Does the Bic Estimate and Forecast Better Than the AIc?

We test two questions: (i) Is the Bayesian Information Criterion (BIC) more parsimonious than Akaike Information Criterion (AIC)? and (ii) Is BIC better than AIC for forecasting purposes?By using simulated data, we provide statistical inference of both hypotheses individually and then jointly with a multiple hypotheses testing procedure to control better for type-I error.Both testing procedures deliver the same result: The BIC shows an in-and out-of-sample superiority over AIC only in a long-sample context.