Visualization and assessment of spatio-temporal covariance properties

Huang Huang, Ying Sun

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random fields in geostatistical data. For second-order stationary random fields, there exist subclasses of covariance functions that assume a simpler spatio-temporal dependence structure with separability and full symmetry. However, it is challenging to visualize and assess separability and full symmetry from spatio-temporal observations. In this work, we propose a functional data analysis approach that constructs test functions using the cross-covariances from time series observed at each pair of spatial locations. These test functions of temporal lags summarize the properties of separability or symmetry for the given spatial pairs. We use functional boxplots to visualize the functional median and the variability of the test functions, where the extent of departure from zero at all temporal lags indicates the degree of non-separability or asymmetry. We also develop a rank-based nonparametric testing procedure for assessing the significance of the non-separability or asymmetry. Essentially, the proposed methods only require the analysis of temporal covariance functions. Thus, a major advantage over existing approaches is that there is no need to estimate any covariance matrix for selected spatio-temporal lags. The performances of the proposed methods are examined by simulations with various commonly used spatio-temporal covariance models. To illustrate our methods in practical applications, we apply it to real datasets, including weather station data and climate model outputs.
Original languageEnglish (US)
Pages (from-to)100272
JournalSpatial Statistics
StatePublished - Nov 23 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-2015-CRG4-2582
Acknowledgements: The authors thank the reviewers for their valuable comments that greatly improved the quality of this article. This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award OSR-2015-CRG4-2582. The authors also thank the North American Regional Climate Change Assessment Program (NARCCAP) for providing the data used in this paper. NARCCAP is funded by the National Science Foundation (NSF), the U.S. Department of Energy (DoE), the National Oceanic and Atmospheric Administration (NOAA), and the U.S. Environmental Protection Agency Office of Research and Development (EPA) .


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