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Towards a complete picture of stationary covariance functions on spheres cross time

Lookup NU author(s): Professor Emilio Porcu

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Abstract

© 2019, Institute of Mathematical Statistics. All rights reserved.With the advent of wide-spread global and continental-scale spatiotemporal datasets, increased attention has been given to covariance functions on spheres over time. This paper provides results for stationary covariance functions of random fields defined over d-dimensional spheres cross time. Specifically, we provide a bridge between the characterization in Berg and Porcu (2017) for covariance functions on spheres cross time and Gneiting’s lemma (Gneiting, 2002) that deals with planar surfaces. We then prove that there is a valid class of covariance functions similar in form to the Gneiting class of space-time covariance functions (Gneiting, 2002) that replaces the squared Euclidean distance with the great circle distance. Notably, the provided class is shown to be positive definite on every d-dimensional sphere cross time, while the Gneiting class is positive definite over Rd × R for fixed d only. In this context, we illustrate the value of our adapted Gneiting class by comparing examples from this class to currently established nonseparable covariance classes using out-of-sample predictive criteria. These comparisons are carried out on two climate reanalysis datasets from the National Centers for Environmental Prediction and National Center for Atmospheric Research. For these datasets, we show that examples from our covariance class have better predictive performance than competing models.

Publication metadata

Author(s): White P, Porcu E

Publication type: Article

Publication status: Published

Journal: Electronic Journal of Statistics

Year: 2019

Volume: 13

Issue: 2

Pages: 2566-2594

Online publication date: 02/08/2019

Acceptance date: 02/04/2016

ISSN (electronic): 1935-7524

Publisher: Institute of Mathematical Statistics

URL: https://doi.org/10.1214/19-EJS1593

DOI: 10.1214/19-EJS1593

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