Advances in Applied Probability

Spatio-temporal variograms and covariance models

Chunsheng Ma

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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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Adv. in Appl. Probab. Volume 37, Number 3 (2005), 706-725.

First available in Project Euclid: 23 September 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G12: General second-order processes
Secondary: 60G10: Stationary processes 60G60: Random fields

Covariance intrinsically stationary isotropic positive definite power-law decay Schoenberg-Lévy kernel stationary variogram


Ma, Chunsheng. Spatio-temporal variograms and covariance models. Adv. in Appl. Probab. 37 (2005), no. 3, 706--725. doi:10.1239/aap/1127483743.

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