Exercise

# 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**?

Instructions

**50 XP**

##### Possible Answers

- The variance shoots up and then returns to \(\omega/(1-\alpha-\beta)\).
- The larger is \(\alpha\), the larger is the immediate impact of the shock.
- Holding fixed \(\alpha\), the larger is \(\beta\), the longer is the duration of the impact.
- The triangles show the variance when \(\alpha=0.1\) and \(\beta=0.8\).