A general spatial ARMA Model: theory and application

In this paper the theoretical framework of a higher order spatial auto-regressive moving-average (SARMA) model is presented. The SARMA model is the spatial analogue of the well-known class of ARMA models that is developed to model time-series processes. It is shown that in time ARMA models observations in time are related to past values using so-called time link matrices. In spatial ARMA models observations in space are usually related to neighboring values using spatial link matrices. The idea behind both types of link matrices is that a certain structure is imposed on the data before the actual parameters are estimated. The problem of choosing the 'right' (spatial) link matrix is also present in modeling ARMA time series processes. The advantage of the general SARMA model is that the scale of spatial processes can be modeled explicitly: a separate spatial link parameter can be estimated for each (higher order) spatial link. In addition, criteria for model selection are presented that can be used to choose from alternative models. The theoretical findings are applied in a hedonic pricing framework: a SARMA model is estimated that is able to detect both the extent and the scale of spatial spillovers of Dutch wetlands.