Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions
本文证明多元霍克斯过程的格兰杰因果结构完全由模型的链接函数编码，并基于时间离散化版本提出一种新的非参数估计量，证明了其一致性，应用于模拟数据和老鼠脊髓背角神经尖峰序列数据。
Hawkes ( ) 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.