GARCH(1,1) reaction to one-off shocks

The GARCH approach models the variance using the prediction errors \(e_t\) (also called shocks or unexpected returns). The parameter \(\alpha\) determines the reactivity to \(e_t^2\) , while \(\beta\) is the weight on the previous variance prediction.

In this exercise, we consider the series of squared prediction errors e2 <- c(10,25,rep(10,20)). We plot the variance for:

• \(\alpha=0.1\) and \(\beta=0.8\)
• \(\alpha=0.19\) and \(\beta=0.8\)
• \(\alpha=0.1\) and \(\beta=0.89\).

We set \(\omega\) such that the long term variance is 10.

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Which statement about the effect of the shock on the variance is wrong?