Locally stationary Hawkes processes

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.
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Article dans une revue
Stochastic Processes and their Applications, Elsevier, 2016, 126 (6), pp.Pages 1710-1743. 〈http://www.sciencedirect.com/science/article/pii/S0304414915003075〉. 〈10.1016/j.spa.2015.12.003〉
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Contributeur : François Roueff <>
Soumis le : jeudi 21 mai 2015 - 11:51:38
Dernière modification le : vendredi 20 juillet 2018 - 11:13:08
Document(s) archivé(s) le : mardi 15 septembre 2015 - 06:31:03

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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. 〈http://www.sciencedirect.com/science/article/pii/S0304414915003075〉. 〈10.1016/j.spa.2015.12.003〉. 〈hal-01153882〉

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