Choosing suitable linear coregionalization models for spatio-temporal data

In multivariate spatio-temporal Geostatistics, direct and cross-correlations among the variables of interest are measured by the matrix-valued covariance function. In this paper, a new and complete procedure useful for selecting an appropriate spatio-temporal linear coregionalization model (ST-LCM) with suitable models for the basic components is proposed. Thus, after detecting the spatio-temporal correlation of the latent components, through simultaneous diagonalization of the sample covariance matrices, some essential characteristics of each component are tested so that an aware choice for basic covariance models can be made. In the literature, some statistical tests to assess separability and symmetry of the covariance matrix, as well as the adequacy of the LCM were proposed; however in this paper further aspects on the basic components are investigated. All steps of the proposed procedure for analyzing and modeling the components of an ST- LCM are discussed in a case study where a very large spatio-temporal data set, concerning two environmental variables, is considered.