Can Statistical Models of Stock Returns "Explain" Empirical Regularities?

Statistical models are usually thought of as means for describing statistical regularities. Concerning stock returns, many empirical regularities have been documented in the literature together with their corresponding models. The main task of this paper is to investigate, under the prism of the philosophy of science, the conditions that a statistical model has to satisfy in order to be deemed as explanatory adequate for the existing regularities. We distinguish two alternative sets of criteria for the explanatory adequacy of a statistical model. The first one is given by the Deductive-Statistical model of explanation, put forward by Hempel (1962). The second set, which contains much stricter conditions than the first, corresponds to the Deductive-Probabilistic-Nomological model suggested by Railton (1978). It is shown that the two most important statistical models of stock returns, namely the multivariate GARCH model and the Factor Model with persistent betas, are D-S explanatory. It is also shown that the Factor Model partially satisfies the D-N-P conditions for explanatory adequacy whereas the GARCH model fails completely in this respect.