Estimation for misspecified ergodic diffusion processes from discrete observations

¹ Graduate School of Engineering Science, Osaka University Toyonaka, Osaka 560-8531, Japan; uchida@sigmath.es.osaka-u.ac.jp
² Japan Science and Technology Agency, CREST, Japan
³ Graduate School of Mathematical Sciences, University of Tokyo 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

Received: 17 November 2008
Revised: 30 September 2009

Abstract

The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of the minimum contrast estimator is proved. In particular, the rate of convergence for the minimum contrast estimator of diffusion coefficient parameter in a misspecified model is different from the one in the correctly specified parametric model.