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.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)