Although a very rich list of classes of space-time covariance functions exists, specific tools for selecting the appropriate class for a given data set are needed. Thus, the main topic of this paper is to present the new R package, covatest, which can be used for testing some characteristics of a covariance function, such as symmetry, separability and type of non-separability, as well as for testing the adequacy of some classes of space-time covariance models. These last aspects can be relevant for choosing a suitable class of covariance models. The proposed results have been applied to an environmental case study.

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