Geostatistical models and new computational aspects for space-time predictions: Some statistical tests and a case study on environmental data

Non-separable models are receiving a lot of attention, since they are more flexible to handle empirical covariance functions showed up in applications. When phenomena can not be described by physical laws and their space-time covariance models can not be obtained as solutions of partial differential equations, it is advisable to choose an appropriate class of spacetime covariance models for the given data set, on the basis of the main characteristics, such as full symmetry, separability, behavior at the origin, anisotropy aspects, as well as type of non separability and asymptotic behavior of the empirical covariance function. In particular, a particular attention will be turned on the type of non separability of a space-time covariance function and variability along space and time exhibited by the spatial and temporal marginal covariances. Moreover, a technique for testing some classes of covariance functions, as well as applications to the classes of Rodrigues and Diggle models (Rodrigues and Diggle, 2010), product-sum models (De Iaco et al., 2001), Gneiting models (Gneiting, 2002), integrated product models (De Iaco et al., 2002; Ma, 2003) and Cressie-Huang models (Cressie and Huang, 1999) are also provided. A case study on an environmental variable is presented.