Hawkes autoregressive processes: a new model for multiscale and heterogeneous processes
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914607937880064 |
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| author | Leblanc, Théo |
| author_facet | Leblanc, Théo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hawkes autoregressive processes: a new model for multiscale and heterogeneous processes Leblanc, Théo Probability Statistics Theory 60G55, 62M10, 60G10, 60F15 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. |
| title | Hawkes autoregressive processes: a new model for multiscale and heterogeneous processes |
| topic | Probability Statistics Theory 60G55, 62M10, 60G10, 60F15 |
| url | https://arxiv.org/abs/2511.10132 |