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Asymptotic Distribution of the Score Test for Detecting Marks in Hawkes Processes

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Abstract

The asymptotic distribution of the score test of the null hypothesis that marks do not impact the intensity of a Hawkes marked self-exciting point process is shown to be chi-squared. For local asymptotic power, the distribution against local alternatives is also established as non-central chisquared. These asymptotic results are derived using existing asymptotic results for likelihood estimates of the unmarked Hawkes process model together with mild additional conditions on the moments and ergodicity of the marks process and an additional uniform boundedness assumption, shown to be true for the exponential decay Hawkes process.

Suggested Citation

  • 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.
    • Handle: RePEc:uts:rpaper:404
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    File URL: https://arxiv.org/pdf/1904.13147.pdf
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    References listed on IDEAS

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    1. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    2. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    3. Simon Clinet & Yoann Potiron, 2016. "Statistical inference for the doubly stochastic self-exciting process," Papers 1607.05831, arXiv.org, revised Jun 2017.
    4. 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.
    5. Patrick J. Laub & Thomas Taimre & Philip K. Pollett, 2015. "Hawkes Processes," Papers 1507.02822, arXiv.org.
    6. Alan G. Hawkes, 2018. "Hawkes processes and their applications to finance: a review," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 193-198, February.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Marked Hawkes point process; Ergodicity; Quasi likelihood; Score test; Inferential statistics; Local power;
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