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

TL;DR

This paper introduces a formal framework and visualization techniques for analyzing covariance properties in multivariate spatio-temporal data, along with a statistical test to assess the suitability of simplified covariance models.

Contribution

It provides a rigorous, rank-based testing procedure and visualization methods for covariance properties, enhancing model selection and interpretation in multivariate spatio-temporal analysis.

Findings

The proposed method accurately identifies covariance properties in synthetic data.

Application to wind speed data demonstrates practical utility in renewable energy studies.

Visualization aids in intuitive understanding of complex covariance structures.

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.