Asymptotic Normality of Convoluted Smoothed Kernel Estimation for Scalar Diffusion Model

  • Yuping SongEmail author
  • Weijie Hou
  • Guang Yang


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.


Diffusion models Volatility function Asymptotic normality Bias and variance reduction Nonstationary high frequency financial data 

Mathematics Subject Classification (2010)

Primary 62G20 62M05 Secondary 60J75 62P20 


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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. 1.School of Finance and BusinessShanghai Normal UniversityShanghaiPeople’s Republic of China
  2. 2.College of Mathematics and SciencesShanghai Normal UniversityShanghaiPeople’s Republic of China

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