Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions

Michael Eichler, R. Dahlhaus, J. Dueck

Research output: Contribution to journalSpecial issueAcademicpeer-review

Abstract

Hawkes (1971a) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this article, it is shown that the Granger causality structure of such processes is fully encoded in the corresponding link functions of the model. A new nonparametric estimator of the link functions based on a time-discretized version of the point process is introduced by using an infinite order autoregression. Consistency of the new estimator is derived. The estimator is applied to simulated data and to neural spike train data from the spinal dorsal horn of a rat.

Original languageEnglish
Pages (from-to)225-242
Number of pages18
JournalJournal of Time Series Analysis
Volume38
Issue number2
Early online date2016
DOIs
Publication statusPublished - Mar 2017

Keywords

  • Hawkes process
  • Granger causality
  • graphical model
  • mutually exciting process
  • nonparametric estimation
  • EXCITING POINT-PROCESSES
  • CONTINUOUS-TIME
  • FINANCIAL DATA
  • NONCAUSALITY
  • SPECTRA
  • SERIES

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