Locally stationary Hawkes processes

François Roueff, Rainer von Sachs and Laure Sansonnet

Stochastic Processes and their Applications, 2016, vol. 126, issue 6, 1710-1743

Abstract: This paper addresses the generalization 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 functional of a locally stationary Hawkes process. This allows us to define a local mean density 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: Locally stationary processes; Hawkes processes; Bartlett spectrum; Time–frequency analysis; Point processes (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:6:p:1710-1743

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DOI: 10.1016/j.spa.2015.12.003

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