129]   [,130]   [,131]   [,132]   [,133]   [,134]   [,135]   [,136]
## [1,] 3.293581 3.285421 3.460548 3.290121 3.284318 3.290451 3.281936 3.461735
## [2,] 3.322581 3.317644 3.489548 3.322344 3.319763 3.322674 3.317381 3.493958
##        [,137]   [,138]   [,139]   [,140]
## [1,] 3.291308 3.285505 3.291639 3.283123
## [2,] 3.326753 3.324172 3.327084 3.321790

garch11.g #95

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(2,1)
## Mean Model   : ARFIMA(2,0,1)
## Distribution : ged 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error    t value Pr(>|t|)
## mu      0.152824    0.010108  15.118716 0.000000
## ar1    -0.572469    0.014667 -39.030311 0.000000
## ar2     0.029208    0.008070   3.619388 0.000295
## ma1     0.578253    0.014712  39.305248 0.000000
## omega   0.150732    0.047942   3.144033 0.001666
## alpha1  0.000001    0.056416   0.000025 0.999980
## alpha2  0.072971    0.061400   1.188450 0.234656
## beta1   0.794807    0.039471  20.136558 0.000000
## gamma1  0.076046    0.070832   1.073600 0.283002
## gamma2  0.031041    0.084478   0.367447 0.713286
## shape   0.983528    0.043402  22.661053 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.152824    0.004833   31.624166 0.000000
## ar1    -0.572469    0.004978 -115.003974 0.000000
## ar2     0.029208    0.003333    8.762760 0.000000
## ma1     0.578253    0.005108  113.216349 0.000000
## omega   0.150732    0.062686    2.404559 0.016192
## alpha1  0.000001    0.066894    0.000021 0.999983
## alpha2  0.072971    0.075814    0.962498 0.335799
## beta1   0.794807    0.043566   18.243771 0.000000
## gamma1  0.076046    0.080880    0.940230 0.347100
## gamma2  0.031041    0.105406    0.294491 0.768383
## shape   0.983528    0.048580   20.245393 0.000000
## 
## LogLikelihood : -2761.246 
## 
## Information Criteria
## ------------------------------------
##                    
## Akaike       3.2905
## Bayes        3.3259
## Shibata      3.2904
## Hannan-Quinn 3.3036
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                      0.4698  0.4931
## Lag[2*(p+q)+(p+q)-1][8]     2.1952  1.0000
## Lag[4*(p+q)+(p+q)-1][14]    3.7947  0.9822
## d.o.f=3
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                       1.208  0.2718
## Lag[2*(p+q)+(p+q)-1][8]      3.888  0.5255
## Lag[4*(p+q)+(p+q)-1][14]     5.211  0.7430
## d.o.f=3
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[4] 0.0003124 0.500 2.000  0.9859
## ARCH Lag[6] 2.8254963 1.461 1.711  0.3346
## ARCH Lag[8] 3.4112747 2.368 1.583  0.4695
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  2.9607
## Individual Statistics:              
## mu     0.13647
## ar1    0.07545
## ar2    0.04714
## ma1    0.08046
## omega  0.31078
## alpha1 0.24252
## alpha2 0.12200
## beta1  0.17713
## gamma1 0.04832
## gamma2 0.04882
## shape  0.39308
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          2.49 2.75 3.27
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value    prob sig
## Sign Bias           0.2072 0.83589    
## Negative Sign Bias  0.7278 0.46681    
## Positive Sign Bias  1.7873 0.07407   *
## Joint Effect        4.8524 0.18293    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     31.57      0.03492
## 2    30     43.52      0.04076
## 3    40     58.41      0.02358
## 4    50     63.22      0.08333
## 
## 
## Elapsed time : 1.554978

4.2. SP500 - GJR-GARCH - AIC

garch1.n<-ugarchfit(data=SP500,spec=model.a10.g11.n) #1
garch2.n<-ugarchfit(data=SP500,spec=model.a10.g12.n) #2
garch3.n<-ugarchfit(data=SP500,spec=model.a10.g21.n) #3
garch4.n<-ugarchfit(data=SP500,spec=model.a10.g22.n) #4
garch5.n<-ugarchfit(data=SP500,spec=model.a11.g11.n) #5
garch6.n<-ugarchfit(data=SP500,spec=model.a11.g12.n) #6
garch7.n<-ugarchfit(data=SP500,spec=model.a11.g21.n) #7
garch8.n<-ugarchfit(data=SP500,spec=model.a11.g22.n) #8
garch9.n<-ugarchfit(data=SP500,spec=model.a21.g11.n) #9
garch10.n<-ugarchfit(data=SP500,spec=model.a21.g12.n) #10
garch11.n<-ugarchfit(data=SP500,spec=model.a21.g21.n) #11
garch12.n<-ugarchfit(data=SP500,spec=model.a21.g22.n) #12
garch13.n<-ugarchfit(data=SP500,spec=model.a12.g11.n) #13
garch14.n<-ugarchfit(data=SP500,spec=model.a12.g12.n) #14
garch15.n<-ugarchfit(data=SP500,spec=model.a12.g21.n) #15
garch16.n<-ugarchfit(data=SP500,spec=model.a12.g22.n) #16
garch17.n<-ugarchfit(data=SP500,spec=model.a22.g11.n) #17
garch18.n<-ugarchfit(data=SP500,spec=model.a22.g12.n) #18
garch19.n<-ugarchfit(data=SP500,spec=model.a22.g21.n) #19
garch20.n<-ugarchfit(data=SP500,spec=model.a22.g22.n) #20
garch21.n<-ugarchfit(data=SP500,spec=model.a20.g11.n) #21
garch22.n<-ugarchfit(data=SP500,spec=model.a20.g12.n) #22
garch23.n<-ugarchfit(data=SP500,spec=model.a20.g21.n) #23
garch24.n<-ugarchfit(data=SP500,spec=model.a20.g22.n) #24
garch25.n<-ugarchfit(data=SP500,spec=model.a02.g11.n) #25
garch26.n<-ugarchfit(data=SP500,spec=model.a02.g12.n) #26
garch27.n<-ugarchfit(data=SP500,spec=model.a02.g21.n) #27
garch28.n<-ugarchfit(data=SP500,spec=model.a02.g22.n) #28
garch1.s<-ugarchfit(data=SP500,spec=model.a10.g11.s) #29
garch2.s<-ugarchfit(data=SP500,spec=model.a10.g12.s) #30
garch3.s<-ugarchfit(data=SP500,spec=model.a10.g21.s) #31
garch4.s<-ugarchfit(data=SP500,spec=model.a10.g22.s) #32
garch5.s<-ugarchfit(data=SP500,spec=model.a11.g11.s) #33
garch6.s<-ugarchfit(data=SP500,spec=model.a11.g12.s) #34
garch7.s<-ugarchfit(data=SP500,spec=model.a11.g21.s) #35
garch8.s<-ugarchfit(data=SP500,spec=model.a11.g22.s) #36
garch9.s<-ugarchfit(data=SP500,spec=model.a21.g11.s) #37
garch10.s<-ugarchfit(data=SP500,spec=model.a21.g12.s) #38
garch11.s<-ugarchfit(data=SP500,spec=model.a21.g21.s) #39
garch12.s<-ugarchfit(data=SP500,spec=model.a21.g22.s) #40
garch13.s<-ugarchfit(data=SP500,spec=model.a12.g11.s) #41
garch14.s<-ugarchfit(data=SP500,spec=model.a12.g12.s) #42
garch15.s<-ugarchfit(data=SP500,spec=model.a12.g21.s) #43
garch16.s<-ugarchfit(data=SP500,spec=model.a12.g22.s) #44
garch17.s<-ugarchfit(data=SP500,spec=model.a22.g11.s) #45
garch18.s<-ugarchfit(data=SP500,spec=model.a22.g12.s) #46
garch19.s<-ugarchfit(data=SP500,spec=model.a22.g21.s) #47
garch20.s<-ugarchfit(data=SP500,spec=model.a22.g22.s) #48
garch21.s<-ugarchfit(data=SP500,spec=model.a20.g11.s) #49
garch22.s<-ugarchfit(data=SP500,spec=model.a20.g12.s) #50
garch23.s<-ugarchfit(data=SP500,spec=model.a20.g21.s) #51
garch24.s<-ugarchfit(data=SP500,spec=model.a20.g22.s) #52
garch25.s<-ugarchfit(data=SP500,spec=model.a02.g11.s) #53
garch26.s<-ugarchfit(data=SP500,spec=model.a02.g12.s) #54
garch27.s<-ugarchfit(data=SP500,spec=model.a02.g21.s) #55
garch28.s<-ugarchfit(data=SP500,spec=model.a02.g22.s) #56
garch1.ss<-ugarchfit(data=SP500,spec=model.a10.g11.ss) #57
garch2.ss<-ugarchfit(data=SP500,spec=model.a10.g12.ss) #58
garch3.ss<-ugarchfit(data=SP500,spec=model.a10.g21.ss) #59
garch4.ss<-ugarchfit(data=SP500,spec=model.a10.g22.ss) #60
garch5.ss<-ugarchfit(data=SP500,spec=model.a11.g11.ss) #61
garch6.ss<-ugarchfit(data=SP500,spec=model.a11.g12.ss) #62
garch7.ss<-ugarchfit(data=SP500,spec=model.a11.g21.ss) #63
garch8.ss<-ugarchfit(data=SP500,spec=model.a11.g22.ss) #64
garch9.ss<-ugarchfit(data=SP500,spec=model.a21.g11.ss) #65
garch10.ss<-ugarchfit(data=SP500,spec=model.a21.g12.ss) #66
garch11.ss<-ugarchfit(data=SP500,spec=model.a21.g21.ss) #67
garch12.ss<-ugarchfit(data=SP500,spec=model.a21.g22.ss) #68
garch13.ss<-ugarchfit(data=SP500,spec=model.a12.g11.ss) #69
garch14.ss<-ugarchfit(data=SP500,spec=model.a12.g12.ss) #70
garch15.ss<-ugarchfit(data=SP500,spec=model.a12.g21.ss) #71
garch16.ss<-ugarchfit(data=SP500,spec=model.a12.g22.ss) #72
garch17.ss<-ugarchfit(data=SP500,spec=model.a22.g11.ss) #73
garch18.ss<-ugarchfit(data=SP500,spec=model.a22.g12.ss) #74
garch19.ss<-ugarchfit(data=SP500,spec=model.a22.g21.ss) #75
garch20.ss<-ugarchfit(data=SP500,spec=model.a22.g22.ss) #76
garch21.ss<-ugarchfit(data=SP500,spec=model.a20.g11.ss) #77
garch22.ss<-ugarchfit(data=SP500,spec=model.a20.g12.ss) #78
garch23.ss<-ugarchfit(data=SP500,spec=model.a20.g21.ss) #79
garch24.ss<-ugarchfit(data=SP500,spec=model.a20.g22.ss) #80
garch25.ss<-ugarchfit(data=SP500,spec=model.a02.g11.ss) #81
garch26.ss<-ugarchfit(data=SP500,spec=model.a02.g12.ss) #82
garch27.ss<-ugarchfit(data=SP500,spec=model.a02.g21.ss) #83
garch28.ss<-ugarchfit(data=SP500,spec=model.a02.g22.ss) #84
garch1.g<-ugarchfit(data=SP500,spec=model.a10.g11.g) #85
garch2.g<-ugarchfit(data=SP500,spec=model.a10.g12.g) #86
garch3.g<-ugarchfit(data=SP500,spec=model.a10.g21.g) #87
garch4.g<-ugarchfit(data=SP500,spec=model.a10.g22.g) #88
garch5.g<-ugarchfit(data=SP500,spec=model.a11.g11.g) #89
garch6.g<-ugarchfit(data=SP500,spec=model.a11.g12.g) #90
garch7.g<-ugarchfit(data=SP500,spec=model.a11.g21.g) #91
garch8.g<-ugarchfit(data=SP500,spec=model.a11.g22.g) #92
garch9.g<-ugarchfit(data=SP500,spec=model.a21.g11.g) #93
garch10.g<-ugarchfit(data=SP500,spec=model.a21.g12.g) #94
garch11.g<-ugarchfit(data=SP500,spec=model.a21.g21.g) #95
garch12.g<-ugarchfit(data=SP500,spec=model.a21.g22.g) #96
garch13.g<-ugarchfit(data=SP500,spec=model.a12.g11.g) #97
garch14.g<-ugarchfit(data=SP500,spec=model.a12.g12.g) #98
garch15.g<-ugarchfit(data=SP500,spec=model.a12.g21.g) #99
garch16.g<-ugarchfit(data=SP500,spec=model.a12.g22.g) #100
garch17.g<-ugarchfit(data=SP500,spec=model.a22.g11.g) #101
garch18.g<-ugarchfit(data=SP500,spec=model.a22.g12.g) #102
garch19.g<-ugarchfit(data=SP500,spec=model.a22.g21.g) #103
garch20.g<-ugarchfit(data=SP500,spec=model.a22.g22.g) #104
garch21.g<-ugarchfit(data=SP500,spec=model.a20.g11.g) #105
garch22.g<-ugarchfit(data=SP500,spec=model.a20.g12.g) #106
garch23.g<-ugarchfit(data=SP500,spec=model.a20.g21.g) #107
garch24.g<-ugarchfit(data=SP500,spec=model.a20.g22.g) #108
garch25.g<-ugarchfit(data=SP500,spec=model.a02.g11.g) #109
garch26.g<-ugarchfit(data=SP500,spec=model.a02.g12.g) #110
garch27.g<-ugarchfit(data=SP500,spec=model.a02.g21.g) #111
garch28.g<-ugarchfit(data=SP500,spec=model.a02.g22.g) #112
garch1.sg<-ugarchfit(data=SP500,spec=model.a10.g11.sg) #113
garch2.sg<-ugarchfit(data=SP500,spec=model.a10.g12.sg) #114
garch3.sg<-ugarchfit(data=SP500,spec=model.a10.g21.sg) #115
garch4.sg<-ugarchfit(data=SP500,spec=model.a10.g22.sg) #116
garch5.sg<-ugarchfit(data=SP500,spec=model.a11.g11.sg) #117
garch6.sg<-ugarchfit(data=SP500,spec=model.a11.g12.sg) #118
garch7.sg<-ugarchfit(data=SP500,spec=model.a11.g21.sg) #119
garch8.sg<-ugarchfit(data=SP500,spec=model.a11.g22.sg) #120
garch9.sg<-ugarchfit(data=SP500,spec=model.a21.g11.sg) #121
garch10.sg<-ugarchfit(data=SP500,spec=model.a21.g12.sg) #122
garch11.sg<-ugarchfit(data=SP500,spec=model.a21.g21.sg) #123
garch12.sg<-ugarchfit(data=SP500,spec=model.a21.g22.sg) #124
garch13.sg<-ugarchfit(data=SP500,spec=model.a12.g11.sg) #125
garch14.sg<-ugarchfit(data=SP500,spec=model.a12.g12.sg) #126
garch15.sg<-ugarchfit(data=SP500,spec=model.a12.g21.sg) #127
garch16.sg<-ugarchfit(data=SP500,spec=model.a12.g22.sg) #128
garch17.sg<-ugarchfit(data=SP500,spec=model.a22.g11.sg) #129
garch18.sg<-ugarchfit(data=SP500,spec=model.a22.g12.sg) #130
garch19.sg<-ugarchfit(data=SP500,spec=model.a22.g21.sg) #131
garch20.sg<-ugarchfit(data=SP500,spec=model.a22.g22.sg) #132
garch21.sg<-ugarchfit(data=SP500,spec=model.a20.g11.sg) #133
garch22.sg<-ugarchfit(data=SP500,spec=model.a20.g12.sg) #134
garch23.sg<-ugarchfit(data=SP500,spec=model.a20.g21.sg) #135
garch24.sg<-ugarchfit(data=SP500,spec=model.a20.g22.sg) #136
garch25.sg<-ugarchfit(data=SP500,spec=model.a02.g11.sg) #137
garch26.sg<-ugarchfit(data=SP500,spec=model.a02.g12.sg) #138
garch27.sg<-ugarchfit(data=SP500,spec=model.a02.g21.sg) #139
garch28.sg<-ugarchfit(data=SP500,spec=model.a02.g22.sg) #140

model.aic.list <- list(garch1.n, garch1.s, garch1.ss, garch1.g, garch1.sg, garch2.n, garch2.s, garch2.ss, garch2.g, garch2.sg, garch3.n, garch3.s, garch3.ss, garch3.g, garch3.sg, garch4.n, garch4.s, garch4.ss, garch4.g, garch4.sg, garch5.n, garch5.s, garch5.ss, garch5.g, garch5.sg, garch6.n, garch6.s, garch6.ss, garch6.g, garch6.sg, garch7.n, garch7.s, garch7.ss, garch7.g, garch7.sg, garch8.n, garch8.s, garch8.ss, garch8.g, garch8.sg, garch9.n, garch9.s, garch9.ss, garch9.g, garch9.sg, garch10.n, garch10.s, garch10.ss, garch10.g, garch10.sg, garch11.n, garch11.s, garch11.ss, garch11.g, garch11.sg, garch12.n, garch12.s, garch12.ss, garch12.g, garch12.sg, garch13.n, garch13.s, garch13.ss, garch13.g, garch13.sg, garch14.n, garch14.s, garch14.ss, garch14.g, garch14.sg, garch15.n, garch15.s, garch15.ss, garch15.g, garch15.sg, garch16.n, garch16.s, garch16.ss, garch16.g, garch16.sg, garch17.n, garch17.s, garch17.ss, garch17.g, garch17.sg, garch18.n, garch18.s, garch18.ss, garch18.g, garch18.sg, garch19.n, garch19.s, garch19.ss, garch19.g, garch19.sg, garch20.n, garch20.s, garch20.ss, garch20.g, garch20.sg, garch21.n, garch21.s, garch21.ss, garch21.g, garch21.sg, garch22.n, garch22.s, garch22.ss, garch22.g, garch22.sg, garch23.n, garch23.s, garch23.ss, garch23.g, garch23.sg, garch24.n, garch24.s, garch24.ss, garch24.g, garch24.sg, garch25.n, garch25.s, garch25.ss, garch25.g, garch25.sg, garch26.n, garch26.s, garch26.ss, garch26.g, garch26.sg, garch27.n, garch27.s, garch27.ss, garch27.g, garch27.sg, garch28.n, garch28.s, garch28.ss, garch28.g, garch28.sg)
model.aic <- sapply(model.aic.list, infocriteria)[-4,][-3,]
min(model.aic[1,])

## [1] 2.800754

model.aic 

##          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
## [1,] 3.027340 2.821990 2.806293 2.855981 2.837833 3.027317 2.823261 2.807598
## [2,] 3.046674 2.844546 2.832071 2.878537 2.863611 3.049873 2.849039 2.836598
##          [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16]
## [1,] 2.857280 2.839172 3.029011 2.823122 2.806182 2.857639 2.838287 3.029665
## [2,] 2.883058 2.868173 3.054790 2.852122 2.838405 2.886639 2.870510 3.058666
##         [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24]
## [1,] 2.824309 2.805894 2.858825 2.839474 3.028413 2.823037 2.806466 2.857168
## [2,] 2.856531 2.841339 2.891048 2.874919 3.050969 2.848816 2.835467 2.882946
##         [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32]
## [1,] 2.837419 3.028359 2.824308 2.807774 2.858466 2.838755 3.030052 2.823890
## [2,] 2.866419 3.054137 2.853308 2.839996 2.887467 2.870978 3.059052 2.856113
##         [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40]
## [1,] 2.805765 2.857313 2.836806 3.030702 2.825077 2.806952 2.858500 2.837993
## [2,] 2.841210 2.889535 2.872251 3.062925 2.860522 2.845619 2.893945 2.876660
##         [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48]
## [1,] 3.029573 2.817786 2.807694 2.853314 2.838660 3.029321 2.823999 2.808881
## [2,] 3.055351 2.846786 2.839916 2.882315 2.870883 3.058321 2.856222 2.844326
##         [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56]
## [1,] 2.856293 2.839847 3.030988 2.823105 2.806806 2.855061 2.837659 3.031669
## [2,] 2.888516 2.875292 3.063211 2.858550 2.845473 2.890506 2.876326 3.067114
##         [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64]
## [1,] 2.820106 2.807993 2.856248 2.838846 3.029392 2.822732 2.800953 2.853450
## [2,] 2.858773 2.849882 2.894915 2.880735 3.055170 2.851732 2.833176 2.882451
##         [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72]
## [1,] 2.838586 3.029334 2.819105 2.802140 2.859639 2.839773 3.031000 2.818971
## [2,] 2.870809 3.058334 2.851328 2.837585 2.891862 2.875218 3.063222 2.854416
##         [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]   [,80]
## [1,] 2.800754 2.855143 2.837563 3.031680 2.820158 2.801732 2.856925 2.83875
## [2,] 2.839421 2.890588 2.876230 3.067125 2.858826 2.843622 2.895593 2.88064
##         [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88]
## [1,] 3.018165 2.818816 2.802019 2.854086 2.832413 3.014551 2.825186 2.803206
## [2,] 3.047166 2.851038 2.837464 2.886309 2.867858 3.046774 2.860631 2.841873
##         [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96]
## [1,] 2.855273 2.833600 3.015628 2.820077 2.801537 2.856481 2.832102 3.021827
## [2,] 2.890718 2.872267 3.051073 2.858744 2.843426 2.895148 2.873991 3.060494
##         [,97]    [,98]    [,99]   [,100]   [,101]   [,102]   [,103]   [,104]
## [1,] 2.821264 2.802724 2.857168 2.833289 3.028484 2.823203 2.807073 2.857294
## [2,] 2.863154 2.847836 2.899058 2.878401 3.051039 2.848981 2.836074 2.883072
##        [,105]   [,106]  [,107]   [,108]   [,109]   [,110]   [,111]   [,112]
## [1,] 2.838256 3.028300 2.82439 2.808260 2.858481 2.839443 3.029988 2.824156
## [2,] 2.867256 3.054079 2.85339 2.840483 2.887482 2.871665 3.058988 2.856379
##        [,113]   [,114]   [,115]   [,116]   [,117]   [,118]   [,119]   [,120]
## [1,] 2.806547 2.858821 2.838169 3.030645 2.825343 2.806752 2.860008 2.839356
## [2,] 2.841992 2.891044 2.873614 3.062867 2.860788 2.845419 2.895453 2.878023
##        [,121]   [,122]   [,123]   [,124]   [,125]   [,126]   [,127]   [,128]
## [1,] 3.028510 2.823159 2.806881 2.857281 2.837958 3.028322 2.824346 2.808068
## [2,] 3.051066 2.848937 2.835881 2.883059 2.866959 3.054101 2.853347 2.840291
##        [,129]   [,130]   [,131]   [,132]   [,133]   [,134]   [,135]   [,136]
## [1,] 2.858468 2.839145 3.030010 2.824072 2.806274 2.858794 2.837609 3.030666
## [2,] 2.887468 2.871368 3.059011 2.856294 2.841719 2.891017 2.873054 3.062889
##        [,137]   [,138]   [,139]   [,140]
## [1,] 2.825259 2.807461 2.859981 2.838796
## [2,] 2.860704 2.846128 2.895426 2.877464

garch17.ss #73

## 
## *---------------------------------*
## *          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      0.072625    0.018474    3.93111 0.000085
## ar1    -0.787935    0.024344  -32.36735 0.000000
## ar2     0.169096    0.024797    6.81933 0.000000
## ma1     0.707231    0.000242 2918.68150 0.000000
## ma2    -0.269857    0.001536 -175.67066 0.000000
## omega   0.036224    0.009064    3.99632 0.000064
## alpha1  0.007325    0.019290    0.37974 0.704138
## beta1   0.860156    0.021052   40.85838 0.000000
## gamma1  0.223402    0.044205    5.05378 0.000000
## skew    0.816617    0.030286   26.96335 0.000000
## shape   4.569138    0.502081    9.10040 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error   t value Pr(>|t|)
## mu      0.072625    0.018265    3.9761 0.000070
## ar1    -0.787935    0.021464  -36.7091 0.000000
## ar2     0.169096    0.021369    7.9131 0.000000
## ma1     0.707231    0.000279 2538.8851 0.000000
## ma2    -0.269857    0.000716 -377.0784 0.000000
## omega   0.036224    0.012512    2.8952 0.003789
## alpha1  0.007325    0.022117    0.3312 0.740492
## beta1   0.860156    0.029759   28.9045 0.000000
## gamma1  0.223402    0.054283    4.1155 0.000039
## skew    0.816617    0.029929   27.2852 0.000000
## shape   4.569138    0.564914    8.0882 0.000000
## 
## LogLikelihood : -2349.701 
## 
## Information Criteria
## ------------------------------------
##                    
## Akaike       2.8020
## Bayes        2.8375
## Shibata      2.8019
## Hannan-Quinn 2.8151
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                       1.519  0.2178
## Lag[2*(p+q)+(p+q)-1][11]     4.121  0.9998
## Lag[4*(p+q)+(p+q)-1][19]     7.054  0.9035
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                     0.1863  0.6660
## Lag[2*(p+q)+(p+q)-1][5]    0.5441  0.9507
## Lag[4*(p+q)+(p+q)-1][9]    0.9670  0.9876
## d.o.f=2
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[3]   0.00945 0.500 2.000  0.9226
## ARCH Lag[5]   0.17637 1.440 1.667  0.9710
## ARCH Lag[7]   0.43960 2.315 1.543  0.9835
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  5.1249
## Individual Statistics:              
## mu     1.44132
## ar1    0.06541
## ar2    0.08096
## ma1    0.07984
## ma2    0.08095
## omega  1.73739
## alpha1 2.45834
## beta1  3.08655
## gamma1 2.72127
## skew   0.24595
## shape  3.08265
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          2.49 2.75 3.27
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value    prob sig
## Sign Bias           2.2402 0.02521  **
## Negative Sign Bias  1.4315 0.15247    
## Positive Sign Bias  0.2826 0.77748    
## Joint Effect        7.9074 0.04796  **
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     29.05      0.06515
## 2    30     34.83      0.21025
## 3    40     43.97      0.26907
## 4    50     45.71      0.60721
## 
## 
## Elapsed time : 1.502003

4.3. MERVAL - GJR-GARCH - AIC

garch1.n<-ugarchfit(data=MERVAL,spec=model.a10.g11.n) #1
garch2.n<-ugarchfit(data=MERVAL,spec=model.a10.g12.n) #2
garch3.n<-ugarchfit(data=MERVAL,spec=model.a10.g21.n) #3
garch4.n<-ugarchfit(data=MERVAL,spec=model.a10.g22.n) #4
garch5.n<-ugarchfit(data=MERVAL,spec=model.a11.g11.n) #5
garch6.n<-ugarchfit(data=MERVAL,spec=model.a11.g12.n) #6
garch7.n<-ugarchfit(data=MERVAL,spec=model.a11.g21.n) #7
garch8.n<-ugarchfit(data=MERVAL,spec=model.a11.g22.n) #8
garch9.n<-ugarchfit(data=MERVAL,spec=model.a21.g11.n) #9
garch10.n<-ugarchfit(data=MERVAL,spec=model.a21.g12.n) #10
garch11.n<-ugarchfit(data=MERVAL,spec=model.a21.g21.n) #11
garch12.n<-ugarchfit(data=MERVAL,spec=model.a21.g22.n) #12
garch13.n<-ugarchfit(data=MERVAL,spec=model.a12.g11.n) #13
garch14.n<-ugarchfit(data=MERVAL,spec=model.a12.g12.n) #14
garch15.n<-ugarchfit(data=MERVAL,spec=model.a12.g21.n) #15
garch16.n<-ugarchfit(data=MERVAL,spec=model.a12.g22.n) #16
garch17.n<-ugarchfit(data=MERVAL,spec=model.a22.g11.n) #17
garch18.n<-ugarchfit(data=MERVAL,spec=model.a22.g12.n) #18
garch19.n<-ugarchfit(data=MERVAL,spec=model.a22.g21.n) #19
garch20.n<-ugarchfit(data=MERVAL,spec=model.a22.g22.n) #20
garch21.n<-ugarchfit(data=MERVAL,spec=model.a20.g11.n) #21
garch22.n<-ugarchfit(data=MERVAL,spec=model.a20.g12.n) #22
garch23.n<-ugarchfit(data=MERVAL,spec=model.a20.g21.n) #23
garch24.n<-ugarchfit(data=MERVAL,spec=model.a20.g22.n) #24
garch25.n<-ugarchfit(data=MERVAL,spec=model.a02.g11.n) #25
garch26.n<-ugarchfit(data=MERVAL,spec=model.a02.g12.n) #26
garch27.n<-ugarchfit(data=MERVAL,spec=model.a02.g21.n) #27
garch28.n<-ugarchfit(data=MERVAL,spec=model.a02.g22.n) #28
garch1.s<-ugarchfit(data=MERVAL,spec=model.a10.g11.s) #29
garch2.s<-ugarchfit(data=MERVAL,spec=model.a10.g12.s) #30
garch3.s<-ugarchfit(data=MERVAL,spec=model.a10.g21.s) #31
garch4.s<-ugarchfit(data=MERVAL,spec=model.a10.g22.s) #32
garch5.s<-ugarchfit(data=MERVAL,spec=model.a11.g11.s) #33
garch6.s<-ugarchfit(data=MERVAL,spec=model.a11.g12.s) #34
garch7.s<-ugarchfit(data=MERVAL,spec=model.a11.g21.s) #35
garch8.s<-ugarchfit(data=MERVAL,spec=model.a11.g22.s) #36
garch9.s<-ugarchfit(data=MERVAL,spec=model.a21.g11.s) #37
garch10.s<-ugarchfit(data=MERVAL,spec=model.a21.g12.s) #38
garch11.s<-ugarchfit(data=MERVAL,spec=model.a21.g21.s) #39
garch12.s<-ugarchfit(data=MERVAL,spec=model.a21.g22.s) #40
garch13.s<-ugarchfit(data=MERVAL,spec=model.a12.g11.s) #41
garch14.s<-ugarchfit(data=MERVAL,spec=model.a12.g12.s) #42
garch15.s<-ugarchfit(data=MERVAL,spec=model.a12.g21.s) #43
garch16.s<-ugarchfit(data=MERVAL,spec=model.a12.g22.s) #44
garch17.s<-ugarchfit(data=MERVAL,spec=model.a22.g11.s) #45
garch18.s<-ugarchfit(data=MERVAL,spec=model.a22.g12.s) #46
garch19.s<-ugarchfit(data=MERVAL,spec=model.a22.g21.s) #47
garch20.s<-ugarchfit(data=MERVAL,spec=model.a22.g22.s) #48
garch21.s<-ugarchfit(data=MERVAL,spec=model.a20.g11.s) #49
garch22.s<-ugarchfit(data=MERVAL,spec=model.a20.g12.s) #50
garch23.s<-ugarchfit(data=MERVAL,spec=model.a20.g21.s) #51
garch24.s<-ugarchfit(data=MERVAL,spec=model.a20.g22.s) #52
garch25.s<-ugarchfit(data=MERVAL,spec=model.a02.g11.s) #53
garch26.s<-ugarchfit(data=MERVAL,spec=model.a02.g12.s) #54
garch27.s<-ugarchfit(data=MERVAL,spec=model.a02.g21.s) #55
garch28.s<-ugarchfit(data=MERVAL,spec=model.a02.g22.s) #56
garch1.ss<-ugarchfit(data=MERVAL,spec=model.a10.g11.ss) #57
garch2.ss<-ugarchfit(data=MERVAL,spec=model.a10.g12.ss) #58
garch3.ss<-ugarchfit(data=MERVAL,spec=model.a10.g21.ss) #59
garch4.ss<-ugarchfit(data=MERVAL,spec=model.a10.g22.ss) #60
garch5.ss<-ugarchfit(data=MERVAL,spec=model.a11.g11.ss) #61
garch6.ss<-ugarchfit(data=MERVAL,spec=model.a11.g12.ss) #62
garch7.ss<-ugarchfit(data=MERVAL,spec=model.a11.g21.ss) #63
garch8.ss<-ugarchfit(data=MERVAL,spec=model.a11.g22.ss) #64
garch9.ss<-ugarchfit(data=MERVAL,spec=model.a21.g11.ss) #65
garch10.ss<-ugarchfit(data=MERVAL,spec=model.a21.g12.ss) #66
garch11.ss<-ugarchfit(data=MERVAL,spec=model.a21.g21.ss) #67
garch12.ss<-ugarchfit(data=MERVAL,spec=model.a21.g22.ss) #68
garch13.ss<-ugarchfit(data=MERVAL,spec=model.a12.g11.ss) #69
garch14.ss<-ugarchfit(data=MERVAL,spec=model.a12.g12.ss) #70
garch15.ss<-ugarchfit(data=MERVAL,spec=model.a12.g21.ss) #71
garch16.ss<-ugarchfit(data=MERVAL,spec=model.a12.g22.ss) #72
garch17.ss<-ugarchfit(data=MERVAL,spec=model.a22.g11.ss) #73
garch18.ss<-ugarchfit(data=MERVAL,spec=model.a22.g12.ss) #74
garch19.ss<-ugarchfit(data=MERVAL,spec=model.a22.g21.ss) #75
garch20.ss<-ugarchfit(data=MERVAL,spec=model.a22.g22.ss) #76
garch21.ss<-ugarchfit(data=MERVAL,spec=model.a20.g11.ss) #77
garch22.ss<-ugarchfit(data=MERVAL,spec=model.a20.g12.ss) #78
garch23.ss<-ugarchfit(data=MERVAL,spec=model.a20.g21.ss) #79
garch24.ss<-ugarchfit(data=MERVAL,spec=model.a20.g22.ss) #80
garch25.ss<-ugarchfit(data=MERVAL,spec=model.a02.g11.ss) #81
garch26.ss<-ugarchfit(data=MERVAL,spec=model.a02.g12.ss) #82
garch27.ss<-ugarchfit(data=MERVAL,spec=model.a02.g21.ss) #83
garch28.ss<-ugarchfit(data=MERVAL,spec=model.a02.g22.ss) #84
garch1.g<-ugarchfit(data=MERVAL,spec=model.a10.g11.g) #85
garch2.g<-ugarchfit(data=MERVAL,spec=model.a10.g12.g) #86
garch3.g<-ugarchfit(data=MERVAL,spec=model.a10.g21.g) #87
garch4.g<-ugarchfit(data=MERVAL,spec=model.a10.g22.g) #88
garch5.g<-ugarchfit(data=MERVAL,spec=model.a11.g11.g) #89
garch6.g<-ugarchfit(data=MERVAL,spec=model.a11.g12.g) #90
garch7.g<-ugarchfit(data=MERVAL,spec=model.a11.g21.g) #91
garch8.g<-ugarchfit(data=MERVAL,spec=model.a11.g22.g) #92
garch9.g<-ugarchfit(data=MERVAL,spec=model.a21.g11.g) #93
garch10.g<-ugarchfit(data=MERVAL,spec=model.a21.g12.g) #94
garch11.g<-ugarchfit(data=MERVAL,spec=model.a21.g21.g) #95
garch12.g<-ugarchfit(data=MERVAL,spec=model.a21.g22.g) #96
garch13.g<-ugarchfit(data=MERVAL,spec=model.a12.g11.g) #97
garch14.g<-ugarchfit(data=MERVAL,spec=model.a12.g12.g) #98
garch15.g<-ugarchfit(data=MERVAL,spec=model.a12.g21.g) #99
garch16.g<-ugarchfit(data=MERVAL,spec=model.a12.g22.g) #100
garch17.g<-ugarchfit(data=MERVAL,spec=model.a22.g11.g) #101
garch18.g<-ugarchfit(data=MERVAL,spec=model.a22.g12.g) #102
garch19.g<-ugarchfit(data=MERVAL,spec=model.a22.g21.g) #103
garch20.g<-ugarchfit(data=MERVAL,spec=model.a22.g22.g) #104
garch21.g<-ugarchfit(data=MERVAL,spec=model.a20.g11.g) #105
garch22.g<-ugarchfit(data=MERVAL,spec=model.a20.g12.g) #106
garch23.g<-ugarchfit(data=MERVAL,spec=model.a20.g21.g) #107
garch24.g<-ugarchfit(data=MERVAL,spec=model.a20.g22.g) #108
garch25.g<-ugarchfit(data=MERVAL,spec=model.a02.g11.g) #109
garch26.g<-ugarchfit(data=MERVAL,spec=model.a02.g12.g) #110
garch27.g<-ugarchfit(data=MERVAL,spec=model.a02.g21.g) #111
garch28.g<-ugarchfit(data=MERVAL,spec=model.a02.g22.g) #112
garch1.sg<-ugarchfit(data=MERVAL,spec=model.a10.g11.sg) #113
garch2.sg<-ugarchfit(data=MERVAL,spec=model.a10.g12.sg) #114
garch3.sg<-ugarchfit(data=MERVAL,spec=model.a10.g21.sg) #115
garch4.sg<-ugarchfit(data=MERVAL,spec=model.a10.g22.sg) #116
garch5.sg<-ugarchfit(data=MERVAL,spec=model.a11.g11.sg) #117
garch6.sg<-ugarchfit(data=MERVAL,spec=model.a11.g12.sg) #118
garch7.sg<-ugarchfit(data=MERVAL,spec=model.a11.g21.sg) #119
garch8.sg<-ugarchfit(data=MERVAL,spec=model.a11.g22.sg) #120
garch9.sg<-ugarchfit(data=MERVAL,spec=model.a21.g11.sg) #121
garch10.sg<-ugarchfit(data=MERVAL,spec=model.a21.g12.sg) #122
garch11.sg<-ugarchfit(data=MERVAL,spec=model.a21.g21.sg) #123
garch12.sg<-ugarchfit(data=MERVAL,spec=model.a21.g22.sg) #124
garch13.sg<-ugarchfit(data=MERVAL,spec=model.a12.g11.sg) #125
garch14.sg<-ugarchfit(data=MERVAL,spec=model.a12.g12.sg) #126
garch15.sg<-ugarchfit(data=MERVAL,spec=model.a12.g21.sg) #127
garch16.sg<-ugarchfit(data=MERVAL,spec=model.a12.g22.sg) #128
garch17.sg<-ugarchfit(data=MERVAL,spec=model.a22.g11.sg) #129
garch18.sg<-ugarchfit(data=MERVAL,spec=model.a22.g12.sg) #130
garch19.sg<-ugarchfit(data=MERVAL,spec=model.a22.g21.sg) #131
garch20.sg<-ugarchfit(data=MERVAL,spec=model.a22.g22.sg) #132
garch21.sg<-ugarchfit(data=MERVAL,spec=model.a20.g11.sg) #133
garch22.sg<-ugarchfit(data=MERVAL,spec=model.a20.g12.sg) #134
garch23.sg<-ugarchfit(data=MERVAL,spec=model.a20.g21.sg) #135
garch24.sg<-ugarchfit(data=MERVAL,spec=model.a20.g22.sg) #136
garch25.sg<-ugarchfit(data=MERVAL,spec=model.a02.g11.sg) #137
garch26.sg<-ugarchfit(data=MERVAL,spec=model.a02.g12.sg) #138
garch27.sg<-ugarchfit(data=MERVAL,spec=model.a02.g21.sg) #139
garch28.sg<-ugarchfit(data=MERVAL,spec=model.a02.g22.sg) #140

model.aic.list <- list(garch1.n, garch1.s, garch1.ss, garch1.g, garch1.sg, garch2.n, garch2.s, garch2.ss, garch2.g, garch2.sg, garch3.n, garch3.s, garch3.ss, garch3.g, garch3.sg, garch4.n, garch4.s, garch4.ss, garch4.g, garch4.sg, garch5.n, garch5.s, garch5.ss, garch5.g, garch5.sg, garch6.n, garch6.s, garch6.ss, garch6.g, garch6.sg, garch7.n, garch7.s, garch7.ss, garch7.g, garch7.sg, garch8.n, garch8.s, garch8.ss, garch8.g, garch8.sg, garch9.n, garch9.s, garch9.ss, garch9.g, garch9.sg, garch10.n, garch10.s, garch10.ss, garch10.g, garch10.sg, garch11.n, garch11.s, garch11.ss, garch11.g, garch11.sg, garch12.n, garch12.s, garch12.ss, garch12.g, garch12.sg, garch13.n, garch13.s, garch13.ss, garch13.g, garch13.sg, garch14.n, garch14.s, garch14.ss, garch14.g, garch14.sg, garch15.n, garch15.s, garch15.ss, garch15.g, garch15.sg, garch16.n, garch16.s, garch16.ss, garch16.g, garch16.sg, garch17.n, garch17.s, garch17.ss, garch17.g, garch17.sg, garch18.n, garch18.s, garch18.ss, garch18.g, garch18.sg, garch19.n, garch19.s, garch19.ss, garch19.g, garch19.sg, garch20.n, garch20.s, garch20.ss, garch20.g, garch20.sg, garch21.n, garch21.s, garch21.ss, garch21.g, garch21.sg, garch22.n, garch22.s, garch22.ss, garch22.g, garch22.sg, garch23.n, garch23.s, garch23.ss, garch23.g, garch23.sg, garch24.n, garch24.s, garch24.ss, garch24.g, garch24.sg, garch25.n, garch25.s, garch25.ss, garch25.g, garch25.sg, garch26.n, garch26.s, garch26.ss, garch26.g, garch26.sg, garch27.n, garch27.s, garch27.ss, garch27.g, garch27.sg, garch28.n, garch28.s, garch28.ss, garch28.g, garch28.sg)
model.aic <- sapply(model.aic.list, infocriteria)[-4,][-3,]
min(model.aic[1,])

## [1] 4.91483

model.aic 

##          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
## [1,] 5.150358 4.925687 4.926555 4.946671 4.947003 5.151604 4.925390 4.926315
## [2,] 5.169691 4.948243 4.952333 4.969227 4.972781 5.174160 4.951168 4.955315
##          [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]   [,16]
## [1,] 4.947271 4.947656 5.144403 4.916753 4.917925 4.941888 4.942503 5.14559
## [2,] 4.973049 4.976657 5.170181 4.945753 4.950148 4.970889 4.974726 5.17459
##         [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24]
## [1,] 4.917940 4.919112 4.943075 4.943689 5.149483 4.923898 4.924756 4.945931
## [2,] 4.950163 4.954557 4.975298 4.979134 5.172039 4.949676 4.953757 4.971710
##         [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32]
## [1,] 4.946051 5.150779 4.923626 4.924535 4.946458 4.946635 5.142225 4.914830
## [2,] 4.975052 5.176558 4.952627 4.956758 4.975458 4.978857 5.171225 4.947053
##         [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40]
## [1,] 4.915993 4.940653 4.940954 5.143412 4.916017 4.917180 4.941840 4.942142
## [2,] 4.951438 4.972876 4.976399 5.175635 4.951462 4.955847 4.977285 4.980809
##         [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48]
## [1,] 5.150650 4.925064 4.925879 4.944924 4.944957 5.151837 4.924788 4.925667
## [2,] 5.176428 4.954064 4.958102 4.973924 4.977180 5.180838 4.957010 4.961112
##         [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56]
## [1,] 4.945438 4.945545 5.142782 4.917205 4.918341 4.939446 4.939825 5.143969
## [2,] 4.977661 4.980990 5.175005 4.952650 4.957008 4.974891 4.978492 5.179414
##         [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64]
## [1,] 4.918392 4.919529 4.940633 4.941013 5.150667 4.925058 4.925874 4.944931
## [2,] 4.957059 4.961418 4.979300 4.982902 5.176446 4.954059 4.958096 4.973932
##         [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72]
## [1,] 4.944940 5.151854 4.924783 4.925662 4.945445 4.945512 5.142859 4.917222
## [2,] 4.977163 5.180855 4.957005 4.961107 4.977668 4.980957 5.175082 4.952667
##         [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]   [,80]
## [1,] 4.918359 4.939425 4.939763 5.132218 4.918409 4.919546 4.940612 4.94095
## [2,] 4.957026 4.974870 4.978430 5.167663 4.957076 4.961435 4.979279 4.98284
##         [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88]
## [1,] 5.149818 4.926231 4.927023 4.946110 4.940554 5.152269 4.925287 4.926161
## [2,] 5.178819 4.958454 4.962468 4.978333 4.975998 5.184492 4.960732 4.964828
##         [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96]
## [1,] 4.947767 4.946678 5.140492 4.917073 4.917219 4.939504 4.940905 5.152289
## [2,] 4.983212 4.985345 5.175937 4.955740 4.959109 4.978171 4.982794 5.190956
##         [,97]    [,98]    [,99]   [,100]   [,101]   [,102]   [,103]   [,104]
## [1,] 4.917274 4.919407 4.941794 4.942092 5.151389 4.926319 4.927070 4.947201
## [2,] 4.959163 4.964519 4.983683 4.987204 5.173945 4.952097 4.956071 4.972979
##        [,105]   [,106]   [,107]   [,108]   [,109]   [,110]   [,111]   [,112]
## [1,] 4.947781 5.152576 4.926005 4.926826 4.947742 4.948368 5.145179 4.917015
## [2,] 4.976782 5.178354 4.955006 4.959049 4.976742 4.980591 5.174179 4.949238
##        [,113]   [,114]   [,115]   [,116]   [,117]   [,118]   [,119]   [,120]
## [1,] 4.918149 4.941918 4.942709 5.146366 4.918202 4.919336 4.943104 4.943896
## [2,] 4.953594 4.974141 4.978154 5.178588 4.953647 4.958003 4.978549 4.982563
##        [,121]   [,122]  [,123]   [,124]   [,125]   [,126]   [,127]   [,128]
## [1,] 5.151535 4.926260 4.92701 4.947271 4.947856 5.152722 4.925944 4.926763
## [2,] 5.174091 4.952038 4.95601 4.973049 4.976857 5.178500 4.954945 4.958985
##        [,129]   [,130]   [,131]   [,132]   [,133]   [,134]   [,135]   [,136]
## [1,] 4.947813 4.948441 5.144950 4.916938 4.918068 4.942028 4.942794 5.146137
## [2,] 4.976814 4.980663 5.173951 4.949160 4.953513 4.974250 4.978239 5.178360
##        [,137]   [,138]   [,139]   [,140]
## [1,] 4.918125 4.919255 4.943215 4.943981
## [2,] 4.953570 4.957922 4.978660 4.982648

garch4.s #32

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(2,2)
## Mean Model   : ARFIMA(1,0,0)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.320383    0.057646    5.557755 0.000000
## ar1     0.008863    0.023856    0.371522 0.710249
## omega   0.063548    0.027412    2.318233 0.020437
## alpha1  0.030545    0.027287    1.119375 0.262980
## alpha2  0.000000    0.027683    0.000005 0.999996
## beta1   0.960001    0.000655 1465.638458 0.000000
## beta2   0.000000    0.001830    0.000024 0.999981
## gamma1  0.329554    0.055005    5.991360 0.000000
## gamma2 -0.313669    0.053316   -5.883231 0.000000
## shape   3.774177    0.350900   10.755691 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error     t value Pr(>|t|)
## mu      0.320383    0.058869    5.442274  0.00000
## ar1     0.008863    0.021747    0.407551  0.68360
## omega   0.063548    0.030888    2.057373  0.03965
## alpha1  0.030545    0.026252    1.163499  0.24463
## alpha2  0.000000    0.026084    0.000006  1.00000
## beta1   0.960001    0.000825 1163.792379  0.00000
## beta2   0.000000    0.000448    0.000097  0.99992
## gamma1  0.329554    0.031671   10.405639  0.00000
## gamma2 -0.313669    0.030196  -10.387804  0.00000
## shape   3.774177    0.408661    9.235478  0.00000
## 
## LogLikelihood : -4133.364 
## 
## Information Criteria
## ------------------------------------
##                    
## Akaike       4.9179
## Bayes        4.9502
## Shibata      4.9179
## Hannan-Quinn 4.9299
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic p-value
## Lag[1]                      1.537  0.2151
## Lag[2*(p+q)+(p+q)-1][2]     1.625  0.3709
## Lag[4*(p+q)+(p+q)-1][5]     4.158  0.2014
## d.o.f=1
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                      0.1079  0.7426
## Lag[2*(p+q)+(p+q)-1][11]    0.8701  0.9979
## Lag[4*(p+q)+(p+q)-1][19]    1.4264  0.9999
## d.o.f=4
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[5]    0.0492 0.500 2.000  0.8245
## ARCH Lag[7]    1.0062 1.473 1.746  0.7556
## ARCH Lag[9]    1.1398 2.402 1.619  0.9113
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  5.879
## Individual Statistics:              
## mu     0.26179
## ar1    0.12955
## omega  0.40149
## alpha1 0.18668
## alpha2 0.18996
## beta1  0.23249
## beta2  0.25701
## gamma1 0.07910
## gamma2 0.08466
## shape  0.06743
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          2.29 2.54 3.05
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value   prob sig
## Sign Bias           0.1670 0.8674    
## Negative Sign Bias  0.8071 0.4197    
## Positive Sign Bias  0.9614 0.3365    
## Joint Effect        1.5799 0.6639    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     13.15       0.8309
## 2    30     34.76       0.2126
## 3    40     37.09       0.5573
## 4    50     50.88       0.3996
## 
## 
## Elapsed time : 0.7109129

4.4. CROBEX - GJR-GARCH - AIC

garch1.n<-ugarchfit(data=CROBEX,spec=model.a10.g11.n) #1
garch2.n<-ugarchfit(data=CROBEX,spec=model.a10.g12.n) #2
garch3.n<-ugarchfit(data=CROBEX,spec=model.a10.g21.n) #3
garch4.n<-ugarchfit(data=CROBEX,spec=model.a10.g22.n) #4
garch5.n<-ugarchfit(data=CROBEX,spec=model.a11.g11.n) #5
garch6.n<-ugarchfit(data=CROBEX,spec=model.a11.g12.n) #6
garch7.n<-ugarchfit(data=CROBEX,spec=model.a11.g21.n) #7
garch8.n<-ugarchfit(data=CROBEX,spec=model.a11.g22.n) #8
garch9.n<-ugarchfit(data=CROBEX,spec=model.a21.g11.n) #9
garch10.n<-ugarchfit(data=CROBEX,spec=model.a21.g12.n) #10
garch11.n<-ugarchfit(data=CROBEX,spec=model.a21.g21.n) #11
garch12.n<-ugarchfit(data=CROBEX,spec=model.a21.g22.n) #12
garch13.n<-ugarchfit(data=CROBEX,spec=model.a12.g11.n) #13
garch14.n<-ugarchfit(data=CROBEX,spec=model.a12.g12.n) #14
garch15.n<-ugarchfit(data=CROBEX,spec=model.a12.g21.n) #15
garch16.n<-ugarchfit(data=CROBEX,spec=model.a12.g22.n) #16
garch17.n<-ugarchfit(data=CROBEX,spec=model.a22.g11.n) #17
garch18.n<-ugarchfit(data=CROBEX,spec=model.a22.g12.n) #18
garch19.n<-ugarchfit(data=CROBEX,spec=model.a22.g21.n) #19
garch20.n<-ugarchfit(data=CROBEX,spec=model.a22.g22.n) #20
garch21.n<-ugarchfit(data=CROBEX,spec=model.a20.g11.n) #21
garch22.n<-ugarchfit(data=CROBEX,spec=model.a20.g12.n) #22
garch23.n<-ugarchfit(data=CROBEX,spec=model.a20.g21.n) #23
garch24.n<-ugarchfit(data=CROBEX,spec=model.a20.g22.n) #24
garch25.n<-ugarchfit(data=CROBEX,spec=model.a02.g11.n) #25
garch26.n<-ugarchfit(data=CROBEX,spec=model.a02.g12.n) #26
garch27.n<-ugarchfit(data=CROBEX,spec=model.a02.g21.n) #27
garch28.n<-ugarchfit(data=CROBEX,spec=model.a02.g22.n) #28
garch1.s<-ugarchfit(data=CROBEX,spec=model.a10.g11.s) #29
garch2.s<-ugarchfit(data=CROBEX,spec=model.a10.g12.s) #30
garch3.s<-ugarchfit(data=CROBEX,spec=model.a10.g21.s) #31
garch4.s<-ugarchfit(data=CROBEX,spec=model.a10.g22.s) #32
garch5.s<-ugarchfit(data=CROBEX,spec=model.a11.g11.s) #33
garch6.s<-ugarchfit(data=CROBEX,spec=model.a11.g12.s) #34
garch7.s<-ugarchfit(data=CROBEX,spec=model.a11.g21.s) #35
garch8.s<-ugarchfit(data=CROBEX,spec=model.a11.g22.s) #36
garch9.s<-ugarchfit(data=CROBEX,spec=model.a21.g11.s) #37
garch10.s<-ugarchfit(data=CROBEX,spec=model.a21.g12.s) #38
garch11.s<-ugarchfit(data=CROBEX,spec=model.a21.g21.s) #39
garch12.s<-ugarchfit(data=CROBEX,spec=model.a21.g22.s) #40
garch13.s<-ugarchfit(data=CROBEX,spec=model.a12.g11.s) #41
garch14.s<-ugarchfit(data=CROBEX,spec=model.a12.g12.s) #42
garch15.s<-ugarchfit(data=CROBEX,spec=model.a12.g21.s) #43
garch16.s<-ugarchfit(data=CROBEX,spec=model.a12.g22.s) #44
garch17.s<-ugarchfit(data=CROBEX,spec=model.a22.g11.s) #45
garch18.s<-ugarchfit(data=CROBEX,spec=model.a22.g12.s) #46
garch19.s<-ugarchfit(data=CROBEX,spec=model.a22.g21.s) #47
garch20.s<-ugarchfit(data=CROBEX,spec=model.a22.g22.s) #48
garch21.s<-ugarchfit(data=CROBEX,spec=model.a20.g11.s) #49
garch22.s<-ugarchfit(data=CROBEX,spec=model.a20.g12.s) #50
garch23.s<-ugarchfit(data=CROBEX,spec=model.a20.g21.s) #51
garch24.s<-ugarchfit(data=CROBEX,spec=model.a20.g22.s) #52
garch25.s<-ugarchfit(data=CROBEX,spec=model.a02.g11.s) #53
garch26.s<-ugarchfit(data=CROBEX,spec=model.a02.g12.s) #54
garch27.s<-ugarchfit(data=CROBEX,spec=model.a02.g21.s) #55
garch28.s<-ugarchfit(data=CROBEX,spec=model.a02.g22.s) #56
garch1.ss<-ugarchfit(data=CROBEX,spec=model.a10.g11.ss) #57
garch2.ss<-ugarchfit(data=CROBEX,spec=model.a10.g12.ss) #58
garch3.ss<-ugarchfit(data=CROBEX,spec=model.a10.g21.ss) #59
garch4.ss<-ugarchfit(data=CROBEX,spec=model.a10.g22.ss) #60
garch5.ss<-ugarchfit(data=CROBEX,spec=model.a11.g11.ss) #61
garch6.ss<-ugarchfit(data=CROBEX,spec=model.a11.g12.ss) #62
garch7.ss<-ugarchfit(data=CROBEX,spec=model.a11.g21.ss) #63
garch8.ss<-ugarchfit(data=CROBEX,spec=model.a11.g22.ss) #64
garch9.ss<-ugarchfit(data=CROBEX,spec=model.a21.g11.ss) #65
garch10.ss<-ugarchfit(data=CROBEX,spec=model.a21.g12.ss) #66
garch11.ss<-ugarchfit(data=CROBEX,spec=model.a21.g21.ss) #67
garch12.ss<-ugarchfit(data=CROBEX,spec=model.a21.g22.ss) #68
garch13.ss<-ugarchfit(data=CROBEX,spec=model.a12.g11.ss) #69
garch14.ss<-ugarchfit(data=CROBEX,spec=model.a12.g12.ss) #70
garch15.ss<-ugarchfit(data=CROBEX,spec=model.a12.g21.ss) #71
garch16.ss<-ugarchfit(data=CROBEX,spec=model.a12.g22.ss) #72
garch17.ss<-ugarchfit(data=CROBEX,spec=model.a22.g11.ss) #73
garch18.ss<-ugarchfit(data=CROBEX,spec=model.a22.g12.ss) #74
garch19.ss<-ugarchfit(data=CROBEX,spec=model.a22.g21.ss) #75
garch20.ss<-ugarchfit(data=CROBEX,spec=model.a22.g22.ss) #76
garch21.ss<-ugarchfit(data=CROBEX,spec=model.a20.g11.ss) #77
garch22.ss<-ugarchfit(data=CROBEX,spec=model.a20.g12.ss) #78
garch23.ss<-ugarchfit(data=CROBEX,spec=model.a20.g21.ss) #79
garch24.ss<-ugarchfit(data=CROBEX,spec=model.a20.g22.ss) #80
garch25.ss<-ugarchfit(data=CROBEX,spec=model.a02.g11.ss) #81
garch26.ss<-ugarchfit(data=CROBEX,spec=model.a02.g12.ss) #82
garch27.ss<-ugarchfit(data=CROBEX,spec=model.a02.g21.ss) #83
garch28.ss<-ugarchfit(data=CROBEX,spec=model.a02.g22.ss) #84
garch1.g<-ugarchfit(data=CROBEX,spec=model.a10.g11.g) #85
garch2.g<-ugarchfit(data=CROBEX,spec=model.a10.g12.g) #86
garch3.g<-ugarchfit(data=CROBEX,spec=model.a10.g21.g) #87
garch4.g<-ugarchfit(data=CROBEX,spec=model.a10.g22.g) #88
garch5.g<-ugarchfit(data=CROBEX,spec=model.a11.g11.g) #89
garch6.g<-ugarchfit(data=CROBEX,spec=model.a11.g12.g) #90
garch7.g<-ugarchfit(data=CROBEX,spec=model.a11.g21.g) #91
garch8.g<-ugarchfit(data=CROBEX,spec=model.a11.g22.g) #92
garch9.g<-ugarchfit(data=CROBEX,spec=model.a21.g11.g) #93
garch10.g<-ugarchfit(data=CROBEX,spec=model.a21.g12.g) #94
garch11.g<-ugarchfit(data=CROBEX,spec=model.a21.g21.g) #95
garch12.g<-ugarchfit(data=CROBEX,spec=model.a21.g22.g) #96
garch13.g<-ugarchfit(data=CROBEX,spec=model.a12.g11.g) #97
garch14.g<-ugarchfit(data=CROBEX,spec=model.a12.g12.g) #98
garch15.g<-ugarchfit(data=CROBEX,spec=model.a12.g21.g) #99
garch16.g<-ugarchfit(data=CROBEX,spec=model.a12.g22.g) #100
garch17.g<-ugarchfit(data=CROBEX,spec=model.a22.g11.g) #101
garch18.g<-ugarchfit(data=CROBEX,spec=model.a22.g12.g) #102
garch19.g<-ugarchfit(data=CROBEX,spec=model.a22.g21.g) #103
garch20.g<-ugarchfit(data=CROBEX,spec=model.a22.g22.g) #104
garch21.g<-ugarchfit(data=CROBEX,spec=model.a20.g11.g) #105
garch22.g<-ugarchfit(data=CROBEX,spec=model.a20.g12.g) #106
garch23.g<-ugarchfit(data=CROBEX,spec=model.a20.g21.g) #107
garch24.g<-ugarchfit(data=CROBEX,spec=model.a20.g22.g) #108
garch25.g<-ugarchfit(data=CROBEX,spec=model.a02.g11.g) #109
garch26.g<-ugarchfit(data=CROBEX,spec=model.a02.g12.g) #110
garch27.g<-ugarchfit(data=CROBEX,spec=model.a02.g21.g) #111
garch28.g<-ugarchfit(data=CROBEX,spec=model.a02.g22.g) #112
garch1.sg<-ugarchfit(data=CROBEX,spec=model.a10.g11.sg) #113
garch2.sg<-ugarchfit(data=CROBEX,spec=model.a10.g12.sg) #114
garch3.sg<-ugarchfit(data=CROBEX,spec=model.a10.g21.sg) #115
garch4.sg<-ugarchfit(data=CROBEX,spec=model.a10.g22.sg) #116
garch5.sg<-ugarchfit(data=CROBEX,spec=model.a11.g11.sg) #117
garch6.sg<-ugarchfit(data=CROBEX,spec=model.a11.g12.sg) #118
garch7.sg<-ugarchfit(data=CROBEX,spec=model.a11.g21.sg) #119
garch8.sg<-ugarchfit(data=CROBEX,spec=model.a11.g22.sg) #120
garch9.sg<-ugarchfit(data=CROBEX,spec=model.a21.g11.sg) #121
garch10.sg<-ugarchfit(data=CROBEX,spec=model.a21.g12.sg) #122
garch11.sg<-ugarchfit(data=CROBEX,spec=model.a21.g21.sg) #123
garch12.sg<-ugarchfit(data=CROBEX,spec=model.a21.g22.sg) #124
garch13.sg<-ugarchfit(data=CROBEX,spec=model.a12.g11.sg) #125
garch14.sg<-ugarchfit(data=CROBEX,spec=model.a12.g12.sg) #126
garch15.sg<-ugarchfit(data=CROBEX,spec=model.a12.g21.sg) #127
garch16.sg<-ugarchfit(data=CROBEX,spec=model.a12.g22.sg) #128
garch17.sg<-ugarchfit(data=CROBEX,spec=model.a22.g11.sg) #129
garch18.sg<-ugarchfit(data=CROBEX,spec=model.a22.g12.sg) #130
garch19.sg<-ugarchfit(data=CROBEX,spec=model.a22.g21.sg) #131
garch20.sg<-ugarchfit(data=CROBEX,spec=model.a22.g22.sg) #132
garch21.sg<-ugarchfit(data=CROBEX,spec=model.a20.g11.sg) #133
garch22.sg<-ugarchfit(data=CROBEX,spec=model.a20.g12.sg) #134
garch23.sg<-ugarchfit(data=CROBEX,spec=model.a20.g21.sg) #135
garch24.sg<-ugarchfit(data=CROBEX,spec=model.a20.g22.sg) #136
garch25.sg<-ugarchfit(data=CROBEX,spec=model.a02.g11.sg) #137
garch26.sg<-ugarchfit(data=CROBEX,spec=model.a02.g12.sg) #138
garch27.sg<-ugarchfit(data=CROBEX,spec=model.a02.g21.sg) #139
garch28.sg<-ugarchfit(data=CROBEX,spec=model.a02.g22.sg) #140

model.aic.list <- list(garch1.n, garch1.s, garch1.ss, garch1.g, garch1.sg, garch2.n, garch2.s, garch2.ss, garch2.g, garch2.sg, garch3.n, garch3.s, garch3.ss, garch3.g, garch3.sg, garch4.n, garch4.s, garch4.ss, garch4.g, garch4.sg, garch5.n, garch5.s, garch5.ss, garch5.g, garch5.sg, garch6.n, garch6.s, garch6.ss, garch6.g, garch6.sg, garch7.n, garch7.s, garch7.ss, garch7.g, garch7.sg, garch8.n, garch8.s, garch8.ss, garch8.g, garch8.sg, garch9.n, garch9.s, garch9.ss, garch9.g, garch9.sg, garch10.n, garch10.s, garch10.ss, garch10.g, garch10.sg, garch11.n, garch11.s, garch11.ss, garch11.g, garch11.sg, garch12.n, garch12.s, garch12.ss, garch12.g, garch12.sg, garch13.n, garch13.s, garch13.ss, garch13.g, garch13.sg, garch14.n, garch14.s, garch14.ss, garch14.g, garch14.sg, garch15.n, garch15.s, garch15.ss, garch15.g, garch15.sg, garch16.n, garch16.s, garch16.ss, garch16.g, garch16.sg, garch17.n, garch17.s, garch17.ss, garch17.g, garch17.sg, garch18.n, garch18.s, garch18.ss, garch18.g, garch18.sg, garch19.n, garch19.s, garch19.ss, garch19.g, garch19.sg, garch20.n, garch20.s, garch20.ss, garch20.g, garch20.sg, garch21.n, garch21.s, garch21.ss, garch21.g, garch21.sg, garch22.n, garch22.s, garch22.ss, garch22.g, garch22.sg, garch23.n, garch23.s, garch23.ss, garch23.g, garch23.sg, garch24.n, garch24.s, garch24.ss, garch24.g, garch24.sg, garch25.n, garch25.s, garch25.ss, garch25.g, garch25.sg, garch26.n, garch26.s, garch26.ss, garch26.g, garch26.sg, garch27.n, garch27.s, garch27.ss, garch27.g, garch27.sg, garch28.n, garch28.s, garch28.ss, garch28.g, garch28.sg)
model.aic <- sapply(model.aic.list, infocriteria)[-4,][-3,]
min(model.aic[1,])

## [1] 1.987336

model.aic 

##          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]    [,8]
## [1,] 2.261127 1.988384 1.989112 2.012789 2.011632 2.262564 1.989637 1.99036
## [2,] 2.280460 2.010940 2.014891 2.035345 2.037410 2.285120 2.015416 2.01936
##          [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16]
## [1,] 2.014130 2.012982 2.260014 1.990391 1.991080 2.014948 2.013754 2.261201
## [2,] 2.039908 2.041982 2.285792 2.019391 2.023302 2.043949 2.045976 2.290201
##         [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24]
## [1,] 1.991578 1.992267 2.016135 2.014940 2.256198 1.987336 1.987970 2.012615
## [2,] 2.023800 2.027711 2.048358 2.050385 2.278754 2.013115 2.016971 2.038394
##         [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32]
## [1,] 2.009269 2.257627 1.988598 1.989226 2.013381 2.010619 2.256082 1.989487
## [2,] 2.038269 2.283405 2.017599 2.021449 2.042381 2.042842 2.285082 2.021710
##         [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40]
## [1,] 1.990118 2.014219 2.011485 2.257269 1.990674 1.991305 2.015998 2.012765
## [2,] 2.025563 2.046441 2.046930 2.289491 2.026119 2.029973 2.051443 2.051432
##         [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48]
## [1,] 2.257220 1.988564 1.989208 2.013926 2.010642 2.258407 1.989742 1.990379
## [2,] 2.282998 2.017565 2.021431 2.042927 2.042865 2.287407 2.021965 2.025824
##         [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56]
## [1,] 2.015111 2.011831 2.256828 1.990627 1.991256 2.015427 2.012709 2.258015
## [2,] 2.047334 2.047276 2.289050 2.026072 2.029923 2.050872 2.051376 2.293460
##         [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64]
## [1,] 1.991814 1.992443 2.016603 2.013896 2.257203 1.988541 1.989187 2.013929
## [2,] 2.030481 2.034332 2.055270 2.055785 2.282981 2.017542 2.021410 2.042929
##         [,65]   [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72]
## [1,] 2.010615 2.25839 1.989719 1.990358 2.015115 2.011827 2.256815 1.990603
## [2,] 2.042837 2.28739 2.021941 2.025803 2.047338 2.047272 2.289037 2.026048
##         [,73]    [,74]    [,75]    [,76]    [,77]   [,78]    [,79]    [,80]
## [1,] 1.991233 2.015405 2.012662 2.258002 1.991790 1.99242 2.016588 2.013870
## [2,] 2.029900 2.050850 2.051329 2.293447 2.030457 2.03431 2.055255 2.055759
##         [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88]
## [1,] 2.258805 1.989644 1.990381 2.014462 2.011856 2.257777 1.990760 1.991335
## [2,] 2.287806 2.021867 2.025826 2.046685 2.047301 2.290000 2.026205 2.030002
##         [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96]
## [1,] 2.016324 2.013014 2.257982 1.991789 1.992210 2.008392 2.013888 2.259169
## [2,] 2.051769 2.051681 2.293427 2.030456 2.034099 2.047060 2.055777 2.297836
##         [,97]    [,98]    [,99]   [,100]   [,101]   [,102]   [,103]   [,104]
## [1,] 1.992976 1.991853 2.017784 2.015086 2.261731 1.989500 1.990197 2.013808
## [2,] 2.034865 2.036964 2.059673 2.060198 2.284287 2.015279 2.019197 2.039586
##        [,105]   [,106]   [,107]   [,108]   [,109]   [,110]   [,111]   [,112]
## [1,] 2.012588 2.262918 1.990672 1.991362 2.014994 2.013775 2.260524 1.991438
## [2,] 2.041589 2.288696 2.019673 2.023584 2.043995 2.045998 2.289524 2.023661
##        [,113]   [,114]   [,115]   [,116]   [,117]   [,118]   [,119]   [,120]
## [1,] 1.992100 2.015848 2.014557 2.261711 1.992625 1.993287 2.017035 2.015744
## [2,] 2.027545 2.048071 2.050002 2.293933 2.028070 2.031954 2.052480 2.054411
##        [,121]   [,122]   [,123]   [,124]   [,125]   [,126]   [,127]   [,128]
## [1,] 2.261856 1.989523 1.990219 2.013817 2.012592 2.263042 1.990695 1.991385
## [2,] 2.284411 2.015301 2.019220 2.039595 2.041592 2.288821 2.019695 2.023607
##        [,129]   [,130]   [,131]   [,132]   [,133]   [,134]   [,135]   [,136]
## [1,] 2.015005 2.013780 2.260596 1.991459 1.992121 2.015862 2.014560 2.261783
## [2,] 2.044005 2.046003 2.289597 2.023681 2.027566 2.048085 2.050005 2.294006
##        [,137]   [,138]   [,139]   [,140]
## [1,] 1.992646 1.993308 2.017048 2.015747
## [2,] 2.028091 2.031975 2.052493 2.054415

garch22.n #22

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(1,2)
## Mean Model   : ARFIMA(2,0,0)
## Distribution : norm 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error  t value Pr(>|t|)
## mu      0.033971    0.018684   1.8182 0.069034
## ar1     0.018756    0.028714   0.6532 0.513628
## ar2     0.033345    0.028035   1.1894 0.234287
## omega   0.067211    0.012929   5.1984 0.000000
## alpha1  0.039791    0.012379   3.2142 0.001308
## beta1   0.802618    0.310806   2.5824 0.009812
## beta2   0.000000    0.262523   0.0000 1.000000
## gamma1  0.097512    0.009433  10.3378 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error  t value Pr(>|t|)
## mu      0.033971    0.021428  1.58532 0.112894
## ar1     0.018756    0.028466  0.65890 0.509960
## ar2     0.033345    0.032534  1.02492 0.305403
## omega   0.067211    0.028025  2.39826 0.016473
## alpha1  0.039791    0.039332  1.01166 0.311702
## beta1   0.802618    0.494429  1.62332 0.104520
## beta2   0.000000    0.417828  0.00000 1.000000
## gamma1  0.097512    0.098275  0.99223 0.321084
## 
## LogLikelihood : -1898.508 
## 
## Information Criteria
## ------------------------------------
##                    
## Akaike       2.2629
## Bayes        2.2887
## Shibata      2.2629
## Hannan-Quinn 2.2725
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic  p-value
## Lag[1]                     0.4092 0.522391
## Lag[2*(p+q)+(p+q)-1][5]    4.1577 0.044064
## Lag[4*(p+q)+(p+q)-1][9]   10.0225 0.009019
## d.o.f=2
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                          statistic   p-value
## Lag[1]                      0.4558 4.996e-01
## Lag[2*(p+q)+(p+q)-1][8]    35.1777 8.239e-09
## Lag[4*(p+q)+(p+q)-1][14]   61.2404 2.576e-14
## d.o.f=3
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale   P-Value
## ARCH Lag[4]    0.1899 0.500 2.000 6.630e-01
## ARCH Lag[6]   58.8238 1.461 1.711 6.883e-15
## ARCH Lag[8]   67.6487 2.368 1.583 0.000e+00
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  2.3864
## Individual Statistics:              
## mu     0.73534
## ar1    0.08326
## ar2    0.09515
## omega  0.10382
## alpha1 0.20532
## beta1  0.18268
## beta2  0.18645
## gamma1 0.15056
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          1.89 2.11 2.59
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value   prob sig
## Sign Bias           0.6755 0.4994    
## Negative Sign Bias  0.2221 0.8243    
## Positive Sign Bias  0.1158 0.9079    
## Joint Effect        0.5258 0.9132    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     220.3    3.010e-36
## 2    30     239.4    5.724e-35
## 3    40     254.4    2.072e-33
## 4    50     259.4    2.082e-30
## 
## 
## Elapsed time : 0.5723221

4.5. MASI - GJR-GARCH - AIC

garch1.n<-ugarchfit(data=MASI,spec=model.a10.g11.n) #1
garch2.n<-ugarchfit(data=MASI,spec=model.a10.g12.n) #2
garch3.n<-ugarchfit(data=MASI,spec=model.a10.g21.n) #3
garch4.n<-ugarchfit(data=MASI,spec=model.a10.g22.n) #4
garch5.n<-ugarchfit(data=MASI,spec=model.a11.g11.n) #5
garch6.n<-ugarchfit(data=MASI,spec=model.a11.g12.n) #6
garch7.n<-ugarchfit(data=MASI,spec=model.a11.g21.n) #7
garch8.n<-ugarchfit(data=MASI,spec=model.a11.g22.n) #8
garch9.n<-ugarchfit(data=MASI,spec=model.a21.g11.n) #9
garch10.n<-ugarchfit(data=MASI,spec=model.a21.g12.n) #10
garch11.n<-ugarchfit(data=MASI,spec=model.a21.g21.n) #11
garch12.n<-ugarchfit(data=MASI,spec=model.a21.g22.n) #12
garch13.n<-ugarchfit(data=MASI,spec=model.a12.g11.n) #13
garch14.n<-ugarchfit(data=MASI,spec=model.a12.g12.n) #14
garch15.n<-ugarchfit(data=MASI,spec=model.a12.g21.n) #15
garch16.n<-ugarchfit(data=MASI,spec=model.a12.g22.n) #16
garch17.n<-ugarchfit(data=MASI,spec=model.a22.g11.n) #17
garch18.n<-ugarchfit(data=MASI,spec=model.a22.g12.n) #18
garch19.n<-ugarchfit(data=MASI,spec=model.a22.g21.n) #19
garch20.n<-ugarchfit(data=MASI,spec=model.a22.g22.n) #20
garch21.n<-ugarchfit(data=MASI,spec=model.a20.g11.n) #21
garch22.n<-ugarchfit(data=MASI,spec=model.a20.g12.n) #22
garch23.n<-ugarchfit(data=MASI,spec=model.a20.g21.n) #23
garch24.n<-ugarchfit(data=MASI,spec=model.a20.g22.n) #24
garch25.n<-ugarchfit(data=MASI,spec=model.a02.g11.n) #25
garch26.n<-ugarchfit(data=MASI,spec=model.a02.g12.n) #26
garch27.n<-ugarchfit(data=MASI,spec=model.a02.g21.n) #27
garch28.n<-ugarchfit(data=MASI,spec=model.a02.g22.n) #28
garch1.s<-ugarchfit(data=MASI,spec=model.a10.g11.s) #29
garch2.s<-ugarchfit(data=MASI,spec=model.a10.g12.s) #30
garch3.s<-ugarchfit(data=MASI,spec=model.a10.g21.s) #31
garch4.s<-ugarchfit(data=MASI,spec=model.a10.g22.s) #32
garch5.s<-ugarchfit(data=MASI,spec=model.a11.g11.s) #33
garch6.s<-ugarchfit(data=MASI,spec=model.a11.g12.s) #34
garch7.s<-ugarchfit(data=MASI,spec=model.a11.g21.s) #35
garch8.s<-ugarchfit(data=MASI,spec=model.a11.g22.s) #36
garch9.s<-ugarchfit(data=MASI,spec=model.a21.g11.s) #37
garch10.s<-ugarchfit(data=MASI,spec=model.a21.g12.s) #38
garch11.s<-ugarchfit(data=MASI,spec=model.a21.g21.s) #39
garch12.s<-ugarchfit(data=MASI,spec=model.a21.g22.s) #40
garch13.s<-ugarchfit(data=MASI,spec=model.a12.g11.s) #41
garch14.s<-ugarchfit(data=MASI,spec=model.a12.g12.s) #42
garch15.s<-ugarchfit(data=MASI,spec=model.a12.g21.s) #43
garch16.s<-ugarchfit(data=MASI,spec=model.a12.g22.s) #44
garch17.s<-ugarchfit(data=MASI,spec=model.a22.g11.s) #45
garch18.s<-ugarchfit(data=MASI,spec=model.a22.g12.s) #46
garch19.s<-ugarchfit(data=MASI,spec=model.a22.g21.s) #47
garch20.s<-ugarchfit(data=MASI,spec=model.a22.g22.s) #48
garch21.s<-ugarchfit(data=MASI,spec=model.a20.g11.s) #49
garch22.s<-ugarchfit(data=MASI,spec=model.a20.g12.s) #50
garch23.s<-ugarchfit(data=MASI,spec=model.a20.g21.s) #51
garch24.s<-ugarchfit(data=MASI,spec=model.a20.g22.s) #52
garch25.s<-ugarchfit(data=MASI,spec=model.a02.g11.s) #53
garch26.s<-ugarchfit(data=MASI,spec=model.a02.g12.s) #54
garch27.s<-ugarchfit(data=MASI,spec=model.a02.g21.s) #55
garch28.s<-ugarchfit(data=MASI,spec=model.a02.g22.s) #56
garch1.ss<-ugarchfit(data=MASI,spec=model.a10.g11.ss) #57
garch2.ss<-ugarchfit(data=MASI,spec=model.a10.g12.ss) #58
garch3.ss<-ugarchfit(data=MASI,spec=model.a10.g21.ss) #59
garch4.ss<-ugarchfit(data=MASI,spec=model.a10.g22.ss) #60
garch5.ss<-ugarchfit(data=MASI,spec=model.a11.g11.ss) #61
garch6.ss<-ugarchfit(data=MASI,spec=model.a11.g12.ss) #62
garch7.ss<-ugarchfit(data=MASI,spec=model.a11.g21.ss) #63
garch8.ss<-ugarchfit(data=MASI,spec=model.a11.g22.ss) #64
garch9.ss<-ugarchfit(data=MASI,spec=model.a21.g11.ss) #65
garch10.ss<-ugarchfit(data=MASI,spec=model.a21.g12.ss) #66
garch11.ss<-ugarchfit(data=MASI,spec=model.a21.g21.ss) #67
garch12.ss<-ugarchfit(data=MASI,spec=model.a21.g22.ss) #68
garch13.ss<-ugarchfit(data=MASI,spec=model.a12.g11.ss) #69
garch14.ss<-ugarchfit(data=MASI,spec=model.a12.g12.ss) #70
garch15.ss<-ugarchfit(data=MASI,spec=model.a12.g21.ss) #71
garch16.ss<-ugarchfit(data=MASI,spec=model.a12.g22.ss) #72
garch17.ss<-ugarchfit(data=MASI,spec=model.a22.g11.ss) #73
garch18.ss<-ugarchfit(data=MASI,spec=model.a22.g12.ss) #74
garch19.ss<-ugarchfit(data=MASI,spec=model.a22.g21.ss) #75
garch20.ss<-ugarchfit(data=MASI,spec=model.a22.g22.ss) #76
garch21.ss<-ugarchfit(data=MASI,spec=model.a20.g11.ss) #77
garch22.ss<-ugarchfit(data=MASI,spec=model.a20.g12.ss) #78
garch23.ss<-ugarchfit(data=MASI,spec=model.a20.g21.ss) #79
garch24.ss<-ugarchfit(data=MASI,spec=model.a20.g22.ss) #80
garch25.ss<-ugarchfit(data=MASI,spec=model.a02.g11.ss) #81
garch26.ss<-ugarchfit(data=MASI,spec=model.a02.g12.ss) #82
garch27.ss<-ugarchfit(data=MASI,spec=model.a02.g21.ss) #83
garch28.ss<-ugarchfit(data=MASI,spec=model.a02.g22.ss) #84
garch1.g<-ugarchfit(data=MASI,spec=model.a10.g11.g) #85
garch2.g<-ugarchfit(data=MASI,spec=model.a10.g12.g) #86
garch3.g<-ugarchfit(data=MASI,spec=model.a10.g21.g) #87
garch4.g<-ugarchfit(data=MASI,spec=model.a10.g22.g) #88
garch5.g<-ugarchfit(data=MASI,spec=model.a11.g11.g) #89
garch6.g<-ugarchfit(data=MASI,spec=model.a11.g12.g) #90
garch7.g<-ugarchfit(data=MASI,spec=model.a11.g21.g) #91
garch8.g<-ugarchfit(data=MASI,spec=model.a11.g22.g) #92
garch9.g<-ugarchfit(data=MASI,spec=model.a21.g11.g) #93
garch10.g<-ugarchfit(data=MASI,spec=model.a21.g12.g) #94
garch11.g<-ugarchfit(data=MASI,spec=model.a21.g21.g) #95
garch12.g<-ugarchfit(data=MASI,spec=model.a21.g22.g) #96
garch13.g<-ugarchfit(data=MASI,spec=model.a12.g11.g) #97
garch14.g<-ugarchfit(data=MASI,spec=model.a12.g12.g) #98
garch15.g<-ugarchfit(data=MASI,spec=model.a12.g21.g) #99
garch16.g<-ugarchfit(data=MASI,spec=model.a12.g22.g) #100
garch17.g<-ugarchfit(data=MASI,spec=model.a22.g11.g) #101
garch18.g<-ugarchfit(data=MASI,spec=model.a22.g12.g) #102
garch19.g<-ugarchfit(data=MASI,spec=model.a22.g21.g) #103
garch20.g<-ugarchfit(data=MASI,spec=model.a22.g22.g) #104
garch21.g<-ugarchfit(data=MASI,spec=model.a20.g11.g) #105
garch22.g<-ugarchfit(data=MASI,spec=model.a20.g12.g) #106
garch23.g<-ugarchfit(data=MASI,spec=model.a20.g21.g) #107
garch24.g<-ugarchfit(data=MASI,spec=model.a20.g22.g) #108
garch25.g<-ugarchfit(data=MASI,spec=model.a02.g11.g) #109
garch26.g<-ugarchfit(data=MASI,spec=model.a02.g12.g) #110
garch27.g<-ugarchfit(data=MASI,spec=model.a02.g21.g) #111
garch28.g<-ugarchfit(data=MASI,spec=model.a02.g22.g) #112
garch1.sg<-ugarchfit(data=MASI,spec=model.a10.g11.sg) #113
garch2.sg<-ugarchfit(data=MASI,spec=model.a10.g12.sg) #114
garch3.sg<-ugarchfit(data=MASI,spec=model.a10.g21.sg) #115
garch4.sg<-ugarchfit(data=MASI,spec=model.a10.g22.sg) #116
garch5.sg<-ugarchfit(data=MASI,spec=model.a11.g11.sg) #117
garch6.sg<-ugarchfit(data=MASI,spec=model.a11.g12.sg) #118
garch7.sg<-ugarchfit(data=MASI,spec=model.a11.g21.sg) #119
garch8.sg<-ugarchfit(data=MASI,spec=model.a11.g22.sg) #120
garch9.sg<-ugarchfit(data=MASI,spec=model.a21.g11.sg) #121
garch10.sg<-ugarchfit(data=MASI,spec=model.a21.g12.sg) #122
garch11.sg<-ugarchfit(data=MASI,spec=model.a21.g21.sg) #123
garch12.sg<-ugarchfit(data=MASI,spec=model.a21.g22.sg) #124
garch13.sg<-ugarchfit(data=MASI,spec=model.a12.g11.sg) #125
garch14.sg<-ugarchfit(data=MASI,spec=model.a12.g12.sg) #126
garch15.sg<-ugarchfit(data=MASI,spec=model.a12.g21.sg) #127
garch16.sg<-ugarchfit(data=MASI,spec=model.a12.g22.sg) #128
garch17.sg<-ugarchfit(data=MASI,spec=model.a22.g11.sg) #129
garch18.sg<-ugarchfit(data=MASI,spec=model.a22.g12.sg) #130
garch19.sg<-ugarchfit(data=MASI,spec=model.a22.g21.sg) #131
garch20.sg<-ugarchfit(data=MASI,spec=model.a22.g22.sg) #132
garch21.sg<-ugarchfit(data=MASI,spec=model.a20.g11.sg) #133
garch22.sg<-ugarchfit(data=MASI,spec=model.a20.g12.sg) #134
garch23.sg<-ugarchfit(data=MASI,spec=model.a20.g21.sg) #135
garch24.sg<-ugarchfit(data=MASI,spec=model.a20.g22.sg) #136
garch25.sg<-ugarchfit(data=MASI,spec=model.a02.g11.sg) #137
garch26.sg<-ugarchfit(data=MASI,spec=model.a02.g12.sg) #138
garch27.sg<-ugarchfit(data=MASI,spec=model.a02.g21.sg) #139
garch28.sg<-ugarchfit(data=MASI,spec=model.a02.g22.sg) #140

model.aic.list <- list(garch1.n, garch1.s, garch1.ss, garch1.g, garch1.sg, garch2.n, garch2.s, garch2.ss, garch2.g, garch2.sg, garch3.n, garch3.s, garch3.ss, garch3.g, garch3.sg, garch4.n, garch4.s, garch4.ss, garch4.g, garch4.sg, garch5.n, garch5.s, garch5.ss, garch5.g, garch5.sg, garch6.n, garch6.s, garch6.ss, garch6.g, garch6.sg, garch7.n, garch7.s, garch7.ss, garch7.g, garch7.sg, garch8.n, garch8.s, garch8.ss, garch8.g, garch8.sg, garch9.n, garch9.s, garch9.ss, garch9.g, garch9.sg, garch10.n, garch10.s, garch10.ss, garch10.g, garch10.sg, garch11.n, garch11.s, garch11.ss, garch11.g, garch11.sg, garch12.n, garch12.s, garch12.ss, garch12.g, garch12.sg, garch13.n, garch13.s, garch13.ss, garch13.g, garch13.sg, garch14.n, garch14.s, garch14.ss, garch14.g, garch14.sg, garch15.n, garch15.s, garch15.ss, garch15.g, garch15.sg, garch16.n, garch16.s, garch16.ss, garch16.g, garch16.sg, garch17.n, garch17.s, garch17.ss, garch17.g, garch17.sg, garch18.n, garch18.s, garch18.ss, garch18.g, garch18.sg, garch19.n, garch19.s, garch19.ss, garch19.g, garch19.sg, garch20.n, garch20.s, garch20.ss, garch20.g, garch20.sg, garch21.n, garch21.s, garch21.ss, garch21.g, garch21.sg, garch22.n, garch22.s, garch22.ss, garch22.g, garch22.sg, garch23.n, garch23.s, garch23.ss, garch23.g, garch23.sg, garch24.n, garch24.s, garch24.ss, garch24.g, garch24.sg, garch25.n, garch25.s, garch25.ss, garch25.g, garch25.sg, garch26.n, garch26.s, garch26.ss, garch26.g, garch26.sg, garch27.n, garch27.s, garch27.ss, garch27.g, garch27.sg, garch28.n, garch28.s, garch28.ss, garch28.g, garch28.sg)
model.aic <- sapply(model.aic.list, infocriteria)[-4,][-3,]
min(model.aic[1,])

## [1] 2.00721

model.aic 

##          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
## [1,] 2.257970 2.009284 2.010454 2.032868 2.033911 2.259151 2.007592 2.008764
## [2,] 2.277304 2.031840 2.036232 2.055424 2.059689 2.281707 2.033370 2.037765
##          [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16]
## [1,] 2.033691 2.034709 2.254100 2.010993 2.012162 2.035254 2.036293 2.255287
## [2,] 2.059469 2.063709 2.279878 2.039994 2.044385 2.064255 2.068516 2.284287
##         [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24]
## [1,] 2.009659 2.010828 2.035543 2.036591 2.259098 2.010431 2.011597 2.033974
## [2,] 2.041881 2.046272 2.067766 2.072036 2.281654 2.036209 2.040598 2.059752
##         [,25]    [,26]    [,27]    [,28]    [,29]    [,30]    [,31]    [,32]
## [1,] 2.035108 2.260278 2.008776 2.009948 2.034740 2.035884 2.255136 2.012152
## [2,] 2.064108 2.286057 2.037776 2.042170 2.063741 2.068107 2.284137 2.044375
##         [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40]
## [1,] 2.013319 2.036355 2.037480 2.256323 2.010846 2.012014 2.036604 2.037772
## [2,] 2.048764 2.068578 2.072925 2.288546 2.046291 2.050682 2.072049 2.076439
##         [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48]
## [1,] 2.259350 2.008913 2.010069 2.031996 2.032928 2.260017 2.007210 2.008373
## [2,] 2.285128 2.037913 2.042291 2.060997 2.065151 2.289017 2.039433 2.043818
##         [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56]
## [1,] 2.032789 2.033731 2.255167 2.010404 2.011560 2.034332 2.035282 2.256354
## [2,] 2.065011 2.069176 2.287390 2.045849 2.050227 2.069777 2.073949 2.291799
##         [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]    [,64]
## [1,] 2.009417 2.010571 2.034697 2.035615 2.259137 2.009395 2.010545 2.030875
## [2,] 2.048084 2.052460 2.073364 2.077504 2.284916 2.038396 2.042767 2.059876
##         [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72]
## [1,] 2.031690 2.260242 2.007363 2.008514 2.031542 2.032345 2.255384 2.010853
## [2,] 2.063913 2.289242 2.039586 2.043959 2.063765 2.067790 2.287607 2.046298
##         [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80]
## [1,] 2.012000 2.033220 2.034037 2.256571 2.009442 2.010587 2.033435 2.034199
## [2,] 2.050667 2.068665 2.072704 2.292016 2.048109 2.052476 2.072103 2.076088
##         [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88]
## [1,] 2.259736 2.010017 2.011180 2.033168 2.034114 2.261723 2.008211 2.009381
## [2,] 2.288736 2.042240 2.046625 2.065391 2.069559 2.293946 2.043656 2.048049
##         [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96]
## [1,] 2.034100 2.034908 2.256198 2.011473 2.012635 2.035509 2.036715 2.257664
## [2,] 2.069545 2.073576 2.291642 2.050140 2.054524 2.074176 2.078604 2.296331
##        [,97]    [,98]    [,99]   [,100]   [,101]   [,102]   [,103]   [,104]
## [1,] 2.01038 2.011545 2.036094 2.036797 2.258896 2.010189 2.011355 2.033679
## [2,] 2.05227 2.056657 2.077983 2.081909 2.281451 2.035967 2.040356 2.059457
##        [,105]   [,106]   [,107]   [,108]   [,109]   [,110]   [,111]   [,112]
## [1,] 2.034907 2.260083 2.008393 2.009566 2.034398 2.035551 2.255007 2.011800
## [2,] 2.063908 2.285861 2.037394 2.041789 2.063398 2.067774 2.284008 2.044023
##        [,113]   [,114]   [,115]   [,116]   [,117]   [,118]   [,119]   [,120]
## [1,] 2.012968 2.036037 2.037206 2.256194 2.010475 2.011645 2.036270 2.037442
## [2,] 2.048413 2.068259 2.072651 2.288417 2.045920 2.050312 2.071715 2.076109
##        [,121]   [,122]   [,123]   [,124]   [,125]   [,126]   [,127]   [,128]
## [1,] 2.259261 2.010510 2.011677 2.033984 2.034994 2.260448 2.008754 2.009926
## [2,] 2.281817 2.036289 2.040677 2.059762 2.063995 2.286226 2.037754 2.042148
##       [,129]   [,130]   [,131]   [,132]   [,133]   [,134]   [,135]   [,136]
## [1,] 2.03474 2.035837 2.255435 2.012136 2.013304 2.036347 2.037374 2.256622
## [2,] 2.06374 2.068060 2.284435 2.044359 2.048749 2.068570 2.072819 2.288844
##        [,137]   [,138]   [,139]   [,140]
## [1,] 2.010821 2.011989 2.036609 2.037694
## [2,] 2.046266 2.050657 2.072054 2.076361

garch19.s #47

## 
## *---------------------------------*
## *          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      0.030040    0.014835   2.0250 0.042866
## ar1    -0.917744    0.024578 -37.3399 0.000000
## ar2     0.031751    0.025280   1.2560 0.209124
## ma1     1.032309    0.001246 828.7021 0.000000
## ma2     0.087125    0.001336  65.2128 0.000000
## omega   0.064485    0.020526   3.1416 0.001680
## alpha1  0.091454    0.050406   1.8143 0.069624
## alpha2  0.000000    0.053829   0.0000 1.000000
## beta1   0.792410    0.052608  15.0627 0.000000
## gamma1  0.175930    0.095832   1.8358 0.066385
## gamma2 -0.099030    0.090453  -1.0948 0.273593
## shape   3.140356    0.263723  11.9078 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error  t value Pr(>|t|)
## mu      0.030040    0.016911   1.7764 0.075666
## ar1    -0.917744    0.029137 -31.4974 0.000000
## ar2     0.031751    0.029279   1.0844 0.278170
## ma1     1.032309    0.001069 965.4767 0.000000
## ma2     0.087125    0.002403  36.2624 0.000000
## omega   0.064485    0.023885   2.6998 0.006938
## alpha1  0.091454    0.048312   1.8930 0.058358
## alpha2  0.000000    0.056357   0.0000 1.000000
## beta1   0.792410    0.066023  12.0019 0.000000
## gamma1  0.175930    0.100937   1.7430 0.081339
## gamma2 -0.099030    0.091738  -1.0795 0.280367
## shape   3.140356    0.288281  10.8934 0.000000
## 
## LogLikelihood : -1682.666 
## 
## Information Criteria
## ------------------------------------
##                    
## Akaike       2.0115
## Bayes        2.0501
## Shibata      2.0114
## Hannan-Quinn 2.0258
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                          statistic  p-value
## Lag[1]                       5.963 0.014610
## Lag[2*(p+q)+(p+q)-1][11]    12.913 0.000000
## Lag[4*(p+q)+(p+q)-1][19]    16.509 0.008895
## d.o.f=4
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                      0.2335  0.6290
## Lag[2*(p+q)+(p+q)-1][8]     1.2704  0.9517
## Lag[4*(p+q)+(p+q)-1][14]    2.0283  0.9906
## d.o.f=3
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[4]    0.5381 0.500 2.000  0.4632
## ARCH Lag[6]    0.8294 1.461 1.711  0.7971
## ARCH Lag[8]    0.9565 2.368 1.583  0.9306
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  2.7976
## Individual Statistics:              
## mu     0.22574
## ar1    0.10662
## ar2    0.05648
## ma1    0.09326
## ma2    0.05189
## omega  0.04076
## alpha1 0.08157
## alpha2 0.12885
## beta1  0.08274
## gamma1 0.41106
## gamma2 0.24693
## shape  0.05256
## 
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic:          2.69 2.96 3.51
## Individual Statistic:     0.35 0.47 0.75
## 
## Sign Bias Test
## ------------------------------------
##                    t-value   prob sig
## Sign Bias           0.9000 0.3683    
## Negative Sign Bias  0.1553 0.8766    
## Positive Sign Bias  0.5640 0.5728    
## Joint Effect        1.1566 0.7634    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     11.82       0.8932
## 2    30     23.22       0.7664
## 3    40     27.78       0.9099
## 4    50     47.02       0.5538
## 
## 
## Elapsed time : 1.238464

4.6. MSM30 - GJR-GARCH - AIC

garch1.n<-ugarchfit(data=MSM30,spec=model.a10.g11.n) #1
garch2.n<-ugarchfit(data=MSM30,spec=model.a10.g12.n) #2
garch3.n<-ugarchfit(data=MSM30,spec=model.a10.g21.n) #3
garch4.n<-ugarchfit(data=MSM30,spec=model.a10.g22.n) #4
garch5.n<-ugarchfit(data=MSM30,spec=model.a11.g11.n) #5
garch6.n<-ugarchfit(data=MSM30,spec=model.a11.g12.n) #6
garch7.n<-ugarchfit(data=MSM30,spec=model.a11.g21.n) #7
garch8.n<-ugarchfit(data=MSM30,spec=model.a11.g22.n) #8
garch9.n<-ugarchfit(data=MSM30,spec=model.a21.g11.n) #9
garch10.n<-ugarchfit(data=MSM30,spec=model.a21.g12.n) #10
garch11.n<-ugarchfit(data=MSM30,spec=model.a21.g21.n) #11
garch12.n<-ugarchfit(data=MSM30,spec=model.a21.g22.n) #12
garch13.n<-ugarchfit(data=MSM30,spec=model.a12.g11.n) #13
garch14.n<-ugarchfit(data=MSM30,spec=model.a12.g12.n) #14
garch15.n<-ugarchfit(data=MSM30,spec=model.a12.g21.n) #15
garch16.n<-ugarchfit(data=MSM30,spec=model.a12.g22.n) #16
garch17.n<-ugarchfit(data=MSM30,spec=model.a22.g11.n) #17
garch18.n<-ugarchfit(data=MSM30,spec=model.a22.g12.n) #18
garch19.n<-ugarchfit(data=MSM30,spec=model.a22.g21.n) #19
garch20.n<-ugarchfit(data=MSM30,spec=model.a22.g22.n) #20
garch21.n<-ugarchfit(data=MSM30,spec=model.a20.g11.n) #21
garch22.n<-ugarchfit(data=MSM30,spec=model.a20.g12.n) #22
garch23.n<-ugarchfit(data=MSM30,spec=model.a20.g21.n) #23
garch24.n<-ugarchfit(data=MSM30,spec=model.a20.g22.n) #24
garch25.n<-ugarchfit(data=MSM30,spec=model.a02.g11.n) #25
garch26.n<-ugarchfit(data=MSM30,spec=model.a02.g12.n) #26
garch27.n<-ugarchfit(data=MSM30,spec=model.a02.g21.n) #27
garch28.n<-ugarchfit(data=MSM30,spec=model.a02.g22.n) #28
garch1.s<-ugarchfit(data=MSM30,spec=model.a10.g11.s) #29
garch2.s<-ugarchfit(data=MSM30,spec=model.a10.g12.s) #30
garch3.s<-ugarchfit(data=MSM30,spec=model.a10.g21.s) #31
garch4.s<-ugarchfit(data=MSM30,spec=model.a10.g22.s) #32
garch5.s<-ugarchfit(data=MSM30,spec=model.a11.g11.s) #33
garch6.s<-ugarchfit(data=MSM30,spec=model.a11.g12.s) #34
garch7.s<-ugarchfit(data=MSM30,spec=model.a11.g21.s) #35
garch8.s<-ugarchfit(data=MSM30,spec=model.a11.g22.s) #36
garch9.s<-ugarchfit(data=MSM30,spec=model.a21.g11.s) #37
garch10.s<-ugarchfit(data=MSM30,spec=model.a21.g12.s) #38
garch11.s<-ugarchfit(data=MSM30,spec=model.a21.g21.s) #39
garch12.s<-ugarchfit(data=MSM30,spec=model.a21.g22.s) #40
garch13.s<-ugarchfit(data=MSM30,spec=model.a12.g11.s) #41
garch14.s<-ugarchfit(data=MSM30,spec=model.a12.g12.s) #42
garch15.s<-ugarchfit(data=MSM30,spec=model.a12.g21.s) #43
garch16.s<-ugarchfit(data=MSM30,spec=model.a12.g22.s) #44
garch17.s<-ugarchfit(data=MSM30,spec=model.a22.g11.s) #45
garch18.s<-ugarchfit(data=MSM30,spec=model.a22.g12.s) #46
garch19.s<-ugarchfit(data=MSM30,spec=model.a22.g21.s) #47
garch20.s<-ugarchfit(data=MSM30,spec=model.a22.g22.s) #48
garch21.s<-ugarchfit(data=MSM30,spec=model.a20.g11.s) #49
garch22.s<-ugarchfit(data=MSM30,spec=model.a20.g12.s) #50
garch23.s<-ugarchfit(data=MSM30,spec=model.a20.g21.s) #51
garch24.s<-ugarchfit(data=MSM30,spec=model.a20.g22.s) #52
garch25.s<-ugarchfit(data=MSM30,spec=model.a02.g11.s) #53
garch26.s<-ugarchfit(data=MSM30,spec=model.a02.g12.s) #54
garch27.s<-ugarchfit(data=MSM30,spec=model.a02.g21.s) #55
garch28.s<-ugarchfit(data=MSM30,spec=model.a02.g22.s) #56
garch1.ss<-ugarchfit(data=MSM30,spec=model.a10.g11.ss) #57
garch2.ss<-ugarchfit(data=MSM30,spec=model.a10.g12.ss) #58
garch3.ss<-ugarchfit(data=MSM30,spec=model.a10.g21.ss) #59
garch4.ss<-ugarchfit(data=MSM30,spec=model.a10.g22.ss) #60
garch5.ss<-ugarchfit(data=MSM30,spec=model.a11.g11.ss) #61
garch6.ss<-ugarchfit(data=MSM30,spec=model.a11.g12.ss) #62
garch7.ss<-ugarchfit(data=MSM30,spec=model.a11.g21.ss) #63
garch8.ss<-ugarchfit(data=MSM30,spec=model.a11.g22.ss) #64
garch9.ss<-ugarchfit(data=MSM30,spec=model.a21.g11.ss) #65
garch10.ss<-ugarchfit(data=MSM30,spec=model.a21.g12.ss) #66
garch11.ss<-ugarchfit(data=MSM30,spec=model.a21.g21.ss) #67
garch12.ss<-ugarchfit(data=MSM30,spec=model.a21.g22.ss) #68
garch13.ss<-ugarchfit(data=MSM30,spec=model.a12.g11.ss) #69
garch14.ss<-ugarchfit(data=MSM30,spec=model.a12.g12.ss) #70
garch15.ss<-ugarchfit(data=MSM30,spec=model.a12.g21.ss) #71
garch16.ss<-ugarchfit(data=MSM30,spec=model.a12.g22.ss) #72
garch17.ss<-ugarchfit(data=MSM30,spec=model.a22.g11.ss) #73
garch18.ss<-ugarchfit(data=MSM30,spec=model.a22.g12.ss) #74
garch19.ss<-ugarchfit(data=MSM30,spec=model.a22.g21.ss) #75
garch20.ss<-ugarchfit(data=MSM30,spec=model.a22.g22.ss) #76
garch21.ss<-ugarchfit(data=MSM30,spec=model.a20.g11.ss) #77
garch22.ss<-ugarchfit(data=MSM30,spec=model.a20.g12.ss) #78
garch23.ss<-ugarchfit(data=MSM30,spec=model.a20.g21.ss) #79
garch24.ss<-ugarchfit(data=MSM30,spec=model.a20.g22.ss) #80
garch25.ss<-ugarchfit(data=MSM30,spec=model.a02.g11.ss) #81
garch26.ss<-ugarchfit(data=MSM30,spec=model.a02.g12.ss) #82
garch27.ss<-ugarchfit(data=MSM30,spec=model.a02.g21.ss) #83
garch28.ss<-ugarchfit(data=MSM30,spec=model.a02.g22.ss) #84
garch1.g<-ugarchfit(data=MSM30,spec=model.a10.g11.g) #85
garch2.g<-ugarchfit(data=MSM30,spec=model.a10.g12.g) #86
garch3.g<-ugarchfit(data=MSM30,spec=model.a10.g21.g) #87
garch4.g<-ugarchfit(data=MSM30,spec=model.a10.g22.g) #88
garch5.g<-ugarchfit(data=MSM30,spec=model.a11.g11.g) #89
garch6.g<-ugarchfit(data=MSM30,spec=model.a11.g12.g) #90
garch7.g<-ugarchfit(data=MSM30,spec=model.a11.g21.g) #91
garch8.g<-ugarchfit(data=MSM30,spec=model.a11.g22.g) #92
garch9.g<-ugarchfit(data=MSM30,spec=model.a21.g11.g) #93
garch10.g<-ugarchfit(data=MSM30,spec=model.a21.g12.g) #94
garch11.g<-ugarchfit(data=MSM30,spec=model.a21.g21.g) #95
garch12.g<-ugarchfit(data=MSM30,spec=model.a21.g22.g) #96
garch13.g<-ugarchfit(data=MSM30,spec=model.a12.g11.g) #97
garch14.g<-ugarchfit(data=MSM30,spec=model.a12.g12.g) #98
garch15.g<-ugarchfit(data=MSM30,spec=model.a12.g21.g) #99
garch16.g<-ugarchfit(data=MSM30,spec=model.a12.g22.g) #100
garch17.g<-ugarchfit(data=MSM30,spec=model.a22.g11.g) #101
garch18.g<-ugarchfit(data=MSM30,spec=model.a22.g12.g) #102
garch19.g<-ugarchfit(data=MSM30,spec=model.a22.g21.g) #103
garch20.g<-ugarchfit(data=MSM30,spec=model.a22.g22.g) #104
garch21.g<-ugarchfit(data=MSM30,spec=model.a20.g11.g) #105
garch22.g<-ugarchfit(data=MSM30,spec=model.a20.g12.g) #106
garch23.g<-ugarchfit(data=MSM30,spec=model.a20.g21.g) #107
garch24.g<-ugarchfit(data=MSM30,spec=model.a20.g22.g) #108
garch25.g<-ugarchfit(data=MSM30,spec=model.a02.g11.g) #109
garch26.g<-ugarchfit(data=MSM30,spec=model.a02.g12.g) #110
garch27.g<-ugarchfit(data=MSM30,spec=model.a02.g21.g) #111
garch28.g<-ugarchfit(data=MSM30,spec=model.a02.g22.g) #112
garch1.sg<-ugarchfit(data=MSM30,spec=model.a10.g11.sg) #113
garch2.sg<-ugarchfit(data=MSM30,spec=model.a10.g12.sg) #114
garch3.sg<-ugarchfit(data=MSM30,spec=model.a10.g21.sg) #115
garch4.sg<-ugarchfit(data=MSM30,spec=model.a10.g22.sg) #116
garch5.sg<-ugarchfit(data=MSM30,spec=model.a11.g11.sg) #117
garch6.sg<-ugarchfit(data=MSM30,spec=model.a11.g12.sg) #118
garch7.sg<-ugarchfit(data=MSM30,spec=model.a11.g21.sg) #119
garch8.sg<-ugarchfit(data=MSM30,spec=model.a11.g22.sg) #120
garch9.sg<-ugarchfit(data=MSM30,spec=model.a21.g11.sg) #121
garch10.sg<-ugarchfit(data=MSM30,spec=model.a21.g12.sg) #122
garch11.sg<-ugarchfit(data=MSM30,spec=model.a21.g21.sg) #123
garch12.sg<-ugarchfit(data=MSM30,spec=model.a21.g22.sg) #124
garch13.sg<-ugarchfit(data=MSM30,spec=model.a12.g11.sg) #125
garch14.sg<-ugarchfit(data=MSM30,spec=model.a12.g12.sg) #126
garch15.sg<-ugarchfit(data=MSM30,spec=model.a12.g21.sg) #127
garch16.sg<-ugarchfit(data=MSM30,spec=model.a12.g22.sg) #128
garch17.sg<-ugarchfit(data=MSM30,spec=model.a22.g11.sg) #129
garch18.sg<-ugarchfit(data=MSM30,spec=model.a22.g12.sg) #130
garch19.sg<-ugarchfit(data=MSM30,spec=model.a22.g21.sg) #131
garch20.sg<-ugarchfit(data=MSM30,spec=model.a22.g22.sg) #132
garch21.sg<-ugarchfit(data=MSM30,spec=model.a20.g11.sg) #133
garch22.sg<-ugarchfit(data=MSM30,spec=model.a20.g12.sg) #134
garch23.sg<-ugarchfit(data=MSM30,spec=model.a20.g21.sg) #135
garch24.sg<-ugarchfit(data=MSM30,spec=model.a20.g22.sg) #136
garch25.sg<-ugarchfit(data=MSM30,spec=model.a02.g11.sg) #137
garch26.sg<-ugarchfit(data=MSM30,spec=model.a02.g12.sg) #138
garch27.sg<-ugarchfit(data=MSM30,spec=model.a02.g21.sg) #139
garch28.sg<-ugarchfit(data=MSM30,spec=model.a02.g22.sg) #140

model.aic.list <- list(garch1.n, garch1.s, garch1.ss, garch1.g, garch1.sg, garch2.n, garch2.s, garch2.ss, garch2.g, garch2.sg, garch3.n, garch3.s, garch3.ss, garch3.g, garch3.sg, garch4.n, garch4.s, garch4.ss, garch4.g, garch4.sg, garch5.n, garch5.s, garch5.ss, garch5.g, garch5.sg, garch6.n, garch6.s, garch6.ss, garch6.g, garch6.sg, garch7.n, garch7.s, garch7.ss, garch7.g, garch7.sg, garch8.n, garch8.s, garch8.ss, garch8.g, garch8.sg, garch9.n, garch9.s, garch9.ss, garch9.g, garch9.sg, garch10.n, garch10.s, garch10.ss, garch10.g, garch10.sg, garch11.n, garch11.s, garch11.ss, garch11.g, garch11.sg, garch12.n, garch12.s, garch12.ss, garch12.g, garch12.sg, garch13.n, garch13.s, garch13.ss, garch13.g, garch13.sg, garch14.n, garch14.s, garch14.ss, garch14.g, garch14.sg, garch15.n, garch15.s, garch15.ss, garch15.g, garch15.sg, garch16.n, garch16.s, garch16.ss, garch16.g, garch16.sg, garch17.n, garch17.s, garch17.ss, garch17.g, garch17.sg, garch18.n, garch18.s, garch18.ss, garch18.g, garch18.sg, garch19.n, garch19.s, garch19.ss, garch19.g, garch19.sg, garch20.n, garch20.s, garch20.ss, garch20.g, garch20.sg, garch21.n, garch21.s, garch21.ss, garch21.g, garch21.sg, garch22.n, garch22.s, garch22.ss, garch22.g, garch22.sg, garch23.n, garch23.s, garch23.ss, garch23.g, garch23.sg, garch24.n, garch24.s, garch24.ss, garch24.g, garch24.sg, garch25.n, garch25.s, garch25.ss, garch25.g, garch25.sg, garch26.n, garch26.s, garch26.ss, garch26.g, garch26.sg, garch27.n, garch27.s, garch27.ss, garch27.g, garch27.sg, garch28.n, garch28.s, garch28.ss, garch28.g, garch28.sg)
model.aic <- sapply(model.aic.list, infocriteria)[-4,][-3,]
min(model.aic[1,])

## [1] 1.804686

model.aic 

##          [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
## [1,] 2.087217 1.809100 1.809951 1.824571 1.825232 2.088365 1.810035 1.810808
## [2,] 2.106551 1.831656 1.835729 1.847126 1.851010 2.110921 1.835813 1.839809
##          [,9]    [,10]    [,11]    [,12]    [,13]    [,14]    [,15]    [,16]
## [1,] 1.825766 1.826329 2.082599 1.808952 1.809929 1.824172 1.825005 2.066095
## [2,] 1.851544 1.855330 2.108377 1.837952 1.842152 1.853173 1.857228 2.095095
##         [,17]    [,18]    [,19]    [,20]    [,21]    [,22]    [,23]    [,24]
## [1,] 1.809112 1.810002 1.823324 1.824070 2.088284 1.805061 1.806023 1.819910
## [2,] 1.841335 1.845447 1.855546 1.859515 2.110839 1.830839 1.835024 1.845688
##         [,25]    [,26]    [,27]    [,28]    [,29]    [,30]   [,31]    [,32]
## [1,] 1.820385 2.089433 1.806195 1.807091 1.821138 1.821554 2.08374 1.804686
## [2,] 1.849385 2.115211 1.835195 1.839314 1.850138 1.853777 2.11274 1.836909
##         [,33]    [,34]    [,35]    [,36]    [,37]    [,38]    [,39]    [,40]
## [1,] 1.805700 1.819281 1.819811 2.066604 1.805051 1.805965 1.818545 1.818882
## [2,] 1.841145 1.851504 1.855256 2.098827 1.840496 1.844633 1.853989 1.857549
##         [,41]    [,42]    [,43]    [,44]    [,45]    [,46]    [,47]    [,48]
## [1,] 2.088346 1.807289 1.808276 1.821289 1.821941 2.089533 1.808146 1.809052
## [2,] 2.114124 1.836289 1.840498 1.850289 1.854163 2.118534 1.840369 1.844497
##         [,49]    [,50]    [,51]    [,52]    [,53]    [,54]    [,55]    [,56]
## [1,] 1.822429 1.823028 2.083936 1.806585 1.807597 1.820533 1.821177 2.065674
## [2,] 1.854652 1.858472 2.116158 1.842030 1.846264 1.855978 1.859844 2.101119
##         [,57]    [,58]    [,59]    [,60]    [,61]    [,62]    [,63]  [,64]
## [1,] 1.806970 1.807885 1.819677 1.820203 2.087133 1.806517 1.807494 1.8205
## [2,] 1.845637 1.849774 1.858345 1.862092 2.112911 1.835518 1.839716 1.8495
##         [,65]    [,66]    [,67]    [,68]    [,69]    [,70]    [,71]    [,72]
## [1,] 1.821058 2.088320 1.807379 1.808271 1.821646 1.822132 2.082580 1.805860
## [2,] 1.853281 2.117321 1.839601 1.843716 1.853869 1.857577 2.114803 1.841305
##         [,73]    [,74]    [,75]    [,76]    [,77]    [,78]    [,79]    [,80]
## [1,] 1.806868 1.819729 1.820253 2.064684 1.806236 1.807144 1.818902 1.819202
## [2,] 1.845535 1.855174 1.858920 2.100129 1.844903 1.849034 1.857570 1.861091
##         [,81]    [,82]    [,83]    [,84]    [,85]    [,86]    [,87]    [,88]
## [1,] 2.088941 1.807807 1.808785 1.822472 1.823114 2.090127 1.808727 1.809628
## [2,] 2.117941 1.840030 1.844230 1.854695 1.858559 2.122350 1.844172 1.848296
##         [,89]    [,90]    [,91]    [,92]    [,93]    [,94]    [,95]    [,96]
## [1,] 1.823607 1.824166 2.084406 1.807027 1.808043 1.821831 1.822443 2.066415
## [2,] 1.859052 1.862833 2.119851 1.845694 1.849932 1.860498 1.864332 2.105082
##         [,97]    [,98]   [,99]   [,100]   [,101]   [,102]   [,103]   [,104]
## [1,] 1.807484 1.808371 1.82106 1.821578 2.089247 1.806338 1.807278 1.822058
## [2,] 1.849373 1.853483 1.86295 1.866690 2.111803 1.832116 1.836278 1.847836
##        [,105]   [,106]   [,107]   [,108]   [,109]   [,110]   [,111]   [,112]
## [1,] 1.822336 2.090434 1.807214 1.808067 1.823190 1.823387 2.084702 1.805593
## [2,] 1.851336 2.116212 1.836215 1.840290 1.852191 1.855609 2.113703 1.837815
##        [,113]   [,114]   [,115]   [,116]   [,117]   [,118]   [,119]   [,120]
## [1,] 1.806570 1.821293 1.821655 2.067830 1.806046 1.806900 1.820612 1.820766
## [2,] 1.842015 1.853516 1.857100 2.100053 1.841491 1.845567 1.856057 1.859433
##        [,121]   [,122]   [,123]   [,124]   [,125]   [,126]   [,127]   [,128]
## [1,] 2.088694 1.807508 1.808364 1.823581 1.823823 2.089881 1.808356 1.809110
## [2,] 2.111250 1.833286 1.837365 1.849359 1.852824 2.115659 1.837356 1.841332
##        [,129]   [,130]   [,131]   [,132]   [,133]   [,134]   [,135]   [,136]
## [1,] 1.824712 1.824827 2.084059 1.806588 1.807505 1.822784 1.823063 2.067448
## [2,] 1.853713 1.857050 2.113059 1.838810 1.842950 1.855007 1.858508 2.099671
##        [,137]   [,138]   [,139]   [,140]
## [1,] 1.807063 1.807828 1.822111 1.822053
## [2,] 1.842508 1.846495 1.857556 1.860720

garch4.s #32

## 
## *---------------------------------*
## *          GARCH Model Fit        *
## *---------------------------------*
## 
## Conditional Variance Dynamics    
## -----------------------------------
## GARCH Model  : gjrGARCH(2,2)
## Mean Model   : ARFIMA(1,0,0)
## Distribution : std 
## 
## Optimal Parameters
## ------------------------------------
##         Estimate  Std. Error  t value Pr(>|t|)
## mu     -0.019335    0.014559  -1.3280 0.184180
## ar1     0.177990    0.025145   7.0787 0.000000
## omega   0.119387    0.040367   2.9575 0.003101
## alpha1  0.296491    0.096277   3.0796 0.002073
## alpha2  0.000000    0.117236   0.0000 1.000000
## beta1   0.287720    0.285722   1.0070 0.313938
## beta2   0.241004    0.198149   1.2163 0.223878
## gamma1 -0.153322    0.117150  -1.3088 0.190616
## gamma2  0.173352    0.126374   1.3717 0.170145
## shape   3.192795    0.293515  10.8778 0.000000
## 
## Robust Standard Errors:
##         Estimate  Std. Error  t value Pr(>|t|)
## mu     -0.019335    0.016496 -1.17211 0.241154
## ar1     0.177990    0.029511  6.03130 0.000000
## omega   0.119387    0.049947  2.39025 0.016837
## alpha1  0.296491    0.100608  2.94700 0.003209
## alpha2  0.000000    0.156087  0.00000 1.000000
## beta1   0.287720    0.371928  0.77359 0.439173
## beta2   0.241004    0.268982  0.89599 0.370260
## gamma1 -0.153322    0.159287 -0.96255 0.335773
## gamma2  0.173352    0.194041  0.89338 0.371652
## shape   3.192795    0.354135  9.01576 0.000000
## 
## LogLikelihood : -1514.177 
## 
## Information Criteria
## ------------------------------------
##                    
## Akaike       1.8091
## Bayes        1.8413
## Shibata      1.8090
## Hannan-Quinn 1.8210
## 
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
##                         statistic  p-value
## Lag[1]                      1.299 0.254474
## Lag[2*(p+q)+(p+q)-1][2]     4.477 0.001474
## Lag[4*(p+q)+(p+q)-1][5]     9.235 0.002337
## d.o.f=1
## H0 : No serial correlation
## 
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
##                          statistic p-value
## Lag[1]                     0.07042  0.7907
## Lag[2*(p+q)+(p+q)-1][11]   0.78729  0.9986
## Lag[4*(p+q)+(p+q)-1][19]   1.65624  0.9999
## d.o.f=4
## 
## Weighted ARCH LM Tests
## ------------------------------------
##             Statistic Shape Scale P-Value
## ARCH Lag[5]   0.02525 0.500 2.000  0.8738
## ARCH Lag[7]   0.34650 1.473 1.746  0.9370
## ARCH Lag[9]   0.59338 2.402 1.619  0.9767
## 
## Nyblom stability test
## ------------------------------------
## Joint Statistic:  3.2882
## Individual Statistics:              
## mu     0.24585
## ar1    0.25662
## omega  0.26467
## alpha1 0.04532
## alpha2 0.10813
## beta1  0.19609
## beta2  0.22603
## gamma1 0.22515
## gamma2 0.16162
## shape  0.18857
## 
## 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           1.0303 0.3030    
## Negative Sign Bias  0.3804 0.7037    
## Positive Sign Bias  0.5197 0.6034    
## Joint Effect        1.0633 0.7859    
## 
## 
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
##   group statistic p-value(g-1)
## 1    20     14.79       0.7361
## 2    30     33.83       0.2455
## 3    40     40.55       0.4016
## 4    50     55.09       0.2553
## 
## 
## Elapsed time : 1.040069

5. COPULA

5.1. Mô hình biên phù hợp

SP500_model <-ugarchfit(data=SP500,spec=model.a22.g11.ss)
VNI_model <-ugarchfit(data=VNI,spec=model.a21.g21.g)
MERVAL_model <-ugarchfit(data=MERVAL,spec=model.a10.g22.s)
CROBEX_model <-ugarchfit(data=CROBEX,spec=model.a20.g11.n)
MASI_model <-ugarchfit(data=MASI,spec=model.a22.g21.s)
MSM30_model <-ugarchfit(data=MSM30,spec=model.a10.g22.s)

SP500.res <- residuals(SP500_model)/sigma(SP500_model)
VNI.res <- residuals(VNI_model)/sigma(VNI_model)
MERVAL.res <- residuals(MERVAL_model)/sigma(MERVAL_model)
CROBEX.res <- residuals(CROBEX_model)/sigma(CROBEX_model)
MASI.res <- residuals(MASI_model)/sigma(MASI_model)
MSM30.res <- residuals(MSM30_model)/sigma(MSM30_model)

fitdist(distribution = "sstd", SP500.res, control = list())$pars

##           mu        sigma         skew        shape 
## -0.001428282  0.997839491  0.815876284  4.599623664

fitdist(distribution = "ged", VNI.res, control = list())$pars

##           mu        sigma        shape 
## 0.0005988676 1.0022832274 0.9815752383

fitdist(distribution = "std", MERVAL.res, control = list())$pars

##          mu       sigma       shape 
## 0.003988353 0.992147256 3.833341122

fitdist(distribution = "norm", CROBEX.res, control = list())$pars

##          mu       sigma 
## 0.005003132 0.998559229

fitdist(distribution = "std", MASI.res, control = list())$pars

##           mu        sigma        shape 
## 0.0001140493 1.0097746626 3.1013611981

fitdist(distribution = "std", MSM30.res, control = list())$pars

##         mu      sigma      shape 
## 0.00826355 1.01201152 3.14114170

u <- pdist(distribution = "sstd", q = SP500.res, mu =-0.001428282 , sigma = 0.997839491, skew= 0.815876284,shape = 4.599623664)
v1 <- pdist(distribution = "ged", q = VNI.res, mu = 0.0005988676, sigma = 1.0022832274, shape = 0.9815752383)
v2 <- pdist(distribution = "std", q = MERVAL.res, mu = 0.003988353 , sigma = 0.992147256, shape = 3.833341122)
v3 <- pdist(distribution = "norm", q = CROBEX.res, mu = 0.005003132 , sigma = 0.998559229)
v4 <- pdist(distribution = "std", q = MASI.res, mu = 0.0001140493, sigma = 1.0097746626, shape = 3.1013611981)
v5 <- pdist(distribution = "std", q = MSM30.res, mu = 0.00826355  , sigma = 1.01201152, shape = 3.14114170 )

5.1. SP500 & VNI

BiCopEst(u, v1, family = 1, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    1
## Name:  Gaussian
## 
## Parameter(s)
## ------------
## par:  0.16
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.1 (empirical = 0.08, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  22.29 
## AIC:    -42.58 
## BIC:    -37.15

BiCopEst(u, v1, family = 2, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    2
## Name:  t
## 
## Parameter(s)
## ------------
## par:  0.13
## par2: 5.74
## Dependence measures
## -------------------
## Kendall's tau:    0.08 (empirical = 0.08, p value < 0.01)
## Upper TD:         0.06 
## Lower TD:         0.06 
## 
## Fit statistics
## --------------
## logLik:  44.68 
## AIC:    -85.35 
## BIC:    -74.49

BiCopEst(u, v1, family = 3, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    3
## Name:  Clayton
## 
## Parameter(s)
## ------------
## par:  0.17
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.08 (empirical = 0.08, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.02 
## 
## Fit statistics
## --------------
## logLik:  28.01 
## AIC:    -54.02 
## BIC:    -48.59

BiCopEst(u, v1, family = 13, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    13
## Name:  Survival Clayton
## 
## Parameter(s)
## ------------
## par:  0.2
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.09 (empirical = 0.08, p value < 0.01)
## Upper TD:         0.03 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  19.01 
## AIC:    -36.03 
## BIC:    -30.6

BiCopEst(u, v1, family = 4, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    4
## Name:  Gumbel
## 
## Parameter(s)
## ------------
## par:  1.12
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.11 (empirical = 0.08, p value < 0.01)
## Upper TD:         0.14 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  26.69 
## AIC:    -51.38 
## BIC:    -45.95

BiCopEst(u, v1, family = 14, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    14
## Name:  Survival Gumbel
## 
## Parameter(s)
## ------------
## par:  1.09
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.09 (empirical = 0.08, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.11 
## 
## Fit statistics
## --------------
## logLik:  33.47 
## AIC:    -64.93 
## BIC:    -59.5

BiCopEst(u, v1, family = 5, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    5
## Name:  Frank
## 
## Parameter(s)
## ------------
## par:  0.75
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.08 (empirical = 0.08, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  12.47 
## AIC:    -22.94 
## BIC:    -17.51

BiCopEst(u, v1, family = 6, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    6
## Name:  Joe
## 
## Parameter(s)
## ------------
## par:  1.16
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.08 (empirical = 0.08, p value < 0.01)
## Upper TD:         0.18 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  21.29 
## AIC:    -40.58 
## BIC:    -35.15

BiCopEst(u, v1, family = 16, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    16
## Name:  Survival Joe
## 
## Parameter(s)
## ------------
## par:  1.11
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.08, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.13 
## 
## Fit statistics
## --------------
## logLik:  30.38 
## AIC:    -58.76 
## BIC:    -53.33

BiCopEst(u, v1, family = 7, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    7
## Name:  BB1
## 
## Parameter(s)
## ------------
## par:  0.11
## par2: 1.07
## Dependence measures
## -------------------
## Kendall's tau:    0.11 (empirical = 0.08, p value < 0.01)
## Upper TD:         0.09 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  35.45 
## AIC:    -66.89 
## BIC:    -56.03

BiCopEst(u, v1, family = 17, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    17
## Name:  Survival BB1
## 
## Parameter(s)
## ------------
## par:  0.1
## par2: 1.07
## Dependence measures
## -------------------
## Kendall's tau:    0.11 (empirical = 0.08, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.08 
## 
## Fit statistics
## --------------
## logLik:  37.66 
## AIC:    -71.32 
## BIC:    -60.47

BiCopEst(u, v1, family = 8, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    8
## Name:  BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.12
## Dependence measures
## -------------------
## Kendall's tau:    0.11 (empirical = 0.08, p value < 0.01)
## Upper TD:         0.14 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  26.67 
## AIC:    -49.34 
## BIC:    -38.48

BiCopEst(u, v1, family = 18, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    18
## Name:  Survival BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.09
## Dependence measures
## -------------------
## Kendall's tau:    0.09 (empirical = 0.08, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.12 
## 
## Fit statistics
## --------------
## logLik:  33.45 
## AIC:    -62.9 
## BIC:    -52.04

BiCopEst(u, v1, family = 9, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    9
## Name:  BB7
## 
## Parameter(s)
## ------------
## par:  1.11
## par2: 0.13
## Dependence measures
## -------------------
## Kendall's tau:    0.11 (empirical = 0.08, p value < 0.01)
## Upper TD:         0.13 
## Lower TD:         0.01 
## 
## Fit statistics
## --------------
## logLik:  38.07 
## AIC:    -72.15 
## BIC:    -61.29

BiCopEst(u, v1, family = 19, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    19
## Name:  Survival BB7
## 
## Parameter(s)
## ------------
## par:  1.09
## par2: 0.14
## Dependence measures
## -------------------
## Kendall's tau:    0.11 (empirical = 0.08, p value < 0.01)
## Upper TD:         0.01 
## Lower TD:         0.11 
## 
## Fit statistics
## --------------
## logLik:  39.58 
## AIC:    -75.15 
## BIC:    -64.29

BiCopEst(u, v1, family = 10, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    10
## Name:  BB8
## 
## Parameter(s)
## ------------
## par:  1.16
## par2: 1
## Dependence measures
## -------------------
## Kendall's tau:    0.08 (empirical = 0.08, p value < 0.01)
## Upper TD:         0.18 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  21.29 
## AIC:    -38.58 
## BIC:    -27.72

BiCopEst(u, v1, family = 20, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    20
## Name:  Survival BB8
## 
## Parameter(s)
## ------------
## par:  1.11
## par2: 1
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.08, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.13 
## 
## Fit statistics
## --------------
## logLik:  30.38 
## AIC:    -56.76 
## BIC:    -45.9

5.2. SP500 & MERVAL

BiCopEst(u, v2, family = 1, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    1
## Name:  Gaussian
## 
## Parameter(s)
## ------------
## par:  0.37
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.24 (empirical = 0.25, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  122.63 
## AIC:    -243.26 
## BIC:    -237.83

BiCopEst(u, v2, family = 2, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    2
## Name:  t
## 
## Parameter(s)
## ------------
## par:  0.37
## par2: 8.21
## Dependence measures
## -------------------
## Kendall's tau:    0.24 (empirical = 0.25, p value < 0.01)
## Upper TD:         0.07 
## Lower TD:         0.07 
## 
## Fit statistics
## --------------
## logLik:  136.32 
## AIC:    -268.63 
## BIC:    -257.77

BiCopEst(u, v2, family = 3, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    3
## Name:  Clayton
## 
## Parameter(s)
## ------------
## par:  0.48
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.19 (empirical = 0.25, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.23 
## 
## Fit statistics
## --------------
## logLik:  111.95 
## AIC:    -221.9 
## BIC:    -216.47

BiCopEst(u, v2, family = 13, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    13
## Name:  Survival Clayton
## 
## Parameter(s)
## ------------
## par:  0.44
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.18 (empirical = 0.25, p value < 0.01)
## Upper TD:         0.21 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  83.68 
## AIC:    -165.37 
## BIC:    -159.94

BiCopEst(u, v2, family = 4, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    4
## Name:  Gumbel
## 
## Parameter(s)
## ------------
## par:  1.29
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.23 (empirical = 0.25, p value < 0.01)
## Upper TD:         0.29 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  110.44 
## AIC:    -218.88 
## BIC:    -213.45

BiCopEst(u, v2, family = 14, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    14
## Name:  Survival Gumbel
## 
## Parameter(s)
## ------------
## par:  1.29
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.22 (empirical = 0.25, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.29 
## 
## Fit statistics
## --------------
## logLik:  125.18 
## AIC:    -248.36 
## BIC:    -242.93

BiCopEst(u, v2, family = 5, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    5
## Name:  Frank
## 
## Parameter(s)
## ------------
## par:  2.37
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.25 (empirical = 0.25, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  117.92 
## AIC:    -233.85 
## BIC:    -228.42

BiCopEst(u, v2, family = 6, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    6
## Name:  Joe
## 
## Parameter(s)
## ------------
## par:  1.35
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.16 (empirical = 0.25, p value < 0.01)
## Upper TD:         0.33 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  74.25 
## AIC:    -146.49 
## BIC:    -141.06

BiCopEst(u, v2, family = 16, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    16
## Name:  Survival Joe
## 
## Parameter(s)
## ------------
## par:  1.37
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.17 (empirical = 0.25, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.34 
## 
## Fit statistics
## --------------
## logLik:  100.32 
## AIC:    -198.64 
## BIC:    -193.21

BiCopEst(u, v2, family = 7, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    7
## Name:  BB1
## 
## Parameter(s)
## ------------
## par:  0.26
## par2: 1.16
## Dependence measures
## -------------------
## Kendall's tau:    0.24 (empirical = 0.25, p value < 0.01)
## Upper TD:         0.18 
## Lower TD:         0.1 
## 
## Fit statistics
## --------------
## logLik:  133.38 
## AIC:    -262.76 
## BIC:    -251.9

BiCopEst(u, v2, family = 17, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    17
## Name:  Survival BB1
## 
## Parameter(s)
## ------------
## par:  0.15
## par2: 1.22
## Dependence measures
## -------------------
## Kendall's tau:    0.24 (empirical = 0.25, p value < 0.01)
## Upper TD:         0.02 
## Lower TD:         0.23 
## 
## Fit statistics
## --------------
## logLik:  131.01 
## AIC:    -258.03 
## BIC:    -247.17

BiCopEst(u, v2, family = 8, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    8
## Name:  BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.29
## Dependence measures
## -------------------
## Kendall's tau:    0.23 (empirical = 0.25, p value < 0.01)
## Upper TD:         0.29 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  110.36 
## AIC:    -216.72 
## BIC:    -205.86

BiCopEst(u, v2, family = 18, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    18
## Name:  Survival BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.29
## Dependence measures
## -------------------
## Kendall's tau:    0.22 (empirical = 0.25, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.29 
## 
## Fit statistics
## --------------
## logLik:  125.14 
## AIC:    -246.27 
## BIC:    -235.41

BiCopEst(u, v2, family = 9, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    9
## Name:  BB7
## 
## Parameter(s)
## ------------
## par:  1.19
## par2: 0.38
## Dependence measures
## -------------------
## Kendall's tau:    0.23 (empirical = 0.25, p value < 0.01)
## Upper TD:         0.21 
## Lower TD:         0.16 
## 
## Fit statistics
## --------------
## logLik:  130.46 
## AIC:    -256.92 
## BIC:    -246.06

BiCopEst(u, v2, family = 19, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    19
## Name:  Survival BB7
## 
## Parameter(s)
## ------------
## par:  1.26
## par2: 0.29
## Dependence measures
## -------------------
## Kendall's tau:    0.22 (empirical = 0.25, p value < 0.01)
## Upper TD:         0.09 
## Lower TD:         0.26 
## 
## Fit statistics
## --------------
## logLik:  126.87 
## AIC:    -249.74 
## BIC:    -238.89

5.3. sp500 & CROBEX

BiCopEst(u, v3, family = 1, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    1
## Name:  Gaussian
## 
## Parameter(s)
## ------------
## par:  0.19
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.12 (empirical = 0.1, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  29.37 
## AIC:    -56.75 
## BIC:    -51.32

BiCopEst(u, v3, family = 2, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    2
## Name:  t
## 
## Parameter(s)
## ------------
## par:  0.17
## par2: 11.46
## Dependence measures
## -------------------
## Kendall's tau:    0.11 (empirical = 0.1, p value < 0.01)
## Upper TD:         0.01 
## Lower TD:         0.01 
## 
## Fit statistics
## --------------
## logLik:  48.94 
## AIC:    -93.89 
## BIC:    -83.03

BiCopEst(u, v3, family = 3, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    3
## Name:  Clayton
## 
## Parameter(s)
## ------------
## par:  0.14
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.1, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.01 
## 
## Fit statistics
## --------------
## logLik:  32.69 
## AIC:    -63.38 
## BIC:    -57.95

BiCopEst(u, v3, family = 13, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    13
## Name:  Survival Clayton
## 
## Parameter(s)
## ------------
## par:  0.14
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.07 (empirical = 0.1, p value < 0.01)
## Upper TD:         0.01 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  16.24 
## AIC:    -30.48 
## BIC:    -25.06

BiCopEst(u, v3, family = 4, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    4
## Name:  Gumbel
## 
## Parameter(s)
## ------------
## par:  1.11
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.1 (empirical = 0.1, p value < 0.01)
## Upper TD:         0.13 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  24.38 
## AIC:    -46.77 
## BIC:    -41.34

BiCopEst(u, v3, family = 14, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    14
## Name:  Survival Gumbel
## 
## Parameter(s)
## ------------
## par:  1.09
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.09 (empirical = 0.1, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.12 
## 
## Fit statistics
## --------------
## logLik:  37.66 
## AIC:    -73.32 
## BIC:    -67.89

BiCopEst(u, v3, family = 5, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    5
## Name:  Frank
## 
## Parameter(s)
## ------------
## par:  1.1
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.12 (empirical = 0.1, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  19.62 
## AIC:    -37.24 
## BIC:    -31.81

BiCopEst(u, v3, family = 6, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    6
## Name:  Joe
## 
## Parameter(s)
## ------------
## par:  1.1
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.1, p value < 0.01)
## Upper TD:         0.12 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  13.39 
## AIC:    -24.77 
## BIC:    -19.35

BiCopEst(u, v3, family = 16, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    16
## Name:  Survival Joe
## 
## Parameter(s)
## ------------
## par:  1.1
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.1, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.12 
## 
## Fit statistics
## --------------
## logLik:  31.4 
## AIC:    -60.8 
## BIC:    -55.37

BiCopEst(u, v3, family = 7, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    7
## Name:  BB1
## 
## Parameter(s)
## ------------
## par:  0.1
## par2: 1.06
## Dependence measures
## -------------------
## Kendall's tau:    0.1 (empirical = 0.1, p value < 0.01)
## Upper TD:         0.08 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  41.71 
## AIC:    -79.43 
## BIC:    -68.57

BiCopEst(u, v3, family = 17, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    17
## Name:  Survival BB1
## 
## Parameter(s)
## ------------
## par:  0.08
## par2: 1.07
## Dependence measures
## -------------------
## Kendall's tau:    0.1 (empirical = 0.1, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.09 
## 
## Fit statistics
## --------------
## logLik:  42.49 
## AIC:    -80.97 
## BIC:    -70.11

BiCopEst(u, v3, family = 8, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    8
## Name:  BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.11
## Dependence measures
## -------------------
## Kendall's tau:    0.1 (empirical = 0.1, p value < 0.01)
## Upper TD:         0.13 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  24.31 
## AIC:    -44.61 
## BIC:    -33.75

BiCopEst(u, v3, family = 18, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    18
## Name:  Survival BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.09
## Dependence measures
## -------------------
## Kendall's tau:    0.09 (empirical = 0.1, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.12 
## 
## Fit statistics
## --------------
## logLik:  37.61 
## AIC:    -71.22 
## BIC:    -60.36

BiCopEst(u, v3, family = 9, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    9
## Name:  BB7
## 
## Parameter(s)
## ------------
## par:  1.07
## par2: 0.12
## Dependence measures
## -------------------
## Kendall's tau:    0.09 (empirical = 0.1, p value < 0.01)
## Upper TD:         0.09 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  40.65 
## AIC:    -77.3 
## BIC:    -66.44

BiCopEst(u, v3, family = 19, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    19
## Name:  Survival BB7
## 
## Parameter(s)
## ------------
## par:  1.08
## par2: 0.11
## Dependence measures
## -------------------
## Kendall's tau:    0.09 (empirical = 0.1, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.1 
## 
## Fit statistics
## --------------
## logLik:  41.68 
## AIC:    -79.36 
## BIC:    -68.5

5.4. SP500 & MASI

BiCopEst(u, v4, family = 1, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    1
## Name:  Gaussian
## 
## Parameter(s)
## ------------
## par:  0.1
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.07 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  8.95 
## AIC:    -15.89 
## BIC:    -10.46

BiCopEst(u, v4, family = 2, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    2
## Name:  t
## 
## Parameter(s)
## ------------
## par:  0.1
## par2: 21.92
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  10.72 
## AIC:    -17.44 
## BIC:    -6.59

BiCopEst(u, v4, family = 3, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    3
## Name:  Clayton
## 
## Parameter(s)
## ------------
## par:  0.11
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  8.82 
## AIC:    -15.64 
## BIC:    -10.21

BiCopEst(u, v4, family = 13, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    13
## Name:  Survival Clayton
## 
## Parameter(s)
## ------------
## par:  0.1
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  6.35 
## AIC:    -10.69 
## BIC:    -5.27

BiCopEst(u, v4, family = 4, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    4
## Name:  Gumbel
## 
## Parameter(s)
## ------------
## par:  1.06
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.06, p value < 0.01)
## Upper TD:         0.07 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  7.09 
## AIC:    -12.17 
## BIC:    -6.74

BiCopEst(u, v4, family = 14, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    14
## Name:  Survival Gumbel
## 
## Parameter(s)
## ------------
## par:  1.06
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.07 
## 
## Fit statistics
## --------------
## logLik:  9.81 
## AIC:    -17.63 
## BIC:    -12.2

BiCopEst(u, v4, family = 5, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    5
## Name:  Frank
## 
## Parameter(s)
## ------------
## par:  0.54
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  6.79 
## AIC:    -11.59 
## BIC:    -6.16

BiCopEst(u, v4, family = 6, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    6
## Name:  Joe
## 
## Parameter(s)
## ------------
## par:  1.06
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.03 (empirical = 0.06, p value < 0.01)
## Upper TD:         0.08 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  4.63 
## AIC:    -7.26 
## BIC:    -1.83

BiCopEst(u, v4, family = 16, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    16
## Name:  Survival Joe
## 
## Parameter(s)
## ------------
## par:  1.07
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.04 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.09 
## 
## Fit statistics
## --------------
## logLik:  7.99 
## AIC:    -13.99 
## BIC:    -8.56

BiCopEst(u, v4, family = 7, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    7
## Name:  BB1
## 
## Parameter(s)
## ------------
## par:  0.08
## par2: 1.03
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.06, p value < 0.01)
## Upper TD:         0.04 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  10.3 
## AIC:    -16.61 
## BIC:    -5.75

BiCopEst(u, v4, family = 17, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    17
## Name:  Survival BB1
## 
## Parameter(s)
## ------------
## par:  0.05
## par2: 1.04
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.06 
## 
## Fit statistics
## --------------
## logLik:  10.94 
## AIC:    -17.88 
## BIC:    -7.02

BiCopEst(u, v4, family = 8, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    8
## Name:  BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.05
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.06, p value < 0.01)
## Upper TD:         0.07 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  7.06 
## AIC:    -10.12 
## BIC:    0.74

BiCopEst(u, v4, family = 18, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    18
## Name:  Survival BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.06
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.07 
## 
## Fit statistics
## --------------
## logLik:  9.8 
## AIC:    -15.6 
## BIC:    -4.74

BiCopEst(u, v4, family = 9, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    9
## Name:  BB7
## 
## Parameter(s)
## ------------
## par:  1.04
## par2: 0.09
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.06, p value < 0.01)
## Upper TD:         0.05 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  10.33 
## AIC:    -16.66 
## BIC:    -5.8

BiCopEst(u, v4, family = 19, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    19
## Name:  Survival BB7
## 
## Parameter(s)
## ------------
## par:  1.05
## par2: 0.07
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.06, p value < 0.01)
## Upper TD:         0 
## Lower TD:         0.07 
## 
## Fit statistics
## --------------
## logLik:  11.04 
## AIC:    -18.09 
## BIC:    -7.23

5.5. SP500 & MSM30

BiCopEst(u, v5, family = 1, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    1
## Name:  Gaussian
## 
## Parameter(s)
## ------------
## par:  0.07
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.04 (empirical = 0.04, p value = 0.02)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  3.79 
## AIC:    -5.59 
## BIC:    -0.16

BiCopEst(u, v5, family = 2, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    2
## Name:  t
## 
## Parameter(s)
## ------------
## par:  0.06
## par2: 7.03
## Dependence measures
## -------------------
## Kendall's tau:    0.04 (empirical = 0.04, p value = 0.02)
## Upper TD:         0.03 
## Lower TD:         0.03 
## 
## Fit statistics
## --------------
## logLik:  19.1 
## AIC:    -34.2 
## BIC:    -23.34

BiCopEst(u, v5, family = 3, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    3
## Name:  Clayton
## 
## Parameter(s)
## ------------
## par:  0.09
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.04 (empirical = 0.04, p value = 0.02)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  7.49 
## AIC:    -12.98 
## BIC:    -7.55

BiCopEst(u, v5, family = 13, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    13
## Name:  Survival Clayton
## 
## Parameter(s)
## ------------
## par:  0.08
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.04 (empirical = 0.04, p value = 0.02)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  3.75 
## AIC:    -5.5 
## BIC:    -0.07

BiCopEst(u, v5, family = 4, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    4
## Name:  Gumbel
## 
## Parameter(s)
## ------------
## par:  1.05
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.04, p value = 0.02)
## Upper TD:         0.06 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  5.58 
## AIC:    -9.17 
## BIC:    -3.74

BiCopEst(u, v5, family = 14, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    14
## Name:  Survival Gumbel
## 
## Parameter(s)
## ------------
## par:  1.05
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.04 (empirical = 0.04, p value = 0.02)
## Upper TD:         0 
## Lower TD:         0.06 
## 
## Fit statistics
## --------------
## logLik:  10.08 
## AIC:    -18.17 
## BIC:    -12.74

BiCopEst(u, v5, family = 5, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    5
## Name:  Frank
## 
## Parameter(s)
## ------------
## par:  0.36
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.04 (empirical = 0.04, p value = 0.02)
## Upper TD:         0 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  2.9 
## AIC:    -3.8 
## BIC:    1.63

BiCopEst(u, v5, family = 6, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    6
## Name:  Joe
## 
## Parameter(s)
## ------------
## par:  1.06
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.03 (empirical = 0.04, p value = 0.02)
## Upper TD:         0.08 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  4.35 
## AIC:    -6.7 
## BIC:    -1.27

BiCopEst(u, v5, family = 16, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    16
## Name:  Survival Joe
## 
## Parameter(s)
## ------------
## par:  1.06
## 
## Dependence measures
## -------------------
## Kendall's tau:    0.03 (empirical = 0.04, p value = 0.02)
## Upper TD:         0 
## Lower TD:         0.07 
## 
## Fit statistics
## --------------
## logLik:  9.48 
## AIC:    -16.97 
## BIC:    -11.54

BiCopEst(u, v5, family = 7, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    7
## Name:  BB1
## 
## Parameter(s)
## ------------
## par:  0.06
## par2: 1.03
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.04, p value = 0.02)
## Upper TD:         0.03 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  8.73 
## AIC:    -13.46 
## BIC:    -2.6

BiCopEst(u, v5, family = 17, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    17
## Name:  Survival BB1
## 
## Parameter(s)
## ------------
## par:  0.03
## par2: 1.04
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.04, p value = 0.02)
## Upper TD:         0 
## Lower TD:         0.05 
## 
## Fit statistics
## --------------
## logLik:  10.62 
## AIC:    -17.23 
## BIC:    -6.37

BiCopEst(u, v5, family = 8, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    8
## Name:  BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.05
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.04, p value = 0.02)
## Upper TD:         0.06 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  5.57 
## AIC:    -7.14 
## BIC:    3.72

BiCopEst(u, v5, family = 18, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    18
## Name:  Survival BB6
## 
## Parameter(s)
## ------------
## par:  1
## par2: 1.04
## Dependence measures
## -------------------
## Kendall's tau:    0.04 (empirical = 0.04, p value = 0.02)
## Upper TD:         0 
## Lower TD:         0.06 
## 
## Fit statistics
## --------------
## logLik:  10.08 
## AIC:    -16.16 
## BIC:    -5.3

BiCopEst(u, v5, family = 9, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    9
## Name:  BB7
## 
## Parameter(s)
## ------------
## par:  1.04
## par2: 0.07
## Dependence measures
## -------------------
## Kendall's tau:    0.06 (empirical = 0.04, p value = 0.02)
## Upper TD:         0.05 
## Lower TD:         0 
## 
## Fit statistics
## --------------
## logLik:  9.26 
## AIC:    -14.53 
## BIC:    -3.67

BiCopEst(u, v5, family = 19, method = "mle", se = F) %>% summary()

## Family
## ------ 
## No:    19
## Name:  Survival BB7
## 
## Parameter(s)
## ------------
## par:  1.05
## par2: 0.05
## Dependence measures
## -------------------
## Kendall's tau:    0.05 (empirical = 0.04, p value = 0.02)
## Upper TD:         0 
## Lower TD:         0.06 
## 
## Fit statistics
## --------------
## logLik:  11.11 
## AIC:    -18.22 
## BIC:    -7.36