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Score Test for Marks in Hawkes Processes

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Abstract

A score statistic for detecting the impact of marks in a linear Hawkes self-exciting point process is proposed, with its asymptotic properties, finite sample performance, power properties using simulation and application to real data presented. A major advantage of the proposed inference procedure is the Hawkes process can be fit under the null hypothesis that marks do not impact the intensity process. Hence, for a given record of a point process, the intensity process is estimated once only and then assessed against any number of potential marks without refitting the joint likelihood each time. Marks can be multivariate as well as serially dependent. The score function for any given set of marks is easily constructed as the covariance of functions of future intensities fit to the unmarked process with functions of the marks under assessment. The asymptotic distribution of the score statistic is chi-squared distribution, with degrees of freedom equal to the number of parameters required to specify the boost function. Model based, or non-parametric estimation of required features of the marks marginal moments and serial dependence can be used. The use of sample moments of the marks in the test statistic construction do not impact size and power properties.

Suggested Citation

  • Kylie-Anne Richards & William T. M. Dunsmuir & Gareth W. Peters, 2019. "Score Test for Marks in Hawkes Processes," Research Paper Series 405, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:405
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    File URL: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3381976
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    Cited by:

    1. Simon Clinet, 2020. "Quasi-likelihood analysis for marked point processes and application to marked Hawkes processes," Papers 2001.11624, arXiv.org, revised Aug 2021.
    2. 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.
    3. 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.

    More about this item

    Keywords

    Marked Hawkes point process; Score test statistic; Screening marks; High frequency financial data;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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