Estimation of Time Varying Skewness and Kurtosis with an Application to Value at Risk

Abstract

This paper generalizes the Hyperbolic Asymmetric Power ARCH (HYAPARCH) model to allow for time varying skewness and kurtosis in the conditional distribution. This is done by modeling the conditional skewness and degrees of freedom of the skewed Student's t distribution of Lambert and Laurent (2001) as a function of the conditioning information. The proposed specification nests a large number of models in the literature and represents the first attempt to jointly model long memory in volatility and time variation in the third and fourth moments. The finite sample properties of MLE for this class of model are examined. The results indicate that the ARCH class of processes with time varying ske..