In this paper, we quantify the asymptotic bias of the Florens-Zmirou
(1993, Journal of Applied
Probability 30, 790–804) and Jiang and Knight (1997, Econometric Theory 13,
615–645) estimator for the diffusion coefficient when the step of
discretization is fixed, and then we propose a bias adjustment that
partially compensates for the distortion. Also, we show that our
estimators have all the asymptotic properties of the Florens-Zmirou and
Jiang and Knight estimator when the step of discretization goes to
zero. We provide some examples.I thank
the editor Peter C.B. Phillips and the two referees for comments and
suggestions that led to considerable improvement of the paper. I am
also grateful to Carlos Braumann and Tom Kundert for helpful comments.
This research was supported by the Fundação para a
Ciência e a Tecnologia (FCT) and by POCTI.