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We develop flexible multivariate spatio-temporal Hawkes process models toanalyze patterns of terrorism. Previous applications of point process methodsto political violence data mainly utilize temporal Hawkes process models,neglecting spatial variation in these attack patterns. This limits what can belearned from these models as any effective counter-terrorism strategy requiresknowledge on both when and where attacks are likely to occur. Even the existingwork on spatio-temporal Hawkes processes imposes restrictions on the triggeringfunction that are not well-suited for terrorism data. Therefore, we generalizethe structure of the spatio-temporal triggering function considerably, allowingfor nonseprability, nonstatitionarity, and cross-triggering (i.e., across thegroups). To demonstrate the utility of our models, we analyze two samples ofreal-world terrorism data: Afghanistan (2002-2013) for univariate analysis andNigeria (2009-2017) for bivariate analysis. Jointly, these two studiesdemonstrate that our models outperform standard Hawkes process models, bestingwidely-used alternatives in overall model fit and revealing spatio-temporalpatterns that are, by construction, masked in these models (e.g., increasingdispersion in cross-triggering over time).

Flexible multivariate spatio-temporal Hawkes process models of terrorism