Testing procedures based on maximum likelihood estimation for marked Hawkes processes

Anna Bonnet, Charlotte Dion-Blanc and Maya Sadeler Perrin ()
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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

Computational Statistics, 2025, vol. 40, issue 9, No 26, 5573-5615

Abstract: 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.

Keywords: Hawkes process; Marked process; Test; Goodness-of-fit; Parametric estimation; Likelihood (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-025-01664-9

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