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Question 1: Is it necessary to consider AIC and the BIC criteria when selecting the lag for a VAR, VECM or ARDL model OR can I use something else?
Example: Can I pick 12 lags because the model simply produce great results when I do or do I have to use the AIC/SIC criteria?
Question 2: A simple google search tells me that its possible to select lag 4 when quarterly data, 12 when monthly etc. Is that a valid approach ?
Question 1:
No, it is not strictly necessary to use AIC or BIC, but you need to have an objective method to assess how good your model is. People usually think that AIC and BIC are pre-estimation statistics, but when you run a VAR selection function, what your software is doing is estimating many VAR models and evaluating the likelihood function to compute the criteria. So you may think of AIC and BIC as two ways of assessing how good the models are. They are just telling you that the best model is, e.g., a VAR(2).
When you say that the 12 lags model produce great results, you are saying that based on what criteria/statistics?
If you are saying that because your residuals are not correlated, then you are on the right track, but maybe there is a simpler model that also produces white noise residuals. AIC and BIC may help you to find that model.
If you are saying that because this is the model that yields the best prediction for a particular test data, then you are on the right track also, but then probably you are using a prediction evaluation criteria such as MSE, MAE, etc.
If you are saying that because this is the model that makes your theoretical hypothesis valid, then you are doing bad science. This is not an objective method to evaluate your model. For casual purposes you usually need to do a lot of robustness checks such as varying the lag order to see if significance of coefficients change.
Question 2:
This may not always be a valid approach. Again, you need to evaluate your model using an objective criteria. When using this approach, if your residuals are not correlated and your model is parsimonious compared to other alternatives, then ok, but in many cases this will not be true.
