Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions

Abstract

A general estimation approach combining the attractive features of method of moments with the efficiency of ML is proposed. The moment conditions are computed via the characteristic function. The two major difficulties with the implementation is that one needs to use an infinite set of moment conditions leading to the singularity of the covariance matrix in the GMM context, and the optimal instrument yielding the ML efficiency was previously shown to depend on the unknown probability density function. We resolve the two problems simultaneously in the framework of C-GMM (GMM with a continuum of moment conditions) of Carrasco and Florens (2000a). First, we extend their results to dependent data and provide a reformulation of their estimator that enhances its computational ease. Second, we propose to span the unknown optimal instrument by an infinite basis consisting of simple exponential functions. Since the estimation framework already relies on a continuum of moment conditions, adding a continuum of spanning functions does not pose any problems. As a result, we achieve ML efficiency when we use the values of conditional CF indexed by its argument as moment functions. We also introduce HAC-type estimators so that the estimation methods are not restricted to settings involving martingale difference sequences. Hence, our methods apply to Markovian and non-Markovian dynamic models. Finally, a simulated method of moments type estimator is proposed to deal with the cases where the characteristic function does not have a closed-form expression. Extensive Monte-Carlo study based on the models typically used in term-structure literature favorbaly documents the performance of our methodology.

Keywords: maximum likelihood estimation, jump diffusion processes, generalized method of moments, continuum of moment conditions, characteristic function, term structure models

JEL Classification: C51, C32, G12