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Pré-Publication, Document De Travail Année : 2022

The non-linear discrete-time Hawkes process

Résumé

The non-linear Hawkes process is a point process for which the occurrence of future events depends on the 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 hidden Markov chain time series 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 when the time scale goes to zero. Finally, we suggest a parametric calibration method for the continuous-time Hawkes process based on the regression on the discrete-time approximation.
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Dates et versions

hal-03220800 , version 1 (24-06-2021)
hal-03220800 , version 2 (04-08-2022)

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Lorick Huang, Mahmoud Khabou. The non-linear discrete-time Hawkes process. 2022. ⟨hal-03220800v2⟩
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