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Statistical inference for ergodic point processes and application to Limit Order Book

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  • Clinet, Simon
  • Yoshida, Nakahiro

Abstract

We construct a general procedure for the Quasi Likelihood Analysis applied to a multivariate point process on the real half line in an ergodic framework. When a particular family of laws of large numbers applies to the parametrized stochastic intensity of the model, we establish the consistency, the asymptotic normality and the convergence of moments of both the Quasi Maximum Likelihood estimator and the Quasi Bayesian estimator. We finally illustrate our results by showing how they can be applied to various Limit Order Book models such as the fundamental cases of Markovian models and exponential Hawkes process-based models.

Suggested Citation

  • Clinet, Simon & Yoshida, Nakahiro, 2017. "Statistical inference for ergodic point processes and application to Limit Order Book," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1800-1839.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:6:p:1800-1839
    DOI: 10.1016/j.spa.2016.09.014
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Masatoshi Goda, 2021. "Hawkes process and Edgeworth expansion with application to maximum likelihood estimator," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 277-325, July.
    2. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," Papers 1809.08060, arXiv.org, revised Sep 2021.
    3. Rachele Foschi & Francesca Lilla & Cecilia Mancini, 2020. "Warnings about future jumps: properties of the exponential Hawkes model," Working Papers 13/2020, University of Verona, Department of Economics.
    4. Nakahiro Yoshida, 2022. "Quasi-likelihood analysis and its applications," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 43-60, April.
    5. Yoann Potiron & Per Mykland, 2020. "Local Parametric Estimation in High Frequency Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 679-692, July.
    6. Simon Clinet & Yoann Potiron, 2016. "Statistical inference for the doubly stochastic self-exciting process," Papers 1607.05831, arXiv.org, revised Jun 2017.
    7. Simon Clinet, 2020. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Papers 2001.11624, arXiv.org, revised Aug 2021.
    8. Simon Clinet, 2022. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 189-225, July.
    9. Simon Clinet & William T. M. Dunsmuir & Gareth W. Peters & Kylie-Anne Richards, 2021. "Asymptotic distribution of the score test for detecting marks in hawkes processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 635-668, October.
    10. Simon Clinet & William T. M. Dunsmuir & Gareth W. Peters & Kylie-Anne Richards, 2019. "Asymptotic Distribution of the Score Test for Detecting Marks in Hawkes Processes," Research Paper Series 404, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. Cavaliere, Giuseppe & Lu, Ye & Rahbek, Anders & Stærk-Østergaard, Jacob, 2023. "Bootstrap inference for Hawkes and general point processes," Journal of Econometrics, Elsevier, vol. 235(1), pages 133-165.
    12. Shogo H. Nakakita & Yusuke Kaino & Masayuki Uchida, 2021. "Quasi-likelihood analysis and Bayes-type estimators of an ergodic diffusion plus noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 177-225, February.
    13. Masatoshi Goda, 2023. "Sparse estimation for generalized exponential marked Hawkes process," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 139-169, April.
    14. Maxime Morariu-Patrichi & Mikko Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," CREATES Research Papers 2018-26, Department of Economics and Business Economics, Aarhus University.

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