Fast Multi-resolution Segmentation for Nonstationary Hawkes Process Using Cumulants
Abstract
The stationarity is assumed in vanilla Hawkes process, which reduces the model complexity but introduces a strong assumption. In this paper, we propose a fast multi-resolution segmentation algorithm to capture the time-varying characteristics of nonstationary Hawkes process. The proposed algorithm is based on the first and second order cumulants. Except for the computation efficiency, the algorithm can provide a hierarchical view of the segmentation at different resolutions. We extensively investigate the impact of hyperparameters on the performance of this algorithm. To ease the choice of one hyperparameter, a refined Gaussian process based segmentation algorithm is also proposed which proves to be robust. The proposed algorithm is applied to a real vehicle collision dataset and the outcome shows some interesting hierarchical dynamic time-varying characteristics.
Cite
@article{arxiv.1906.02438,
title = {Fast Multi-resolution Segmentation for Nonstationary Hawkes Process Using Cumulants},
author = {Feng Zhou and Zhidong Li and Xuhui Fan and Yang Wang and Arcot Sowmya and Fang Chen},
journal= {arXiv preprint arXiv:1906.02438},
year = {2019}
}