MPS-RR 2000-4
February 2000

Small dispersion asymptotics for diffusion martingale estimating functions

Michael Sørensen

Abstract

Martingale estimating functions provide a exible and powerful framework for statistical inference about di usion models based on discrete time observations. We supplement the standard results on large sample asymptotics by results on small dispersion asymptotics, which can be applied in situations where the noise term is sufficiently small, compared to the drift term, that a Gaussian approximation to the di usion can be used. The theory, which is based on the stochastic Taylor expansion, covers proper likelihood inference too. It is remarkable that the martingale property of an estimating function also for small dispersion asymptotics ensures that estimators are consistent. A model from mathematical nance is considered in detail. For this example the range of applicability of the small dispersion asymptotics is investigated in a simulation study of the distribution of estimators.

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