Efficient Estimation Using the Characteristic Function

Abstract

The method of moments proposed by Carrasco and Florens (2000) permits to fully exploit the information contained in the characteristic function and yields an estimator which is asymptotically as efficient as the maximum likelihood estimator. However, this estimation procedure depends on a regularization or tuning parameter ∝ that needs to be selected. The aim of the present paper is to provide a way to optimally choose ∝ by minimizing the approximate mean square error (AMSE) of the estimator. Following an approach similar to that of Newey and Smith (2004), we derive a higher-order expansion of the estimator from which we characterize the finite sample dependence of the AMSE on ∝. We provide a data-driven procedure for selecting the regularization parameter that relies on parametric bootstrap. We show that this procedure delivers a root T consistent estimator of ∝. Moreover, the data-driven selection of the regularization parameter preserves the consistency, asymptotic normality and efficiency of the CGMM estimator. Simulation experiments based on a CIR model show the relevance of the proposed approach.

Keywords: Conditional moment restriction, continuum of moment conditions, generalized method of moments, mean square error, stochastic expansion, Tikhonov regularization

JEL Classification: C00, C13, C15