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Recursive computation of the Hawkes cumulants

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  • Privault, Nicolas

Abstract

We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on higher-order cumulants in comparison with existing methods based on differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and also apply to the computation of joint cumulants generated by multidimensional self-exciting processes.

Suggested Citation

  • Privault, Nicolas, 2021. "Recursive computation of the Hawkes cumulants," Statistics & Probability Letters, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:stapro:v:177:y:2021:i:c:s0167715221001231
    DOI: 10.1016/j.spl.2021.109161
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    References listed on IDEAS

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    1. Gabriel Koch Ocker & Krešimir Josić & Eric Shea-Brown & Michael A Buice, 2017. "Linking structure and activity in nonlinear spiking networks," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-47, June.
    2. M. Achab & E. Bacry & J. F. Muzy & M. Rambaldi, 2018. "Analysis of order book flows using a non-parametric estimation of the branching ratio matrix," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 199-212, February.
    3. Lisandro Montangie & Christoph Miehl & Julijana Gjorgjieva, 2020. "Autonomous emergence of connectivity assemblies via spike triplet interactions," PLOS Computational Biology, Public Library of Science, vol. 16(5), pages 1-44, May.
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    Cited by:

    1. Hillairet, Caroline & Réveillac, Anthony & Rosenbaum, Mathieu, 2023. "An expansion formula for Hawkes processes and application to cyber-insurance derivatives," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 89-119.

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