Characteristics of some classes of space–time covariance functions

• A selection of appropriate classes of covariance models represents a priority problem with respect to the choice of a model.
• Knowing the characteristics of various classes of covariances, and their auxiliary functions is helpful in selecting a suitable class.
• Behavior at the origin, asymptotic behavior, nonseparability and anisotropy aspects are studied for some classes of covariance models.
• Features of a suitable class of covariances should match the corresponding characteristics of the empirical space–time covariance surface.
• The nonseparability index and the analysis of the asymptotic behavior of the covariance surface are considered in the case study.

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, nonseparability 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.