Entropy densities with an application to autoregressive conditional skewness and kurtosis
Eric Jondeau and Michael Rockinger*
Journal of Econometrics, 2002, 106(1), 1199-1427.
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. We find that there is little predictability of skewness
and kurtosis for weekly data.
Keywords: Semi-nonparametric estimation; Time-varying skewness and kurtosis;
GARCH .
JEL classification: C40; C61; G10 .
* HEC Lausanne