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 language | English |
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Pages (from-to) | 225-242 |
Number of pages | 18 |
Journal | Journal of Time Series Analysis |
Volume | 38 |
Issue number | 2 |
Early online date | 2016 |
DOIs | |
Publication status | Published - Mar 2017 |
Keywords
- Hawkes process
- Granger causality
- graphical model
- mutually exciting process
- nonparametric estimation
- EXCITING POINT-PROCESSES
- CONTINUOUS-TIME
- FINANCIAL DATA
- NONCAUSALITY
- SPECTRA
- SERIES