Nonparametric state estimation of diffusion processes

Abstract

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.