Spatial association measures for time series with fixed spatial locations

Spatial time series (STS), which refers to time-series data collected at fixed spatial locations, is crucial for understanding the spatiotemporal dynamics of geographical phenomena. Measuring the spatial association based on STS similarity provides valuable insights into the exploratory analysis of spatiotemporal data. However, existing methods are not effective in accurately quantifying such spatial association. To address this gap, this study proposes a conceptual model and a statistical method for identifying spatial clusters that exhibit significantly similar time-varying characteristics within a set of STS data. Conceptually, three representative patterns are defined: positive, negative, and no associations. A positive pattern occurs when spatially adjacent STSs show similar time-varying characteristics, while a negative pattern occurs when they show dissimilar ones. Technically, this study introduces a distance metric to measure similarities among STSs. The spatial association of STS at global and local scales is quantified according to the spatial concentration of these similarities. The validity and applicability of the proposed statistics are verified through synthetic and real-world examples, demonstrating their potential as effective tools for understanding spatiotemporal dynamics from a new perspective.