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Mathematics > Statistics Theory

arXiv:2511.10132 (math)
[Submitted on 13 Nov 2025]

Title:Hawkes autoregressive processes: a new model for multiscale and heterogeneous processes

Authors:Théo Leblanc
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Abstract:Both Hawkes processes and autoregressive processes depend on linear functionals of their past while modelling different types of data. As different datasets obtained through the recording of the same phenomena may be heterogeneous and occur at different timescales, it is important to study multiscale and heterogenous processes, such as those obtained by combining Hawkes and autoregressive processes. In this paper, we present probabilistic results for this new Hawkes autoregressive (HAR) model, including the existence of a stationary version, a cluster representation, exponential moments and asymptotic behaviour. We also derive statistical results for estimating interactions, extending the well-known LASSO estimation method to Hawkes Autoregressive (HAR) processes.
Subjects: Statistics Theory (math.ST); Probability (math.PR)
MSC classes: 60G55, 62M10, 60G10, 62H12
Cite as: arXiv:2511.10132 [math.ST]
  (or arXiv:2511.10132v1 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.2511.10132

Submission history

From: Théo Leblanc [view email]
[v1] Thu, 13 Nov 2025 09:38:56 UTC (143 KB)
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