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Bias Free Threshold Estimation for Jump Intensity Function

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Abstract

In this paper, combining the threshold technique, we reconstruct Nadaraya-Watson estimation using Gamma asymmetric kernels for the unknown jump intensity function of a diffusion process with finite activity jumps. Under mild conditions, we obtain the asymptotic normality for the proposed estimator. Moreover, we have verified the better finite-sampling properties such as bias correction and efficiency gains of the underlying estimator compared with other nonparametric estimators through a Monte Carlo experiment.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Yi-wei Lin

  2. School of Finance and Business, Shanghai Normal University, Shanghai, 200234, China

    Zhen-wei Li & Yu-ping Song

Authors
  1. Yi-wei Lin
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  2. Zhen-wei Li
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  3. Yu-ping Song
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Corresponding author

Correspondence to Yu-ping Song.

Additional information

LIN Yi-wei is supported by the National Natural Science Foundation of China (No.11701331), Shandong Provincial Natural Science Foundation (No. ZR2017QA007) and Young Scholars Program of Shandong University. SONG Yu-ping is supported by Ministry of Education, Humanities and Social Sciences project (No. 18YJCZH153), National Statistical Science Research Project (No. 2018LZ05), Youth Academic Backbone Cultivation Project of Shanghai Normal University (No. 310-AC7031-19-003021), General Research Fund of Shanghai Normal University (SK201720) and Key Subject of Quantitative Economics (No. 310-AC7031-19-004221) and Academic Innovation Team (No. 310-AC7031-19-004228) of Shanghai Normal University.

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Lin, Yw., Li, Zw. & Song, Yp. Bias Free Threshold Estimation for Jump Intensity Function. Appl. Math. J. Chin. Univ. 34, 309–325 (2019). https://doi.org/10.1007/s11766-019-3630-4

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  • DOI: https://doi.org/10.1007/s11766-019-3630-4

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