Asymptotic efficiency of conditional least squares estimators for ARCH models

The conditional least squares (CL) estimators proposed by Tjostheim [1986. Estimation in nonlinear time series models. Stochastic Process. Appl. 21, 251-273] are important and fundamental. The CL estimator applied to the square-transformed ARCH model has an explicit form, which does not depend on the distribution of the innovation. Since the CLs are not asymptotically efficient in general, we give a necessary and sufficient condition that CL is asymptotically efficient based on the LAN approach. Next, a measure of efficiency for CL is introduced. Numerical evaluations of the measure of efficiency for various nonlinear time series models are given. They elucidate some interesting features of CL. (c) 2007 Elsevier B.V. All rights reserved.