Gram–Charlier densities: a multivariate approach

This paper introduces a new family of multivariate distributions based on Gram-Charlier and Edgeworth expansions. This family encompasses many of the univariate semi-nonparametric densities proposed in financial econometrics as marginal of its different formulations. Within this family, we focus on the analysis of the specifications that guarantee positivity to obtain well-defined multivariate semi-nonparametric densities. We compare two different multivariate distributions of the family with the multivariate Edgeworth-Sargan, Normal, Student's t and skewed Student's t in an in- and out-sample framework for financial returns data. Our results show that the proposed specifications provide a quite reasonably good performance being so of interest for applications involving the modelling and forecasting of heavy-tailed distributions.