Hawkes autoregressive processes: a new model for multiscale and heterogeneous processes
Abstract
Both Hawkes processes and autoregressive processes rely on linear functionals of their past, while modeling different types of data. Since datasets arising from observations of the same phenomenon may be heterogeneous and sampled at different time scales, it is natural to study multiscale and heterogeneous processes, such as those obtained by combining Hawkes and autoregressive dynamics. In this paper, we introduce this new Hawkes autoregressive (HAR) model incorporating both continuous- and discrete-time dynamics, and establish several probabilistic results, including the existence of a stationary version, a cluster representation, as well as stability and ergodic properties.
Cite
@article{arxiv.2511.10132,
title = {Hawkes autoregressive processes: a new model for multiscale and heterogeneous processes},
author = {Théo Leblanc},
journal= {arXiv preprint arXiv:2511.10132},
year = {2026}
}
Comments
As suggested by the anonymous referee, we decided to cut the paper in half. The paper now focuses only on the probabilistic study of HAR processes, on which the statistical study fundamentally relies. The statistical analysis, which builds upon these probabilistic results, is postponed to a separate paper. Some results have also been improved