Locally stationary Hawkes processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Roueff, Francois¹  von Sachs, Rainer²  Sansonnet, Laure³ 

[1] Univ Paris Saclay, CNRS, Telecom ParisTech, LTCI, 46 Rue Barrault, F-75634 Paris, France

[2] Catholic Univ Louvain, Inst Stat Biostat & Sci Actuarielles ISBA, IMMAQ, Voie Roman Pays 20,Boite L1-04-01, B-1348 Louvain La Neuve, Belgium

[3] Univ Paris Saclay, INRA, AgroParisTech, UMR MIA Paris, F-75005 Paris, France

关键词: Locally stationary processes;    Hawkes processes;    Bartlett spectrum;    Time-frequency analysis;    Point processes;   

DOI  :  10.1016/j.spa.2015.12.003

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free