Nonparametric Two-Step Estimation of Drift Function in the Jump-Diffusion Model with Noisy Data

doi:10.1007/s11424-022-1041-8

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (6): 2398-2429.DOI: 10.1007/s11424-022-1041-8

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Nonparametric Two-Step Estimation of Drift Function in the Jump-Diffusion Model with Noisy Data

YE Xuguo¹, ZHAO Yanyong², LIN Jinguan², LONG Weifang¹

1. School of Science, Kaili University, Kaili 556011, China;
2. Department of Statistics, Nanjing Audit University, Nanjing 211815, China

Received:2021-02-24 Revised:2021-07-06 Online:2022-11-25 Published:2022-12-23
Contact: ZHAO Yanyong,Email:zhaoyanyong1987@163.com
Supported by:
Ye's research is supported by the National Natural Science Foundation of China under Grant No. 11961038, Young Talents Project of Science and Technology Research Program of Education Department in Guizhou Province (Qianjiao KYword[2018]364), Science and Technology Foundation of Guizhou Province (QianKeHejichu[2019]1286), Cultivating Project of National Natural Science Foundation (QianKeHe talent-development platform[2017]No. 5723, QianKeHe talent-development platform[2017]No. 5723-02). Zhao's research is supported by the National Natural Science Foundation of China under Grant Nos. 12071220, 11701286, Social Science Foundation of Jiangsu Province under Grant No. 20EYC008, the National Statistical Research Project of China under Grant No. 2020LZ35, and Open Project of Jiangsu Key Laboratory of Financial Engineering under Grant No. NSK2021-12. Lin's research is supported by the National Natural Science Foundation of China under Grant Nos. 11831008, 11971235, and the National Statistical Research Project of China under Grant No. 2020LZ19.

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YE Xuguo, ZHAO Yanyong, LIN Jinguan, LONG Weifang. Nonparametric Two-Step Estimation of Drift Function in the Jump-Diffusion Model with Noisy Data[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2398-2429.

This paper considers a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable. A two-step approach to estimate the drift function of a jump-diffusion model {in noisy settings} is proposed. The proposed estimator is shown to be consistent and asymptotically normal in the presence of finite activity jumps. Simulated experiments and a real data application are undertaken to assess the finite sample performance of the newly proposed method.

Key words: Drift function, jump-diffusion processes, microstructure noise, nonparametric estimation

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