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Z-process method for change point problems with applications to discretely observed diffusion processes

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Abstract

The aim of this paper is to develop a general, unified approach, based on some partial estimation functions which we call “Z-process”, to some change point problems in mathematical statistics. The method proposed can be applied not only to ergodic models but also to some models where the Fisher information matrix is random. Applications to some concrete models, including a parametric model for volatilities of diffusion processes are presented. Simulations for randomly time-transformed Brownian bridge process appearing as the limit of the proposed test statistics are performed with computer intensive use.

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Acknowledgments

The authors thank the associate editor and two anonymous referees for their helpful comments.

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Authors and Affiliations

  1. Department of Management, Information and Production Engineering, University of Bergamo, Viale Marconi, 5, 24044, Dalmine, BG, Italy

    Ilia Negri

  2. Faculty of International Research and Education, Waseda University, Tokyo, Japan

    Yoichi Nishiyama

Authors
  1. Ilia Negri
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  2. Yoichi Nishiyama
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Correspondence to Ilia Negri.

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Negri, I., Nishiyama, Y. Z-process method for change point problems with applications to discretely observed diffusion processes. Stat Methods Appl 26, 231–250 (2017). https://doi.org/10.1007/s10260-016-0366-7

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  • DOI: https://doi.org/10.1007/s10260-016-0366-7

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