Efficient Estimation of Second Moment Parameters in ARCH Models

Abstract

This paper studies statistical inference and efficient instrumental variable (IV) estimation in the ARCH model when there are autoregressive (AR) components in the conditional mean. The main focus of the paper is the construction of efficient IV estimators for the second moment parameters. The advantage of the approach over standard conditional maximum likelihood (ML) lies in the fact that no specific form of the conditional distribution is needed and considerable skewness and leptokurtosis are permitted. A novel feature of the asymptotics is that the case of a unit root model with ARCH effects is also included. Some new unit root limit theory is given in this case.