# Why is a GARCH model useful?

As I understand it, one can model changing variance of a time series process with a GARCH model. What I don't understand is, how can one actually make predictions with this? Since $$y_t = \sigma_t \epsilon_t$$ with $\epsilon_t$ being a Gauss-distributed random variable, the expected value of this is always zero. So how does it help to know, how big the variance is, when both an up and a down are equally likely?
Or did I understand something wrong?

• Ok, so it is also not used in combination with for example ARIMA, to give better predictions? – Luca Thiede Nov 20 '17 at 20:20
• Check out existing questions on GARCH models; perhaps your question has already been answered. See e.g. this or these. Actually, I am pretty sure there has been at least one question which is either very similar or the same as yours. – Richard Hardy Nov 20 '17 at 20:22
• See also this and this which may be helpful. – Richard Hardy Nov 20 '17 at 20:31