Nonlinear Poisson autoregression and nonlinear Hawkes processes

Lorick Huang and Mahmoud Khabou

Stochastic Processes and their Applications, 2023, vol. 161, issue C, 201-241

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.

Keywords: Nonlinear Hawkes processes; Integer-valued time series; Weak convergence of Markov processes (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:161:y:2023:i:c:p:201-241

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DOI: 10.1016/j.spa.2023.03.015

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