I am working on time series data and have both conditional mean and conditional variance in the process. My strategy has so far been to fit a GARCH on the residuals of a fitted ARMA model.

But then I stumbled upon some questions (here is a link to one of them), where it stated that you should do the simultaneous one since it's the most effective and otherwise you'll get inconsistent parameter estimates. This was made by @RichardHardy and seems to be really sound advice.

The question I have is if anyone can confirm this and more preferably post a reference to it. I've been searching for some confirmation for hours with no prevail.