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Testing procedures based on maximum likelihood estimation for marked Hawkes processes

Author

Listed:
  • Anna Bonnet

    (LPSM, UMR 8001, Sorbonne Université)

  • Charlotte Dion-Blanc

    (LPSM, UMR 8001, Sorbonne Université)

  • Maya Sadeler Perrin

    (LJK, UMR 5224, Univ. Grenoble Alpes, Grenoble INP)

Abstract

The Hawkes model is a past-dependent point process, widely used in various fields for modeling temporal clustering of events. Extending this framework, the multidimensional marked Hawkes process incorporates multiple interacting event types and additional marks, enhancing its capability to model complex dependencies in multivariate time series data. However, increasing the complexity of the model also increases the computational cost of the associated estimation methods and may induce an overfitting of the model. Therefore, it is essential to find a trade-off between accuracy and artificial complexity of the model. In order to find the appropriate version of Hawkes processes, we address, in this paper, the tasks of model fit evaluation and parameter testing for marked Hawkes processes. This article focuses on parametric Hawkes processes with exponential memory kernels, a popular variant for its theoretical and practical advantages. Our work introduces robust testing methodologies for assessing model parameters and complexity, building upon and extending previous theoretical frameworks. We then validate the practical robustness of these tests through comprehensive numerical studies, especially in scenarios where theoretical guarantees remains incomplete.

Suggested Citation

  • Anna Bonnet & Charlotte Dion-Blanc & Maya Sadeler Perrin, 2025. "Testing procedures based on maximum likelihood estimation for marked Hawkes processes," Computational Statistics, Springer, vol. 40(9), pages 5573-5615, December.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:9:d:10.1007_s00180-025-01664-9
    DOI: 10.1007/s00180-025-01664-9
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    References listed on IDEAS

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    1. Bonnet, Anna & Martinez Herrera, Miguel & Sangnier, Maxime, 2021. "Maximum likelihood estimation for Hawkes processes with self-excitation or inhibition," Statistics & Probability Letters, Elsevier, vol. 179(C).
    2. 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.
    3. 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.
    4. Zhuang J. & Ogata Y. & Vere-Jones D., 2002. "Stochastic Declustering of Space-Time Earthquake Occurrences," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 369-380, June.
    5. Patrick J. Laub & Young Lee & Thomas Taimre, 2021. "The Elements of Hawkes Processes," Springer Books, Springer, number 978-3-030-84639-8, January.
    6. Sergueï Dachian & Yury A. Kutoyants, 2006. "Hypotheses Testing: Poisson Versus Self‐exciting," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 391-408, June.
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