Choosing a space-time covariance function for an environmental data set through the use of some statistical tests

The selection of an appropriate spatio-temporal covariance model for the data under study depends on different characteristics highlighted by the empirical covariance surface. In particular, it is worth: (i) Testing the null hypothesis of full symmetry (Li et al., 2007); if the null hypothesis is accepted, then a fully symmetric space-time covariance function can be considered; (ii) Testing the null hypothesis of separability (Li et al., 2007); if the separability hypothesis is accepted, then the space-time covariance model is simply the product of the spatial and temporal marginals, otherwise a non separable model is needed; (iii) Detecting the type of non separability (De Iaco and Posa, 2015): if the separability hypothesis is rejected, then a technique to detect the type of non separability is applied; (iv) Inspecting the asymptotic behavior of the spatial and temporal marginals, as well as their behavior at the origin; (v) Testing the class of covariances chosen on the basis of the output of the previous steps, and then fitting this model to the sample space-time covariance. In this paper, the procedure for selecting the suitable class of space-time covariance functions has been applied to a simulated data set and to a case study, concerning wind spee data measured over an area located in Southern Italy. In particular, in the case studies, different choices concerning the number of stations and the number of temporal lags to be used in the testing procedures (in particular, the tests for full symmetry, separability and the type of non separability), have been considered and the influence on the p-value has been evaluated.