Fast multi-resolution segmentation for nonstationary Hawkes process using cumulants

Feng Zhou*, Zhidong Li, Xuhui Fan, Yang Wang, Arcot Sowmya, Fang Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The stationarity is assumed in the 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 the 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 hyperparameter, we propose a refined Gaussian process-based segmentation algorithm, which is proved to be a robust method. The proposed algorithm is applied to a real vehicle collision dataset, and the outcome shows some interesting hierarchical dynamic time-varying characteristics.

Original languageEnglish
Pages (from-to)321-330
Number of pages10
JournalInternational Journal of Data Science and Analytics
Issue number4
Publication statusPublished - Oct 2020
Externally publishedYes


  • Hawkes process
  • Nonstationary
  • Segmentation
  • Cumulants


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