Time-frequency analysis of locally stationary Hawkes processes

Locally stationary Hawkes processes have been introduced in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. This class of self-exciting point processes has recently attracted a lot of interest in applications in the life sciences (seismology, genomics, neuro-science,...), but also in the modeling of high-frequency financial data. In this contribution we provide a fully developed nonparametric estimation theory of both local mean density and local Bartlett spectra of a locally stationary Hawkes process. In particular we apply our kernel estimation of the spectrum localised both in time and frequency to two data sets of transaction times revealing pertinent features in the data that had not been made visible by classical non-localised approaches based on models with constant fertility functions over time.

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Document type	Article de périodique (Journal article) – Article de recherche
Access type	Accès libre
Publication date	2018
Language	Anglais
Journal information	"Bernoulli : a journal of mathematical statistics and probability" - Vol. 25, no. 2, p. 1355-1385 (2019)
Peer reviewed	yes
Publisher	International Statistical Institute (The Hague)
issn	1350-7265
e-issn	1573-9759
Publication status	Publié
Affiliation	UCL - SSH/LIDAM/ISBA - Institut de Statistique, Biostatistique et Sciences Actuarielles
Keywords	Time frequency analysis ; Locally stationary time series ; high frequency financial data ; Non-parametric kernel estimation ; Self-exciting point processes
Links	http://www.bernoulli-society.org/index.php/publications/bernoulli-journal/bernoulli-journal-papers http://hdl.handle.net/2078.1/203144[Handle]

See also
	[boreal:183997]	Time-frequency analysis of locally stationary Hawkes processes