Abstract
In multivariate Geostatistics, the linear coregionalization model (LCM) has been widely used over the last decades, in order to describe the spatial dependence which characterizes two or more variables of interest. However, in spatio-temporal multiple modeling, the identification of the main elements of a space–time linear coregionalization model (ST-LCM), as well as of the latent structures underlying the analyzed phenomenon, represents a tough task. In this paper, some computational advances which support the selection of an ST-LCM are described, gathering all the necessary steps which allow the analyst to easily and properly detect the basic space–time components for the phenomenon under study. The implemented algorithm is applied on space–time air quality data measured in Scotland in 2017.
Highlights
In environmental studies, the analysis of the relationships among two or more variables, measured in space and time, is of wide interest
A first attempt to propose a procedure to support the identification of an STLCM for a multivariate data set was given in De Iaco et al (2012), where the authors assumed to model the basic components through the product–sum class
The restriction on this specific class of covariance models to be used for describing the basic components was abandoned in some further applications, only the contribution in De Iaco et al (2019) pointed out that the basic components can be modelled by using different families of covariance models and the choice of the family for one basic component does not influence the choice for the other components, since the selection of each class can be reasonably relied on the main features of the sample basic covariance surfaces
Summary
The analysis of the relationships among two or more variables, measured in space and time, is of wide interest. In this paper, the proposed algorithm focuses, in a very compact and analytic way, on the implementation of the multivariate modeling procedure of an ST-LCM, where no specific class of covariance models is assumed a priori for the basic components. Differently from the common approach which consists in using the same class of models for all the components of the ST-LCM as in De Iaco et al (2003), the new algorithm allows the users to obtain a flexible ST-LCM, whose components can have different properties in terms of symmetry/asymmetry, separability/non-separability and, in case of non-separability, positive/negative nonseparability (De Iaco et al 2019) To our knowledge, these advances have not been tackled in previous works and represent a remarkable step forward of the current state of computational progress in spatio-temporal multivariate analysis.
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