I have been working on a time series where after the first difference, I observe heteroskedasticity. To handle the situation, I found that ARCH/GARCH models are used typically.
When I read about the procedure, they say that the time series is first fitted with a conditional mean model like AR or ARMA and ARCH/GARCH model is applied to the residuals of the fitted AR/ARMA model.
My questions are:
Why do we have to fit AR/ARMA?
Why do we have to apply ARCH/GARCH to the residuals? Is that done to model the volatility in the residuals or the volatility in the actual data (differenced data)?
If it is used to model the volatility of the residuals, how is that going to help in modeling the volatility in the actual data?