Temporal Hawkes Process for Modeling Short-Term Clustering of Crime Events in Ostrava

Abstract

This paper applies a temporal Hawkes process to the analysis of short-term clustering in crime event data. The study uses publicly available records from the Crime Map of the Police of the Czech Republic and focuses on events of general crime in the Ostrava region during the period 2016-2025. A homogeneous Poisson process is used as a baseline model, while the Hawkes process with an exponential kernel is used to capture possible self-exciting behavior in the event sequence. The parameters are estimated by maximum likelihood and the models are compared using log-likelihood, AIC, BIC and residual diagnostics based on the time-rescaling principle. The results show that the temporal Hawkes model provides a substantially better description of the data than the homogeneous Poisson model. The estimated branching ratio is approximately 0.143, which indicates the presence of a measurable but not dominant self-exciting component. The estimated excitation half-life is about 1.11 hours, suggesting that the detected temporal dependence is mainly short-term. The results demonstrate that even a simple one-dimensional Hawkes model can provide an interpretable description of temporal clustering in crime data. At the same time, the analysis highlights the limitations of a stationary temporal model and motivates future extensions including non-stationary background intensity and spatial information.