Stationary random fields in space and time with rational spectral densities

Abstract

This paper introduces three spatio–temporal stationary random fields with simple correlation functions and rational spectral densities. The correlation functions have similar forms, but are defined on different space–time domains or related to different spatial norms. Positive and negative correlations are allowed, and the domain of certain model parameters may rely on the spatial dimensional parameter so that the model may be available in a limited space or in all dimensions. The distinctions are discussed among the three basic correlation models. Moreover, families of spatio–temporal stationary random fields are derived by randomizing the spatial and temporal coordinates of the base random fields. The resulting correlation functions are semiparametric, and include separable spatio–temporal models as special cases.