Multivariate Gram-Charlier densities

Abstract

This paper introduces a new family of multivariate distributions based on Gram-Charlier and Edgeworth expansions. This family encompasses many of the univariate Edgeworth-Sargan (hereafter ES) or Gram-Charlier densities as marginal distributions of the different formulations. Within this family, we focus on the specifications that guarantee positivity so obtaining a well-defined multivariate density. We compare different "positive" multivariate distributions of the family with both the multivariate ES and the Normal in an in- and out-sample framework for financial returns data. Our results show that the proposed model provides a quite reasonably good performance being so of interest for applications involving the modelling and forecasting of heavy-tailed distributions.