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Nonlinear Poisson autoregression and nonlinear Hawkes processes

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  • Huang, Lorick
  • Khabou, Mahmoud

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.

Suggested Citation

  • Huang, Lorick & Khabou, Mahmoud, 2023. "Nonlinear Poisson autoregression and nonlinear Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 201-241.
    • Handle: RePEc:eee:spapps:v:161:y:2023:i:c:p:201-241
    DOI: 10.1016/j.spa.2023.03.015
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    References listed on IDEAS

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