Recent advances to model anisotropic space–time data |
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Authors: | J Mateu E Porcu P Gregori |
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Institution: | (1) Department of Mathematics, Universitat Jaume I, 12071 Castellon, Spain |
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Abstract: | Building new and flexible classes of nonseparable spatio-temporal covariances and variograms has resulted a key point of research
in the last years. The goal of this paper is to present an up-to-date overview of recent spatio-temporal covariance models
taking into account the problem of spatial anisotropy. The resulting structures are proved to have certain interesting mathematical
properties, together with a considerable applicability. In particular, we focus on the problem of modelling anisotropy through
isotropy within components. We present the Bernstein class, and a generalisation of Gneiting’s approach (2002a) to obtain
new classes of space–time covariance functions which are spatially anisotropic. We also discuss some methods for building
covariance functions that attain negative values. We finally present several differentiation and integration operators acting
on particular space–time covariance classes.
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Keywords: | Anisotropy Geostatistics Isotropy within components Space– time covariance functions |
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