When estimating an AR, ADL and VAR model, should I use robust standard errors or HAC errors? In an exercise, I used the robust standard error, and then check for autocorrelation in the residuls (there is none). Is this approach ok?
For dealing with autocorrelation one typically uses either a model that appropriately incorporates the autoregressive structure (e.g., AR, ADL, VAR, ARIMA, etc.) or treats it as a nuisance parameter (i.e., ignores it in the estimation) and corrects the standard errors afterwards.
So in your case (AR/ADL/VAR), there should be no remaining autocorrelation in the residuals and then you also don't need HAC standard errors. If there were remaining autocorrelation, the model itself would need to be improved and not just the standard errors adjusted.
Heteroscedasticity consistent/robust standard errors might make sense in addition to an autoregressive model. However, rather than adjusting for unstructured heteroscedastiticy it is often more natural to check for autoregressive heteroscedasticity (i.e., GARCH-type) effects. If necessary one could then use an AR-GARCH model etc.