Nonlinear Poisson autoregression and nonlinear Hawkes processes
File(s)
Accepted version
Author(s)
Huang, Lorick
Khabou, Mahmoud
Type
Journal Article
Abstract
The nonlinear Hawkes process is a point process for which the occurrence of future events depends on its history, either by excitation or inhibition. This property made it popular in many fields, such as neuro-sciences and social dynamics. In this paper we propose a tractable nonlinear Poisson autoregression as a discrete-time Hawkes process. Our model allows for cross-excitation and inhibition between components, as well as for exogenous random noise on the intensity. We then prove a convergence theorem as the time step goes to zero. Finally, we suggest a parametric calibration method for the continuous-time Hawkes process based on the discrete-time approximation.
Date Issued
2023-07
Date Acceptance
2023-03-30
Citation
Stochastic Processes and their Applications, 2023, 161, pp.201-241
ISSN
0304-4149
Publisher
Elsevier
Start Page
201
End Page
241
Journal / Book Title
Stochastic Processes and their Applications
Volume
161
Copyright Statement
Copyright © Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Identifier
http://dx.doi.org/10.1016/j.spa.2023.03.015
Publication Status
Published
Date Publish Online
2023-04-01