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Biometrika 2002 89(2):451-456; doi:10.1093/biomet/89.2.451
© 2002 by Biometrika Trust
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Nonparametric state estimation of diffusion processes

Isao Shoji1

1 Institute of Policy and Planning Sciences, University of Tsukuba, Tsukuba Ibaraki, 305-8573, Japan shoji@sk.tsukuba.ac.jp

The paper presents a method for estimating nonparametrically the states of one-dimensional diffusion processes.Once certain nuisance parameters have been estimated from the time series, states of a diffusion process can be estimated by the Kalman filter algorithm, so that the method is also useful for filtering and smoothing the states of the process. Numerical comparison of the method with the case of fitting a linear model to data shows that the method is clearly superior in terms of prediction errors.

Key Words: Diffusion process; Kalman filter; Nonparametric model; State estimation; State space model

Received May 2000. Revised October 2001


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