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Basic question I guess. I'm fitting VAR models (and derivatives), and I've tried my hand on model order selection based on regularization but now I'm back to informative criteria (IC).

Thing is my series are stationary on the long run, so the ICs usually select large lag orders, resulting in roots of the characteristic polynomial outside the unit circle, and consequently violates some VAR assumptions.

I know I can avoid this artifact if I stop increasing model order when this happens, but is it a sound strategy?

Also, I think it's important to say I'm interested in inference, not predictive performance.

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