- Recherche et sélection de publications
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Locally stationary Hawkes processes
- François Roueff #1, Rainer von Sachs #2, Laure Sansonnet #3
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| #1 |
Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
- Télécom ParisTech
- CNRS : UMR5141
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| #2 |
Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)
- Université Catholique de Louvain
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| #3 |
Mathématiques et Informatique Appliquées (MIA-Paris)
- Institut national de la recherche agronomique (INRA)
- AgroParisTech
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- References
- Stochastic Processes and their Applications, 2016, vol. 126, n° 6, pp. 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
- Category
- Article in peer reviewed Journal
- Research Area(s)
- Mathematics/Statistics
- Identifier(s)
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DOI 10.1016/j.spa.2015.12.003
HAL ref. hal-01153882
Bibliographic key roueff-vonsachs-sansonnet2016
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- Last update
- on september 02, 2016
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