Corpus ID: 212644521

Strong mixing condition for Hawkes processes and application to Whittle estimation from count data

@article{Cheysson2020StrongMC,
  title={Strong mixing condition for Hawkes processes and application to Whittle estimation from count data},
  author={Felix Cheysson and Gabriel Lang Universit'e Paris-Saclay and AgroParisTech and Inrae and Umr MIA-Paris and Par{\'i}s and France. and Epidemiology and Modeling of bacterial Evasion to Antibacterials Unit and Institut Pasteur and Anti-infective Evasion and Pharmacoepidemiology Team and Centre for Epidemiology and Public Health and Inserm Uvsq},
  journal={arXiv: Statistics Theory},
  year={2020}
}
This paper focuses on the time series generated by the event counts of stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, existing methods of estimation are not applicable. We first establish a strong mixing condition with polynomial decay rate for Hawkes processes, from their Poisson cluster structure. This allows us to propose a spectral approach to the estimation of Hawkes processes, based on Whittle's method… Expand
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