I have heteroskedastic and serrialy correlated (autocorrelated) panel data. I want to test it with both dynamic and static models. For the dynamic test, I use GMM and the results of GMM is parallel to results of Newey-West estimator. Newey-West estimator is OLS estimator that robust disturbances heteroscedastic and autocorrelated of type MA(q)^2. But, whenever I test the model with fixed effect regression, I find completely different results.
How can I understand what type of the autocorrelation my data has and which estimator should I use? I don't understand the differences between these estimators and below commands in terms of application.