A semiparametric spatiotemporal Hawkes-type point process model with periodic background for crime data

Abstract

Past 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 Castell ́ on, 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.