A non-local estimator for locally stationary Hawkes processes
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Deschatre, Thomas Gruet, Pierre Lotz, Antoine |
| author_facet | Deschatre, Thomas Gruet, Pierre Lotz, Antoine |
| contents | We consider the problem of estimating the parameters of a non-stationary Hawkes process with time-dependent reproduction rate and baseline intensity. Our approach relies on the standard maximum likelihood estimator (MLE), coinciding with the conventional approach for stationary point processes characterised by [Ogata, 1978]. In the fully parametric setting, we find that the MLE over a single observation of the process over $[0, T]$ remains consistent and asymptotically normal as $T \to \infty$. Our results extend partially to the semi-nonparametric setting where no specific shape is assumed for the reproduction rate $g \colon [0, 1] \mapsto \mathbb{R}_+$. We construct a time invariance test with null hypothesis that g is constant against the alternative that it is not, and find that it remains consistent over the whole space of continuous functions of [0, 1]. As an application, we employ our procedure in the context of the German intraday power market, where we provide evidence of fluctuations in the endogeneity rate of the order flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02631 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A non-local estimator for locally stationary Hawkes processes Deschatre, Thomas Gruet, Pierre Lotz, Antoine Statistics Theory 62F03, 62F12, 60G55 We consider the problem of estimating the parameters of a non-stationary Hawkes process with time-dependent reproduction rate and baseline intensity. Our approach relies on the standard maximum likelihood estimator (MLE), coinciding with the conventional approach for stationary point processes characterised by [Ogata, 1978]. In the fully parametric setting, we find that the MLE over a single observation of the process over $[0, T]$ remains consistent and asymptotically normal as $T \to \infty$. Our results extend partially to the semi-nonparametric setting where no specific shape is assumed for the reproduction rate $g \colon [0, 1] \mapsto \mathbb{R}_+$. We construct a time invariance test with null hypothesis that g is constant against the alternative that it is not, and find that it remains consistent over the whole space of continuous functions of [0, 1]. As an application, we employ our procedure in the context of the German intraday power market, where we provide evidence of fluctuations in the endogeneity rate of the order flow. |
| title | A non-local estimator for locally stationary Hawkes processes |
| topic | Statistics Theory 62F03, 62F12, 60G55 |
| url | https://arxiv.org/abs/2506.02631 |