Estimation of Hawkes processes from binned observations using Whittle likelihood

Orateur: Félix CHEYSSON
Localisation: Sorbonne Universités, France
Type: Séminaire de probabilités et statistiques
Site: UGE , 4B 125
Date de début: 30/03/2021 - 10:30
Date de fin: 30/03/2021 - 11:30

Hawkes processes are a family of stochastic processes for which the occurrence of any event increases the probability of further events occurring. When count data are only observed in discrete time, we propose a spectral approach for the estimation of Hawkes processes, by means of Whittle's parameter estimation method. To get asymptotic properties for the estimator, we prove alpha-mixing properties for the series of counts, using the Galton-Watson properties of the cluster representation of Hawkes processes. Simulated datasets and an application to the incidence of measles in Tokyo illustrate the performances of the estimation, notably of the Hawkes reproduction function, even when the time between observations is large.