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Time-frequency analysis of locally stationary Hawkes processes

François Roueff #1, Rainer von Sachs #2
#1 Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
  • Télécom ParisTech
  • CNRS : UMR5141
#2 Institut de Statistique, Biostatistique et Sciences Actuarielles (ISBA)
  • Université Catholique de Louvain
References
Bernoulli journal, 2018,
Abstract

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 modelling 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.

Keywords
high frequency financial data;Time frequency analysis;Non-parametric kernel estimation;Self-exciting point processes;Locally stationary time series
Category
Article in peer reviewed Journal
Research Area(s)
Mathematics/Statistics
Identifier(s)
HAL ref. hal-01502252
Bibliographic key roueff:hal-01502252v3
File(s)
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Last update
on january 25, 2019 by Francois Roueff


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