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30 Years of space–time covariance functions


Porcu, Emilio; Furrer, Reinhard; Nychka, Douglas (2021). 30 Years of space–time covariance functions. Wiley Interdisciplinary Reviews: Computational Statistics, 13(2):e1512.

Abstract

In this article, we provide a comprehensive review of space–time covariance functions. As for the spatial domain, we focus on either the d‐dimensional Euclidean space or on the unit d‐dimensional sphere. We start by providing background information about (spatial) covariance functions and their properties along with different types of covariance functions. While we focus primarily on Gaussian processes, many of the results are independent of the underlying distribution, as the covariance only depends on second‐moment relationships. We discuss properties of space–time covariance functions along with the relevant results associated with spectral representations. Special attention is given to the Gneiting class of covariance functions, which has been especially popular in space–time geostatistical modeling. We then discuss some techniques that are useful for constructing new classes of space–time covariance functions. Separate treatment is reserved for spectral models, as well as to what are termed models with special features. We also discuss the problem of estimation of parametric classes of space–time covariance functions. An outlook concludes the paper.

Abstract

In this article, we provide a comprehensive review of space–time covariance functions. As for the spatial domain, we focus on either the d‐dimensional Euclidean space or on the unit d‐dimensional sphere. We start by providing background information about (spatial) covariance functions and their properties along with different types of covariance functions. While we focus primarily on Gaussian processes, many of the results are independent of the underlying distribution, as the covariance only depends on second‐moment relationships. We discuss properties of space–time covariance functions along with the relevant results associated with spectral representations. Special attention is given to the Gneiting class of covariance functions, which has been especially popular in space–time geostatistical modeling. We then discuss some techniques that are useful for constructing new classes of space–time covariance functions. Separate treatment is reserved for spectral models, as well as to what are termed models with special features. We also discuss the problem of estimation of parametric classes of space–time covariance functions. An outlook concludes the paper.

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Additional indexing

Item Type:Journal Article, refereed, further contribution
Communities & Collections:07 Faculty of Science > Institute of Mathematics
07 Faculty of Science > Institute for Computational Science
Dewey Decimal Classification:340 Law
610 Medicine & health
510 Mathematics
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Uncontrolled Keywords:Statistics and Probability
Language:English
Date:1 March 2021
Deposited On:02 Oct 2020 12:32
Last Modified:27 Feb 2021 08:21
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:1939-5108
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1002/wics.1512
Project Information:
  • : FunderSNSF
  • : Grant ID200021_175529
  • : Project TitleDisentangling evidence from huge multivariate space-time data from the earth sciences

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