Time-frequency analysis of locally stationary Hawkes processes - IMT - Institut Mines-Télécom Accéder directement au contenu
Article Dans Une Revue Bernoulli Année : 2019

Time-frequency analysis of locally stationary Hawkes processes

Résumé

Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has recently attracted a lot of interest in applications in the life sciences (seismology, genomics, neuro-science,...), but also in the modelling of high-frequency financial data. In this contribution we provide a fully developed nonparametric estimation theory of both local mean density and local Bartlett spectra of a locally stationary Hawkes process. In particular we apply our kernel estimation of the spectrum localised both in time and frequency to two data sets of transaction times revealing pertinent features in the data that had not been made visible by classical non-localised approaches based on models with constant fertility functions over time.
Fichier principal
Vignette du fichier
article.pdf (1.16 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01502252 , version 1 (05-04-2017)
hal-01502252 , version 2 (13-11-2017)
hal-01502252 , version 3 (29-01-2018)

Identifiants

Citer

François Roueff, Rainer von Sachs. Time-frequency analysis of locally stationary Hawkes processes. Bernoulli, 2019, 25 (2), pp.1355-1385. ⟨10.3150/18-BEJ1023⟩. ⟨hal-01502252v3⟩
358 Consultations
281 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More