Forecasting Heavy-Tailed Densities with Positive Edgeworth and Gram-Charlier Expansions

This article presents a new semi-nonparametric (SNP) density function, named Positive Edgeworth-Sargan (PES). We show that this distribution belongs to the family of (positive) Gram-Charlier (GC) densities and thus it preserves all the good properties of this type of SNP distributions but with a much simpler structure. The in- and out-of-sample performance of the PES is compared with symmetric and skewed GC distributions and other widely used densities in economics and finance. The results confirm the PES as a good alternative to approximate financial returns distribution, specially when skewness is not severe.