Entropy Densities: With an Application to Autoregressive Conditional Skewness and Kurtosis

Abstract

The entropy principle yields, for a given set of moments, a density that involves the smallest amount of prior information,. We first show how entropy densities may be constructed in a numerically efficient way as the minimization of a potential. Next, for the case where the first four moments are given, we characterize the skewness-kurtosis domain for which densities are defined. This domain is found to be much larger than for Hermite or Edgeworth expansions. Last, we show how this technique can be used to estimate a GARCH model where skewness and kurtosis are time varying.

Keywords: Semi-nonparametric estimation, Time-varying skewness and kurtosis, GARCH

JEL Classification: C40, C61, G10