Multivariate spatial phenomena are ubiquitous, spanning domains such as climate, pandemics, air quality, and social economy. Cross-correlation between different quantities of interest at different locations is asymmetric in general. This paper provides the visualization, structure, and properties of asymmetric cross-correlation as well as symmetric auto-correlation. It reviews mainstream multivariate spatial models and analyzes their capability to accommodate asymmetric cross-correlation. It also illustrates the difference in model accuracy with and without asymmetric accommodation using a 1D simulated example.

翻译：多元空间现象普遍存在，涵盖气候、流行病、空气质量和社会经济等多个领域。不同位置的不同关注量之间的互相关通常是非对称的。本文阐述了非对称互相关以及对称自相关的可视化、结构和性质。文章回顾了主流的多元空间模型，并分析了它们容纳非对称互相关的能力。此外，通过一个一维模拟示例，说明了考虑与不考虑非对称性时模型精度的差异。