Estimating the ARCH parameters by solving linear equations

Abstract

This paper discusses the asymptotics of two-stage least squares estimator of the parameters of ARCH models. The estimator is easy to obtain since it involves solving two sets of linear equations. At the same time, the estimator has the same asymptotic efficiency as that of the widely used quasi-maximum likelihood estimator. Simulation results show that, even for small sample size, the performance of our estimator compared to the quasi-maximum likelihood estimator is better.