On Optimal Estimate Functions for Asymmetric GARCH Models.

Abstract

High frequency data exhibit non-constant variance. This paper models the exhibited fluctuations via asymmetric GARCH models. The Maximum Likelihood Estimation (MLE) and Estimating Functions (EF) are used in the estimation of the asymmetric GARCH family models. This EF approach utilizes the third and fourth moments which are common features in financial time series data analysis and does not rely on distributional assumptions of the data. Optimal estimating functions have been constructed as a combination of linear and quadratic estimating functions. The results show that estimates from the estimating functions approach are better than those of the traditional estimation methods such as the MLE especially in cases where distributional assumptions on the data are seriously violated. The implementation of the EF approach to asymmetric GARCH models assuming a generalized student-t distribution innovation reveals the efficiency benefits of the EF approach over the MLE method in parameter estimation especially for non-normal cases.