I am selecting the number of lags for a VAR model. Selection criteria and the LR statistic suggest 0 lags.
Should I simply drop the VAR altogether, even if this goes against my intuition?
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It depends on what you want to do with the model.
If the selection by the information criteria or the test result are counterintuitive, probably you have reasons to blame the sample (too small, not really representative)?
Or probably the pool of candidate models is poor? Maybe the true model is VAR(5) with all but the 5th lag coefficients being zeros, but you do not have such a model in your pool, while a full unrestricted VAR(5) has high estimation variance and thus poor AIC/BIC/LR statistic?