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")

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