Volatility forecast using ARIMA GARCH I am trying to forecast the volatility of the pair of currency USD/GBP. I am using python ans I used a GARCH model on the returns, but later on I found that I can fit an ARIMA-GARCH model to forecast the volatility too, except that I didn't find strong articles/references that explain if using an ARIMA-GARCH will give me the same results (a forecast of the volatility of the pair ).
If I am using a GARCH(1.1) model then I will be applying it on the returns directly, however, if using an ARIMA-GARCH(1.1) model then I will be applying the GARCH model on the residuals of the ARIMA model.
Which of the two methods will better help me achieve my purpose?

Regardless of the conditional mean model (constant, ARMA or something else), GARCH is a model for the conditional variance of the variable of interest (e.g. return on exchange rate).* Combined with a conditional mean model and a distributional assumption for the standardized innovations it becomes a model of the conditional distribution of the random variable of interest; see e.g. this.
Whether a constant mean or an ARMA will be a better fit for your data depends on... your data. Currency exchange rates are notoriously difficult to predict, so I doubt ARMA would do a better job than a constant mean when forecasting out of sample. (In sample ARMA will inevitably provide a better fit as it is a more flexible model, but it is usually the out-of-sample forecast ability that counts.) You may try both models and compare the them in terms of AIC and/or using time-series cross validation via rolling windows.
*Equivalently, GARCH is a model of the variance of the zero-mean residual that is obtained by subtracting the conditional mean from the variable of interest.
