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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.


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

This exercise is part of the course

GARCH Models in R

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