Abstract
Obtaining 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 introduce and develop new spatio-temporal covariance models taking into account the problem of spatial anisotropy. Recent literature has focused on the problem of full symmetry and the problem of anisotropy has been overcome. Here we propose a generalization of Gneiting’s (J Am Stat Assoc 97:590–600, 2002a) approach and obtain new classes of stationary nonseparable spatio-temporal covariance functions which are spatially anisotropic. The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability.
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The Editor and referees are acknowledged with thanks. Their precise comments and suggestions have clearly improved an earlier version of the manuscript.
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Work partially funded by grant MTM2004-06231 from the Spanish Ministry of Science and Education.
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Porcu, E., Gregori, P. & Mateu, J. Nonseparable stationary anisotropic space–time covariance functions. Stoch Environ Res Ris Assess 21, 113–122 (2006). https://doi.org/10.1007/s00477-006-0048-3
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DOI: https://doi.org/10.1007/s00477-006-0048-3