Visualization and assessment of spatio-temporal covariance properties
Type
ArticleAuthors
Huang, Huang
Sun, Ying

KAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Statistics Program
KAUST Grant Number
OSR-2015-CRG4-2582Date
2017-11-23Preprint Posting Date
2017-05-04Online Publication Date
2017-11-23Print Publication Date
2017-11Permanent link to this record
http://hdl.handle.net/10754/626249
Metadata
Show full item recordAbstract
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.Citation
Huang H, Sun Y (2017) Visualization and assessment of spatio-temporal covariance properties. Spatial Statistics. Available: http://dx.doi.org/10.1016/j.spasta.2017.11.004.Sponsors
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) .Publisher
Elsevier BVJournal
Spatial StatisticsarXiv
1705.01789Additional Links
http://www.sciencedirect.com/science/article/pii/S2211675317301306ae974a485f413a2113503eed53cd6c53
10.1016/j.spasta.2017.11.004