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Schémas de discrétisation anticipatifs et estimationdu paramètre de dérive d'une diffusion

Published online by Cambridge University Press:  15 August 2002

Sandie Souchet Samos
Sandie Souchet Samos*
Affiliation:
Université Paris 1, Centre Pierre Mendès France, 90 rue de Tolbiac, 75013 Paris, France; e-mail: ssouchet@caramail.com
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Abstract

Let YT = (Yt)t∈[0,T] be a real ergodic diffusion process which drift depends on an unkown parameter $\theta_{0}\in \mathbb{R}^{p}$ . Our aim is to estimate θ 0 from a discrete observation of the process YT , (Ykδ)k=0,n , for a fixed and small δ, as T = nδ goes to infinity. For that purpose, we adapt the Generalized Method of Moments (see Hansen) to the anticipative and approximate discrete-time trapezoidal scheme, and then to Simpson's.Under some general assumptions, the trapezoidal scheme (respectively Simpson's scheme) provides an estimation of θ 0 with a bias of order δ 2 (resp. δ 4). Moreover, this estimator is asymptotically normal. These results generalize Bergstrom's [1], which were obtained for a Gaussian diffusion process, which drift is linear in θ.

Keywords

Schéma du trapèzeschéma de Simpsonschéma anticipatifdiffusion ergodiqueestimation par variables instrumentalesméthode des moments généraliséscontrastebiais d'estimationefficacité asymptotique en variance.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 4 , 2000 , pp. 233 - 258
Copyright
© EDP Sciences, SMAI, 2000

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