ARCH模型和GARCH模型

基于ARCH（1）模型模拟生成收益序列，残差序列和波动率序列

library(fGarch)

set.seed(1234)

#模型的设定
spec_1<-garchSpec(model=list(omega=.01,alpha=.85,beta=0))

#模型的模拟
simdata_1<-garchSim(spec_1,n=200,extended=T)
plot(simdata_1)

par(mfrow=c(1,3))

acf(simdata_1$eps,main="resid series",xlab="lags")

acf(simdata_1$garch,main="simulations data",xlab="lags")

acf(simdata_1$garch^2,main="squared sim data",xlab="lags")

​编辑​编辑

library(FinTS)

ArchTest(simdata_1$garch,lags=12)

        ARCH LM-test; Null hypothesis: no ARCH effects

data:  simdata_1$garch
Chi-squared = 93.981, df = 12, p-value = 8.327e-15

ArchTest(simdata_1$eps,lags=12)

        ARCH LM-test; Null hypothesis: no ARCH effects

data:  simdata_1$eps
Chi-squared = 10.863, df = 12, p-value = 0.5407

GARCH（1,1）模型的模拟

spec_2<-garchSpec(model=list(omega=.01,alpha=.85,beta=.1))
simdata_2<-garchSim(spec_2,n=200,extended=T)
class(simdata_2)
[1] "timeSeries"
attr(,"package")
[1] "timeSeries"
par(mfrow=c(1,3))
plot(simdata_2)
​编辑​编辑

plot(simdata_2$eps,type="l",xlab="D",)
plot(simdata_2$garch,type="l",xlab="D")
plot(simdata_2$sigma,type="l",xlab="D")
​编辑​编辑

acf(simdata_2$eps,xlag="lags")

acf(simdata_2$garch,xlab="lag")

acf(simdata_2$garch^2,xlab="lag")

ArchTest(simdata_2$garch,lags=12)

        ARCH LM-test; Null hypothesis: no ARCH effects

data:  simdata_2$garch
Chi-squared = 32.738, df = 12, p-value = 0.001063

ArchTest(simdata_2$eps,lags=12)

        ARCH LM-test; Null hypothesis: no ARCH effects

data:  simdata_2$eps
Chi-squared = 12.762, df = 12, p-value = 0.3866