Graphical Modeling for Multivariate Hawkes Processes with Nonparametric\n Link Functions

2016/05/22 by Michael Eichler, Eichler, Michael, Rainer Dahlhaus +3 · 4 citations
Mathematics · #Point processes and geometric inequalities #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.1605.06759

Abstract

Hawkes (1971) introduced a powerful multivariate point process model of\nmutually exciting processes to explain causal structure in data. In this paper\nit is shown that the Granger causality structure of such processes is fully\nencoded in the corresponding link functions of the model. A new nonparametric\nestimator of the link functions based on a time-discretized version of the\npoint process is introduced by using an infinite order autoregression.\nConsistency of the new estimator is derived. The estimator is applied to\nsimulated data and to neural spike train data from the spinal dorsal horn of a\nrat.\n

Citations

• Investigating Causal Relations by Econometric Models and Cross-spectral Methods

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