GARCH modelling is variance modelling. The conditional variance is modelled autoregressively. That is why the model is called generalized autoregressive conditional heteroscedastic. It is not a ideterministic model but stochastic. Where is the deterministic form of the model?

Dear Ette Etuk,

Thank you for your input. Although conditional variance equation takes autoregressive form, it is widely documented that it is indeed deterministic process. However, the conditional mean is stochastic process.

Consider Garch(1,1). It is given by sigma(t)squared=alpha0 + alpha1*y(t-1)squared+ beta1*sigma(t-1)squared. This is not deterministic.

You just stated the specification of GARCH(1,1). It would be better if you could justify that this is stochastic.

Both the conditional mean and conditional variance are deterministic because taking conditional expectations eliminates the random error term.

The exponential GARCH (EGARCH) model is a GARCH variant that models the logarithm of the conditional variance process. In addition to modeling the logarithm, the EGARCH model has additional leverage terms to capture asymmetry in volatility clustering.