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Hybrid estimators for small diffusion processes based on reduced data

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Abstract

We deal with the Bayes type estimators and the maximum likelihood type estimators of both drift and volatility parameters for small diffusion processes defined by stochastic differential equations with small perturbations from high frequency data. From the viewpoint of numerical analysis, initial Bayes type estimators for both drift and volatility parameters based on reduced data are required, and adaptive maximum likelihood type estimators with the initial Bayes type estimators, which are called hybrid estimators, are proposed. The asymptotic properties of the initial Bayes type estimators based on reduced data are derived and it is shown that the hybrid estimators have asymptotic normality and convergence of moments. Furthermore, a concrete example and simulation results are given.

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Acknowledgements

The authors would like to thank the referees for their valuable comments and suggestions. Masayuki Uchida’s research was partially supported by JST CREST, JSPS KAKENHI Grant Numbers JP24300107, JP17H01100 and Cooperative Research Program of the Institute of Statistical Mathematics.

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Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, 560-8531, Japan

    Yusuke Kaino & Masayuki Uchida

  2. Center for Mathematical Modeling and Data Science (MMDS), Osaka University, Toyonaka, Osaka, 560-8531, Japan

    Masayuki Uchida

Authors
  1. Yusuke Kaino
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  2. Masayuki Uchida
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Correspondence to Yusuke Kaino.

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Kaino, Y., Uchida, M. Hybrid estimators for small diffusion processes based on reduced data. Metrika 81, 745–773 (2018). https://doi.org/10.1007/s00184-018-0657-0

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  • DOI: https://doi.org/10.1007/s00184-018-0657-0

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