Dear Mr. Dimpfl, thank you very much for your time and explanation!

If you are estimating impulse response functions, variance decomposition, or testing Granger Causality then your method of choosing lags using AIC(C) or BIC is the way to set up your initial model. You then should then test the model for misspecification (heteroskedasticity, serial correlation, stability, etc,). If your results are satisfactory, you can estimate your model, impose any required identification and do your analysis. MAPE has no part in this analysis.

If you wish to use a VAR for forecasting this approach may provide a starting point. Well-specified "structural" or "causal" models are not necessarily good forecasting models. MAPE is one possible way of evaluating the forecasting ability of a forecasting model.

(I have seen economists estimating MAPE using the model estimated over the entire sample to forecast internal sample points and using these forecasts and the actual values to calculate MAPE. This is not a valid way to evaluate forecasts. In your case adding an extra lag can not increase MAPE and will usually decrease it. This will lead to overfitting.)

In time series econometrics MAPE is calculated as follows. Say we have a sample size of n and are interested in one step ahead forecasts. Take the first m (m

Generally speaking, MAPE may not be the best choice. Please let me recommend this guide to measuring forecasting accuracy:

Chapter Forecast Evaluation Techniques for I4.0 Systems

Btw, if you have time series with non-negative actuals, you can try data transformations to improve forecasts. If you apply data transformations, I would recommend MAE or the AvgRelMAE, in accordance with the considerations mentioned in the above chapter.