31: Numerical Methods for Parameter Estimation of Spatio-Temporal Hawkes Processes

Music City Center 

The Hawkes process is a widely used statistical model used for point processes, where past events increase the intensity of the process. Strong dependence in these processes leads to challenges in point estimation and constructing confidence intervals. Previous studies have shown that asymptotic confidence intervals perform poorly in simulation studies, while the parametric bootstrap achieves nominal coverage. This study explores non-parametric resampling methods, such as the block-bootstrap and subsampling, for constructing confidence regions in highly dependent spatio-temporal Hawkes processes. These methods are applied to a criminology dataset to illustrate their practical implications.

Hawkes Process

Block Bootstrap

Subsampling

Simulation Study

Criminology 

Section on Statistical Computing