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Families of spatio-temporal stationary covariance models. (English) Zbl 1043.62051

Summary: This paper provides simple methods for constructing new families of spatio-temporal stationary covariance models from purely spatial (or purely temporal) stationary covariance models. As an application of the methods developed, we introduce spatio-temporal stationary covariance models with Gaussian and related spatial margins, and develop the Heine family [see V. Heine, Biometrika 42, 170–178 (1955; Zbl 0067.36504)] and the Whittle-Matérn family [see P. Whittle, ibid. 41, 434–449 (1954; Zbl 0058.35601); ibid. 49, 305–314 (1962; Zbl 0114.08003); B. Matérn, Spatial variation. 2nd ed. (1986; Zbl 0608.62122)] of an spatio-temporal stationary covariance models.

MSC:

62H11 Directional data; spatial statistics
62M30 Inference from spatial processes
43A35 Positive definite functions on groups, semigroups, etc.
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