The Integer-valued Moving-Average Random Field

TL;DR

This paper introduces an integer-valued moving average (INMA) model for count random fields, providing explicit formulas for distributions and dependence, and demonstrating its flexibility with Poisson marginals and interpretable dependence structures.

Contribution

It develops a new INMA model with closed-form expressions for distributions and dependence, enhancing modeling of count random fields.

Findings

Derived closed-form expressions for marginal distributions and autocovariances.

Showed INMA can have Poisson marginals and various dependence structures.

Illustrated the interpretability of the dependence structures.

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. 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 illustrated that different and well-interpretable dependence structures are possible.