  Hawkes (1971) introduced a powerful multivariate point process model of
mutually exciting processes to explain causal structure in data. In this paper
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.
