On the Efficiency of Conditional Heteroskedasticity Models

Abstract

This paper discusses how conditional heteroskedasticity models can be estimated efficiently without imposing strong distributional assumptions such as normality. Using the generalized method of moments (GMM) principle, we show that for a class of models with a symmetric conditional distribution, the GMM estimates obtained from the joint estimating equations corresponding to the conditional mean and variance of the model are efficient when the instruments are chosen optimally. A simple ARCH(1) model is used to illustrate the feasibility of the proposed estimation procedure.

Keywords: Financial time series, ARCH, non-normality, generalized method of moments, optimal choice of instruments, maximum likelihood, efficiency