Spatial association measures for univariate static spatial data are widely used. When the data is in the form of a collection of spatial vectors with the same temporal domain of interest, we construct a measure of similarity between the regions' series, using Bergsma's correlation coefficient $\rho$. Due to the special properties of $\rho$, unlike other spatial association measures which test for spatial randomness, our statistic can account for spatial pairwise independence. We have derived the asymptotic behavior of our statistic under null (independence of the regions) and alternate cases (the regions are dependent). We explore the alternate scenario of spatial dependence further, using simulations for the SAR and SMA dependence models. Finally, we provide application to modelling and testing for the presence of spatial association in COVID-19 incidence data, by using our statistic on the residuals obtained after model fitting.

翻译：针对单变量静态空间数据的空间关联度量已被广泛应用。当数据形式为具有相同感兴趣时间域的若干空间向量集合时，我们利用Bergsma相关系数$\rho$构建区域间序列的相似性度量。得益于$\rho$的特殊性质，与检验空间随机性的其他空间关联度量不同，我们的统计量能够识别空间成对独立性。我们推导了统计量在原假设（区域间独立）和备择假设（区域间存在依赖）下的渐近行为。进一步地，我们利用SAR和SMA依赖模型进行模拟，深入探讨了空间依赖的备择情形。最后，通过将统计量应用于模型拟合后得到的残差，对COVID-19发病率数据中的空间关联进行建模与检验，展示了该方法的实际应用。