Characteristics of some classes of space-time covariance functions

Although a wide list of classes of space-time covariance functions is now available, selecting an appropriate class of models for a variable under study is still difficult and it represents a priority problem with respect to the choice of a particular model of a specified class. Then, knowing the characteristics of various classes of covariances, and their auxiliary functions, and matching those with the characteristics of the empirical space-time covariance surface might be helpful in the selection of a suitable class. In this paper some characteristics, such as behavior at the origin, asymptotic behavior, non-separability and anisotropy aspects, are studied for some well known classes of covariance models of stationary space-time random fields. Moreover, some important issues related to modeling choices are described and a case study is presented. (C) 2013 Elsevier B.V. All rights reserved.