  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.
