Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions. (13th September 2016)

• Record Type: Journal Article
• Authors: Eichler, Michael; Dahlhaus, Rainer; Dueck, Johannes
• Other Names: Subba Rao Tata guestEditor.; Tunnicliffe Wilson Granville guestEditor.
• Is Part Of: Journal of time series analysis. Volume 38:Number 2(2017:Mar.)
• Page Start: 225
• Page End: 242
• Publication Date: 2016-09-13
• Subjects: Hawkes process -- Granger causality -- graphical model -- mutually exciting process -- nonparametric estimation; Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12213
• Languages: English
• ISSNs: 0143-9782

Abstract

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.