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Asymptotic Normality of Convoluted Smoothed Kernel Estimation for Scalar Diffusion Model

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Abstract

In this paper, we consider a convoluted smoothed nonparametric approach for the unknown coefficients of diffusion model based on high frequency data. Under regular conditions, we obtain the asymptotic normality for the proposed estimators as the time span T →∞ and sample interval Δn → 0. The procedure and asymptotic behavior can be applied for both Harris recurrent and positive Harris recurrent processes. The finite-sample benefits of the underlying estimators are verified through Monte Carlo simulation and 15-min high-frequency stock index in Shanghai Stock Exchange for an empirical application.

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Acknowledgments

This research work is supported by Ministry of Education, Humanities and Social Sciences Project (No. 18YJCZH153), National Statistical Science Research Project (No. 2018LZ05), the General Research Fund of Shanghai Normal University (No. SK201720) and Funding Programs for Youth Teachers of Shanghai Colleges and Universities (No. A-9103-18-104001). The authors would like to thank the editor and two anonymous referees for their valuable suggestions, which greatly improved our paper.

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Authors and Affiliations

  1. School of Finance and Business, Shanghai Normal University, Shanghai, 200234, People’s Republic of China

    Yuping Song & Weijie Hou

  2. College of Mathematics and Sciences, Shanghai Normal University, Shanghai, 200234, People’s Republic of China

    Guang Yang

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  1. Yuping Song
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  2. Weijie Hou
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  3. Guang Yang
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Correspondence to Yuping Song.

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Song, Y., Hou, W. & Yang, G. Asymptotic Normality of Convoluted Smoothed Kernel Estimation for Scalar Diffusion Model. Methodol Comput Appl Probab 22, 191–221 (2020). https://doi.org/10.1007/s11009-019-09696-7

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  • DOI: https://doi.org/10.1007/s11009-019-09696-7

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