I want to try fitting an ARMA/GARCH model but want a methodological approach rather than fitting different models and picking the best one. However, I'm not sure how to choose my AR and MA terms for my mean equation, same thing for my variance equation. Hence I have the following queries:
Are there any conventions/guidelines for choosing these by looking at the ACF/PACF of returns and squared returns?
How are the coefficients estimated?Are the coefficients of the ARMA estimated first, then a GARCH fitted to the residuals?or are they estimate in parallel?
Also I read on wikipedia that the Ljung-Box test should be applied to the residuals of an ARIMA model to detect the presence of heteroscedasticty, but I saw also some people applying it on squared returns. Are these two the same?If not, what's the difference between the two?