If an ARIMA model converges quickly, would using GARCH improve the forecast performance? By improve I mean provide longer time periods for forecasts. Basically trying to forecast returns.
Without testing it is hard to know. I am assuming you are trying to predict volatility and not returns. Hansen and Lunde (2005) concluded that hardly anything beats a Garch(1,1) for a stock and an exchange rate. But this conclusion could be re markedly different for another assets. There is know way to tell a priori. You need to run the models out-of-sample and see what performs better.