Test and Visualization of Covariance Properties for Multivariate Spatio-Temporal Random Fields

Abstract

The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance function plays a key role in modeling, inference, and prediction. For multivariate space-time data, understanding the spatio-temporal variability, within and across variables, is essential in employing a realistic covariance model. Meanwhile, the complexity of generic covariances often makes model fitting very challenging, and simplified covariance structures, including symmetry and separability, can reduce the model complexity and facilitate the inference procedure. However, a careful examination of these properties is needed in real applications. In the work presented here, we formally define these properties for multivariate spatio-temporal random fields and use functional data analysis techniques to visualize them, hence, providing intuitive interpretations. We then propose a rigorous rank-based testing procedure to conclude whether the simplified properties of covariance are suitable for the underlying multivariate space-time data. The good performance of our method is illustrated through synthetic data, for which we know the true structure. We also investigate the covariance of bivariate wind speed, a key variable in renewable energy, over a coastal and an inland area in Saudi Arabia. The supplementary material is available online, including the R code for our developed methods.

Keywords:

• Bivariate wind vector
• Functional boxplot
• Multivariate spatio-temporal data
• Rank-based test
• Separability
• Symmetry

Disclosure Statement

The authors report that there are no competing interests to declare.

Supplementary Material

supplementary-document.pdf: Proofs and supplementary table

code.zip: R code for our proposed visualization and test methods

shiny.zip: Interactive R ShinyApp showing simulation examples

Additional information

Funding

This publication is based on research supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No: OSR-2018-CRG7-3742 and in part by the Center of Excellence for NEOM Research at KAUST.