Kurtosis analysis in GARCH models with Gram–Charlier-like innovations

The approach based on polynomially-modified distributions, known as Gram–Charlier-like (GCl) expansions, has been proven effective to account for both excess kurtosis and skewness of financial data. In this paper, we examine GARCH models with innovations distributed as GCl expansions (GC-GARCH). The kurtosis gluts ascribable to both time-varying volatility and GCl distributed GARCH innovationsis evaluated. Furthermore, a ‘‘kurtosis targeting’’ approach is devised to estimate the kurtosis of GCl innovations. This leads to GC-GARCH models tailored to fit the kurtosis requirements of financial data