Semi-parametric Spatio-Temporal Hawkes Process for Modelling Road Accidents in Rome

We propose a semi-parametric spatio-temporal Hawkes process with periodic components to model the occurrence of car accidents in a given spatio-temporal window. The overall intensity is split into the sum of a background component capturing the spatio-temporal varying intensity and an excitation component accounting for the possible triggering effect between events. The spatial background is estimated and evaluated on the road network, allowing the derivation of accurate risk maps of road accidents. We constrain the spatio-temporal excitation to preserve an isotropic behaviour in space, and we generalize it to account for the effect of covariates. The estimation is pursued by maximizing the expected complete data log-likelihood using a tailored version of the stochastic-reconstruction algorithm that adopts ad hoc boundary correction strategies. An original application analyses the car accidents that occurred on the Rome road network in the years 2019, 2020, and 2021. Results highlight that car accidents of different types exhibit varying degrees of excitation, ranging from no triggering to a 10% chance of triggering further events.