The Integer-valued Moving-Average Random Field

Abstract

An integer-valued moving average (INMA) model for count random fields is proposed and investigated. Closed-form expressions are derived for both its marginal distribution and spatial dependence structure, for arbitrary model order and also covering the multilateral case. In particular, general expressions for bivariate distributions and autocovariances are provided. It is shown that the INMA random field can be equipped (among others) with a Poisson marginal distribution. It is also demonstrated that different and well-interpretable dependence structures are possible. For illustration, we discuss a real-world data example and propose an INMA approximation to a given spatial dependence structure.