Characterization Theorems for Pseudo-Variograms

12/05/2021

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by   Christopher Dörr, et al.

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Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued function to be a pseudo-variogram, and further provide a Schoenberg-type result connecting pseudo-variograms and multivariate correlation functions. By means of these characterizations, we provide extensions of the popular univariate space-time covariance model of Gneiting to the multivariate case.