Modeling Maximum Entropy Distributions for Financial Returns by Moment Combination and Selection

In empirical finance, conditional distributions of financial returns are often established by specifying the standardized error distributions of GARCH-type models. In this article, we apply the maximum entropy (MaxEnt) approach and propose a moment combination and selection method to explore this distribution-building problem. We demonstrate that this framework is useful for unifying and comparing existing distribution specifications, generating more suitable distribution specifications, and shedding light on the roles of different moments in the distribution-building process. We also show the applicability of our method to real data by means of an empirical study on stock index returns.