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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Submitted on : Thursday, May 21, 2015 - 11:51:38 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. ⟨http://www.sciencedirect.com/science/article/pii/S0304414915003075⟩. ⟨10.1016/j.spa.2015.12.003⟩. ⟨hal-01153882⟩

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