Série Scientifique Scientific Series 2003 s-02 Efficient Estimation of Jump Diffusions and General Dynamic Models with a Continuum of Moment Conditions

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). First, we prove asymptotic properties of the C-GMM estimator applied to dependent data and then provide a reformulation of the 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 nail-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 favorably documents the performance of our methodology. L'estimation des processus de diffusion (affine ou a sauts) est problematique car l'expression de la vraisemblance n'est pas disponible. D'un autre cote, la fonction caracteristique de ces modeles est souvent connue. Cet article propose un estimateur du type methode des moments generalises (GMM) fonde sur la fonction caracteristique. Comme l'on dispose d'un continuum de conditions de moments, on utilise une methode specifique appelee C-GMM. On derive les proprietes asymptotiques de l'estimateur et discute son implementation en pratique. Dans le contexte d'un processus markovien, une condition de moment conditionnelle resulte de la fonction caracteristique conditionnelle. Une question importante est le choix de l'instrument optimal. On montre que, lorsque l'instrument est une fonction exponentielle, l'estimateur C-GMM est asymptotiquement aussi efficace que l'estimateur du maximum de vraisemblance. Il faut noter que la methode C-GMM n'est pas limitee aux processus markoviens et s'applique a des modeles dynamiques tres generaux. De plus, on propose une methode des moments simules qui permet de traiter le cas ou l'expression de la fonction caracteristique n'est pas connue. Finalement, une etude de Monte Carlo sur des modeles frequemment utilises en finance montre que notre estimateur a de bonnes proprietes.

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