Model selection criterion produces non-normal residuals

I was wondering if I can use Akaike or Schwarz criterion even when the residuals that I get from the model when I run the regression are not normal. Is there any normality assumption with these criteria or can I use them all the time regardless?

• I don't know an exact answer to your question, but in general AIC and BIC can be used in many types of models, also those that are not linear and used to model non-normal dependent variables. So I think the normality assumption is not central. – tomka Dec 13 '13 at 23:27
• That's what I thought at first. But I was reading this paper arxiv.org/PS_cache/astro-ph/pdf/0701/0701113v2.pdf and if you read on section 2.2, the first paragraph mentions "gaussian assumptions" – Wilmer E. Henao Dec 13 '13 at 23:31

• Would you agree with my answer? I argue that normality is irrelevant unless the likelihood function implies it. Your statement model adequacy checking including the normality assumption of your residuals considers only a special case and is not correct in general -- because likelihood function may assume a non-normal distribution, e.g. a $t$ distribution is common in case of GARCH models. – Richard Hardy Jan 14 '16 at 18:18