Forecasting Heavy‐Tailed Densities with Positive Edgeworth and Gram‐Charlier Expansions*
提出一种新的半非参数密度函数PES，结构更简单但保留了Gram-Charlier密度的优良性质，实证表明在金融收益分布近似中表现良好，尤其当偏度不严重时。
Abstract 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.