The issue of $PM_{2.5}$ pollution has received significant attention in the literature as it has social, economic, and political implications. Big data sets have been collected by pollution monitoring stations (i.e., nodes) throughout the world, and this has made it possible to quantitatively characterize the dependence of $PM_{2.5}$ pollution in different regions. Here we divide the dependency relationship into three types: association, correlation, and causation. This study conducted such relationships using three approaches: the random matrix theory (RMT), cross-correlation, and convergent cross-mapping (CCM). The aim was to determine the above three relationships between pollution data from different nodes. A random matrix analysis revealed that pollutant time series are not completely random, but are associated. Further analysis shows that $PM_{2.5}$ sequences had clear short-range correlations, yet the long-range correlations were blurred. Moreover, at the collect level, there were no clear causalities among pollutant concentrations from different geographical regions, regardless of distance and direction. These results indicate that the dependence of $PM_{2.5}$ pollution between different sites is complex. Nonetheless, this comprehensive analysis based on big data provided insights into critical issues of general interest, including pollution-induced climate change and pollution abatement.

中文翻译：

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PM2.5 传输变量之间的关联、相关和因果关系

$PM_{2.5}$ 污染问题在文献中受到了极大的关注，因为它具有社会、经济和政治意义。世界各地的污染监测站（即节点）已经收集了大数据集，这使得定量表征不同地区$PM_{2.5}$污染的依赖性成为可能。这里我们将依赖关系分为三类：关联、相关和因果关系。本研究使用三种方法进行此类关系：随机矩阵理论 (RMT)、互相关和收敛交叉映射 (CCM)。目的是确定来自不同节点的污染数据之间的上述三种关系。随机矩阵分析表明，污染物时间序列并非完全随机，而是相关联的。进一步分析表明，$PM_{2.5}$序列具有明显的短程相关性，而长程相关性是模糊的。此外，在收集层面，不同地理区域的污染物浓度之间没有明显的因果关系，无论距离和方向如何。这些结果表明，不同地点之间$PM_{2.5}$污染的依赖性是复杂的。尽管如此，这种基于大数据的综合分析提供了对普遍关注的关键问题的见解，包括污染引起的气候变化和污染减少。这些结果表明，不同地点之间$PM_{2.5}$污染的依赖性是复杂的。尽管如此，这种基于大数据的综合分析提供了对普遍关注的关键问题的见解，包括污染引起的气候变化和污染减少。这些结果表明，不同地点之间$PM_{2.5}$污染的依赖性是复杂的。尽管如此，这种基于大数据的综合分析提供了对普遍关注的关键问题的见解，包括污染引起的气候变化和污染减少。