A two-step estimation of diffusion processes using noisy observations

作者：Ye, Xu-Guo; Lin, Jin-Guan^*; Zhao, Yan-Yong

来源：Journal of Nonparametric Statistics, 2018, 30(1): 145-181.

DOI：10.1080/10485252.2017.1404062

• Diffusion processes
• measurement error
• pre-averaging approach
• Kernel smoothing

This paper considers the estimation of unknown drift and diffusion functions of a one-dimensional diffusion process X-t when the observation Y-t is a discrete sampling of Xt with an additive noise, at times i delta, 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.

• 出版日期2018
• 单位南京审计大学; 凯里学院