GARCH and many other time series models are estimated using maximum likelihood methods (MLE). The common measure of in-sample fit is the information criterion such as Akaike (AIC) or Bayesian (BIC). These are computed using the loglikelihoods.

GARCH and many other time series models are estimated using maximum likelihood methods (MLE). The common measure of in-sample fit is the information criterion such as Akaike (AIC) or Bayesian (BIC). These are computed using the loglikelihoods.

I sometimes use FVU, which may feel more familiar to you if you're used to $R^2$. Its problem is that it doesn't account for parsimony though, that's why it's my last resort tool when AIC is not applicable