A Semiparametric Spatiotemporal Hawkes-Type Point Process Model with Periodic Background for Crime Data

Abstract

SummaryPast studies have shown that crime events are often clustered. This study proposes a spatiotemporal Hawkes-type point process model, which includes a background component with daily and weekly periodization, and a clustering component that is triggered by previous events. We generalize the non-parametric stochastic reconstruction method so that we can estimate each component in the background rate and the triggering response that appears in the model conditional intensity: the background rate includes a daily and a weekly periodicity, a separable spatial component and a long-term background trend. Two relaxation coefficients are introduced to stabilize and secure the estimation process. This model is used to describe the occurrences of violence or robbery cases in Castellón, Spain, during 2 years. The results show that robbery crime is highly influenced by daily life rhythms, revealed by its daily and weekly periodicity, and that about 3% of such crimes can be explained by clustering. Further diagnostic analysis shows that the model could be improved by considering the following ingredients: the daily occurrence patterns are different between weekends and working days; in the city centre, robbery activity shows different temporal patterns, in both weekly periodicity and long-term trend, from other suburb areas.