Stock and bond return predictability: the discrimination power of model selection criteria

The discrimination power of well-known model selection criteria is analyzed when the R-squared is low as in typical asset return predictability studies. It turns out that the discrimination power is low in this situation and this may explain, already in a simple i.i.d. setup, why often in-sample predictability, but no out-of-sample predictability is found. In particular it is possible to give another interpretation to the results of the well-cited Bossaerts and Hillion (Rev. Financial Stud. 12 (1999) 405-428) study. As a consequence, model selection criteria are put in a testing framework and a bootstrap-based procedure is proposed as a diagnostic tool to construct the class of models which are statistically indistinguishable from the best model chosen by a model selection criterion. In an empirical illustration the Pesaran and Timmerman (J. Finance 50 (1995) 1201-1228) results are reanalyzed and it turns out that in this case this class of models can be large. Finally it is shown that similar problems arise in a more hidden way in the context of recent model uncertainty studies using Bayesian model selection criteria. (c) 2005 Elsevier B.V. All rights reserved.