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Locally stationary Hawkes processes
- François Roueff #1
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Laboratoire Traitement et Communication de l'Information [Paris] (LTCI)
- Télécom ParisTech
- CNRS : UMR5141
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- References
- Workshop on Dependence, Stability and Extremes, The Fields Institute, Toronto, Ontario, Canada, May 2016,
- Abstract
We introduce non-stationary Hawkes processes which are defined similarly to standard Hawkes
processes but with a time- (or space-)evolving base intensity and fertility function. The resulting
process is inhomogeneous. However the usual conditions for the existence of a stationary Hawkes
process are easily adapted to obtain a stable non-stationary model. A wildly non-stationary model
cannot be consistently inferred, even from an infinite sample of data. Having in mind the statis-
tical analysis of non-stationary Hawkes processes, we propose an approach inspired from locally
stationary time series. We are thus interested in an asymptotic framework where the dimension of
the observation windows tend to infinity while the time- (or space-)varying parameters are sampled
from a function whose corresponding support remains unchanged. We show that under simple as-
sumptions, the statistical properties of the locally stationary Hawkes process can be approximated
by those of a stationary Hawkes process. In particular, this framework allows us to propose a
time-frequency analysis of Hawkes processes with time varying parameters.
- Keywords
- Category
- Invited speaker to a conference
- Research Area(s)
- Mathematics/Statistics
Statistics/Methodology
- Identifier(s)
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Bibliographic key roueff-fields-toronto2016
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- Last update
- on september 05, 2016
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