# The difference between garch{tseries} and garchFit{fGarch}. the acf of residuals^2 are different. What's wrong?

by linlin   Last Updated September 12, 2019 01:19 AM

I simulate a garch(1,1) series, and use garch and garchFit to build model.

the acf plots of residual of garch and garchFit model is quite similar. But the acf plots of residual^2 are different, the acf of residuals^2 of garch{tseries} shows the process is white noise, but the acf of residuals^2 of garchFit{fGarch} shows that the process is not white noise. Is there anything wrong?

``````# alpha_1 = 0.5 and beta_1 = 0.3
set.seed(2)
a0 <- 0.2
a1 <- 0.5
b1 <- 0.3
w <- rnorm(10000)
eps <- rep(0, 10000)
sigsq <- rep(0, 10000)
for (i in 2:10000) {
sigsq[i] <- a0 + a1 * (eps[i-1]^2) + b1 * sigsq[i-1]
eps[i] <- w[i]*sqrt(sigsq[i])
}

# Plot the correlograms of both the residuals
# and the squared residuals
acf(eps)
acf(eps^2)

# Include the tseries time series library
require(tseries)

# Fit a GARCH model to the series and calculate
# confidence intervals for the parameters at the
# 97.5% level
eps.garch <- garch(eps, trace=FALSE)
confint(eps.garch)
acf(eps.garch$$residuals,na.action = na.pass) acf(eps.garch$$residuals^2,na.action = na.pass) # white noise process

eps.fitgarch <- garchFit(~garch(1,1), data = eps)
acf([email protected])
acf([email protected]^2) # not white noise process```

``````
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