Selection criteria select 0 lags for a VAR model 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?
 A: It depends on what you want to do with the model.


*

*If you want to do forecasting, AIC will asymptotically select the model with the smallest squared forecast error (AIC is said to be efficient). If AIC suggests lag 0, you would be best off just estimating the intercept and skipping any lags.

*If you want to find the true model (and if the true model is in the pool of your candidate models), BIC will asymptotically find it (BIC is said to be consistent). If BIC suggests lag 0, probably your data was not generated by a VAR model.

*If you want to test some hypothesis, build a model within which this is feasible, and do it (e.g. with the likelihood ratio test).


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)? 


*

*Then you could stick with what your intuition suggests until you collect more and better data. 

*Or you could do Bayesian VAR modelling where you can incorporate your intuition directly into the modelling procedure via specifying a prior distribution for the model parameters.


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?


*

*Then you could reconsider the pool of models you are using.

*Or you could use regularized estimation (shrinkage) applied on a relatively large model to strike a good balance between flexibility and overfitting.

