I have read that the presence of autocorrelation detected in the log return can be removed by fitting the simplest plausible ARMA (p, q) model to the data. This autocorrelation was detected using a Ljung-Box test. Furthermore the autocorrelation detected in the squared log returns (using Ljung-Box), indicate that there exists conditional heteroskedasticity of the exchange rate returns series which could be removed by fitting the simplest plausible GARCH model to the ARMA filtered data.
Can someone tell me if this is the correct way how to go about testing the data whether we should fit an ARMA model to the data?
Furthermore can someone direct me to a good reference on why is it more efficient to fit an ARMA-GARCH model at once rather than first fitting an ARMA model, and then fitting a GARCH model on the residuals?