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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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https://hal-imt.archives-ouvertes.fr/hal-01153882
Contributor : François Roueff Connect in order to contact the contributor
Submitted on : Thursday, May 21, 2015 - 11:51:38 AM
Last modification on : Wednesday, October 27, 2021 - 6:48:16 AM
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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