For a project I need to fit a GARCH(1,1) model to the log returns of an index. When using the residuals of an ARMA or ARIMA model it is clear that the (conditional) mean is 0. When using the log returns, do I have to do centering first? I know that log returns tend to be stationary, but that is only for the unconditional moments. And will centering in that case only make the unconditional or also the conditional mean zero? I feel like I'm mixing things up a bit.
I found a similar question here, but that didn't fully help me understand.
Thanks in advance! Any help is appreciated!