A two-step estimation of diffusion processes using noisy observations

Xu-Guo Ye, Jin-Guan Lin and Yan-Yong Zhao

Journal of Nonparametric Statistics, 2018, vol. 30, issue 1, 145-181

Abstract: This paper considers the estimation of unknown drift and diffusion functions of a one-dimensional diffusion process $ X_{t} $ Xt when the observation $ Y_{t} $ Yt is a discrete sampling of $ X_{t} $ Xt with an additive noise, at times $ i\delta $ iδ, $ i=1, \ldots, N $ i=1,…,N. 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.

Date: 2018
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DOI: 10.1080/10485252.2017.1404062

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