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