Fifty years later : new directions in Hawkes processes
Worrall, John (School of Mathematical Sciences, Queensland University of Technology. QUT Centre for Data Science (Austràlia))
Browning, Raiha (School of Mathematical Sciences, Queensland University of Technology. QUT Centre for Data Science (Austràlia))
Wu, Paul (School of Mathematical Sciences, Queensland University of Technology. QUT Centre for Data Science (Austràlia))
Mengersen, Kerrie (School of Mathematical Sciences, Queensland University of Technology. QUT Centre for Data Science (Austràlia))

Date:	2022
Abstract:	The Hawkes process is a self-exciting Poisson point process, characterised by a conditional intensity function. Since its introduction fifty years ago, it has been the subject of numerous research directions and continues to inspire new methodological and theoretical developments as well as new applications. This paper marks half a century of interest in Hawkes processes by presenting a snapshot of four state-of-the-art research directions, categorised as frequentist and Bayesian methods, other modelling approaches and notable theoretical developments. A particular focus is on nonparametric approaches, with advances in kernel estimation and computational efficiencies. A survey of real world applications is provided to illustrate the breadth of application of this remarkable approach.
Note:	Acknowledgement. This research was supported by the ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS) and the Australian Research Council (ARC) Laureate Fellowship Program under the project 'Bayesian Learning for Decision Making in the Big Data Era' (ID: FL150100150).
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Hawkes process ; Point process ; Nonparametric
Published in:	SORT : statistics and operations research transactions, Vol. 46 Núm. 1 (2022) , p. 3-38 (Invited article) , ISSN 2013-8830

Adreça original: https://raco.cat/index.php/SORT/article/view/401109
DOI: 10.2436/20.8080.02.116

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