I found an article where they fit an ARIMA(p,d,q) model to a time series and then fit a GARCH(p,d,q) to the residual of the ARIMA (the parameters (p,d,q) are passed as the volatility model lags to the GARCH model and not as the mean model lags).
I know that the inconsistencies of doing them serially have been discussed here, here and in other posts. However, my question is if it is valid to reuse the lags of the ARIMA to fit the GARCH model. The traditional ARMA(p,q)-GARCH(r,s) does not do so and I could not find any reference supporting this.