I have a conceptual question that I haven't managed to grasp yet and is most likely a econometrics 101 question by here it goes:
If we estimate a GARCH model for a time series, how do we then use this in my model for the returns? For example; I have the return data of an index. I know that I have volatility clustering in this data. I find a suitable GARCH model for the volatility (variance). Now, if I model the returns an a suitable model, i.e. a regression model, and look at the coefficients and the p-values that it spits out, these values are still based on the regular OLS assumptions right? How do I make use of the GARCH in this model so that I can get coefficients and p-values that have accounted for the conditional heteroscedastic variances in the time series?