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Covariance functions and variograms play a fundamental role in exploratoryanalysis and statistical modelling of spatial and spatio-temporal datasets. Inthis paper, we construct a new class of spatial covariance functions using theFourier transform of some higher-order kernels. Further, we extend this classof the spatial covariance functions to the spatio-temporal setting by using theidea used in Ma (2003).

A new class of spatial covariance functions generated by higher-order kernels