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Time-frequency analysis of locally stationary Hawkes processes
- François Roueff
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- References
- Statistics seminar series, LSE, London, Royaume Uni., May 2017,
- Abstract
Self-exciting point processes have 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. We introduce locally stationary Hawkes processes in order to generalise classical Hawkes processes away from stationarity by allowing for a time-varying second-order structure. A convenient way to reveal this interesting feature on a data set is to perform a time-frequency analysis. We introduce such a tool adapted to non-stationary point processes via non-parametric kernel estimation. Moreover, 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 to two data sets of transaction times exhibiting time-evolving characteristics in the data that had not been made visible by classical approaches.
- Keywords
- Category
- Article without proceedings (workshop...)
- Research Area(s)
- Mathematics/Statistics
Statistics/Applications
Statistics/Methodology
- Identifier(s)
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Bibliographic key fr-hawkes-lse-2017
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- Last update
- on february 21, 2018 by Francois Roueff
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