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In various situations in the insurance industry, in finance, in epidemiology,etc., one needs to represent the joint evolution of the number of occurrencesof an event. In this paper, we present a multivariate integer-valuedautoregressive (MINAR) model, derive its properties and apply the model toearthquake occurrences across various pairs of tectonic plates. The model is anextension of Pedelis & Karlis (2011) where cross autocorrelation (spatialcontagion in a seismic context) is considered. We fit various bivariate countmodels and find that for many contiguous tectonic plates, spatial contagion issignificant in both directions. Furthermore, ignoring cross autocorrelation canunderestimate the potential for high numbers of occurrences over theshort-term. Our overall findings seem to further confirm Parsons & Velasco(2001).

Multivariate integer-valued autoregressive models applied to earthquake counts