Spatio-temporal variograms and covariance models
Chunsheng Ma
Source: Adv. in Appl. Probab. Volume 37, Number 3
(2005), 706-725.
Abstract
Variograms and covariance functions are the fundamental tools for modeling dependent data observed over time, space, or space-time. This paper aims at constructing nonseparable spatio-temporal variograms and covariance models. Special attention is paid to an intrinsically stationary spatio-temporal random field whose covariance function is of Schoenberg-Lévy type. The correlation structure is studied for its increment process and for its partial derivative with respect to the time lag, as well as for the superposition over time of a stationary spatio-temporal random field. As another approach, we investigate the permissibility of the linear combination of certain separable spatio-temporal covariance functions to be a valid covariance, and obtain a subclass of stationary spatio-temporal models isotropic in space.
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Keywords: Covariance; intrinsically stationary; isotropic; positive definite; power-law decay; Schoenberg-Lévy kernel; stationary; variogram
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1127483743
Digital Object Identifier: doi:10.1239/aap/1127483743
Mathematical Reviews number (MathSciNet): MR2156556
Zentralblatt MATH identifier: 1077.60031
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