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\iteman{io-port 05637262}
\itemau{Mateu, J.; Porcu, E.; Gregori, P.}
\itemti{Recent advances to model anisotropic space-time data.}
\itemso{Stat. Methods Appl. 17, No. 2, 209-223 (2008).}
\itemab
Summary: 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 {\it T. Gneiting}'s approach [J. Am. Stat. Assoc. 97, No.~458, 590--600 (2002; Zbl 1073.62593)] 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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\itemut{anisotropy; geostatistics; isotropy within components; space-time covariance functions}
\itemli{doi:10.1007/s10260-007-0056-6}
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