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

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Abstract

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.

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Authors and Affiliations

  1. School of Science, Kaili University, Kaili, 556011, China

    Xuguo Ye & Weifang Long

  2. Department of Statistics, Nanjing Audit University, Nanjing, 211815, China

    Yanyong Zhao & Jinguan Lin

Authors
  1. Xuguo Ye
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  2. Yanyong Zhao
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  3. Jinguan Lin
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  4. Weifang Long
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Corresponding author

Correspondence to Yanyong Zhao.

Additional information

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, X., Zhao, Y., Lin, J. et al. Nonparametric Two-Step Estimation of Drift Function in the Jump-Diffusion Model with Noisy Data. J Syst Sci Complex 35, 2398–2429 (2022). https://doi.org/10.1007/s11424-022-1041-8

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  • DOI: https://doi.org/10.1007/s11424-022-1041-8

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