Locally stationary Hawkes processes

François Roueff 1 Rainer von Sachs 2 Laure Sansonnet 3
1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)
3 MIA-Paris - Mathématiques et Informatique Appliquées
Abstract : This paper addresses the generalisation of stationary Hawkes processes in order to allow for a time-evolving second-order analysis. Motivated by the concept of locally stationary autoregressive processes, we apply however inherently different techniques to describe the time-varying dynamics of self-exciting point processes. In particular we derive a stationary approximation of the Laplace transform of a locally stationary Hawkes process. This allows us to define a local intensity function and a local Bartlett spectrum which can be used to compute approximations of first and second order moments of the process. We complete the paper by some insightful simulation studies.
Keywords : point processes 2000 MSC: 60G55 Locally stationary processes Hawkes processes 46N30 62M15 time frequency analysis Bartlett spectrum
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Journal articles
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Contributor : François Roueff <>
Submitted on : Thursday, May 21, 2015 - 11:51:38 AM
Last modification on : Thursday, October 17, 2019 - 12:36:54 PM
Long-term archiving on: Tuesday, September 15, 2015 - 6:31:03 AM

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François Roueff, Rainer von Sachs, Laure Sansonnet. Locally stationary Hawkes processes. Stochastic Processes and their Applications, Elsevier, 2016, 126 (6), pp.Pages 1710-1743. ⟨10.1016/j.spa.2015.12.003⟩. ⟨hal-01153882⟩

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