A two-step estimation of diffusion processes using noisy observations

Abstract

ABSTRACTThis paper considers the estimation of unknown drift and diffusion functions of a one-dimensional diffusion process when the observation is a discrete sampling of with an additive noise, at times , . In order to reduce the noise effect, a two-step estimation method is proposed based on the joint use of the pre-averaging technique and kernel smoothing. Under some suitable conditions, the proposed estimators are consistent and asymptotically normal. A simulation study and a real data application are given to evaluate the finite sample performance of the proposed method in comparison with alternative methods.