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方法已被广泛应用。当数据呈现为具有相同感兴趣时间域的空间向量集合时，我们利用Bergsma相关系数$\rho$构建区域序列间的相似性度量。由于$\rho$的特殊性质，不同于检验空间随机性的传统空间关联度量，我们的统计量能够检验空间成对独立性。我们推导了该统计量在零假设（区域独立）和备择假设（区域依赖）下的渐近行为。通过针对SAR和SMA依赖模型的模拟研究，我们进一步探索了空间依赖的备择场景。最后，我们将该统计量应用于COVID-19发病率数据的模型拟合残差分析，以检验空间关联的存在性。