On the Selection of Irregular, Misspecified Regression Models: a Comment on Folklore

In this paper we will investigate the consequences of applying model selection methods under regularity conditions that are sufficiently general to encompass (i) stochastic models involving non-stationary processes and (ii) situations where the true structure of the process falls outside the class of models under consideration. The properties of selection criteria that use very general measures of model complexity are considered and the results are used to draw attention to the fallacy of traditional beliefs concerning commonly employed model selection criteria.