A general procedure for selecting a class of fully symmetric space-time covariance functions

Sometimes, space-time covariance models can be derived as solutions of partial differential equations, for phenomena which can be described by physical laws. When the complexity of natural processes does not allow such a description, it would be useful to have a guide for selecting an appropriate class of space-time covariance models for a given data set, among the classes constructed in the last years. Thus, the main aim of this paper is to provide a general procedure for space-time modeling, where the first step to be made is not the choice of a particular covariance model but the choice of the class of covariance functions suitable for the variable under study. Hence, starting from a space-time data set, an adequate class of models will be properly chosen by considering the main characteristics, such as full symmetry, separability, behavior at the origin, anisotropy aspects, as well as type of non separability and asymptotic behavior. In the literature, these aspects have never been considered in a unified way; nevertheless, they can be relevant for selecting a suitable class of covariance models. The proposed procedure has been applied to both a simulated data set and an environmental case study. Copyright (C) 2016 John Wiley & Sons, Ltd.