Flexible multivariate spatio-temporal Hawkes process models of terrorism

We develop flexible multivariate spatio-temporal Hawkes process models to analyze patterns of terrorism. Previous applications of point process methods to political violence data mainly utilize temporal Hawkes process models, neglecting spatial variation in these attack patterns. This limits what can be learned from these models as any effective counter-terrorism strategy requires knowledge on both when and where attacks are likely to occur. Even the existing work on spatio-temporal Hawkes processes imposes restrictions on the triggering function that are not well-suited for terrorism data. Therefore, we generalize the structure of the spatio-temporal triggering function considerably, allowing for nonseprability, nonstatitionarity, and cross-triggering (i.e., across the groups). To demonstrate the utility of our models, we analyze two samples of real-world terrorism data: Afghanistan (2002-2013) for univariate analysis and Nigeria (2009-2017) for bivariate analysis. Jointly, these two studies demonstrate that our models outperform standard Hawkes process models, besting widely-used alternatives in overall model fit and revealing spatio-temporal patterns that are, by construction, masked in these models (e.g., increasing dispersion in cross-triggering over time).