Flow Spatiotemporal Moran's I: Measuring the Spatiotemporal Autocorrelation of Flow Data

Flows can reflect the spatiotemporal interactions or movements of geographical objects between different locations. Measuring the spatiotemporal autocorrelation of flows can help determine the overall spatiotemporal trends and local patterns. However, quantitative indicators of flows used to measure spatiotemporal autocorrelation both globally and locally are still rare. Therefore, we propose the global and local flow spatiotemporal Moran's I (FSTI). The global FSTI is used to assess the overall spatiotemporal autocorrelation degree of flows, and the local FSTI is applied to identify local spatiotemporal clusters and outliers. In the FSTI, to reflect flow spatiotemporal adjacency relationships, we establish flow spatiotemporal weights by multiplying the spatial and temporal weights of flows considering spatiotemporal orthogonality. The flow spatial weights include contiguity-based (considering first/higher-order and common border) and Euclidean distance-based weights. The temporal weights consider ordinary and lagged cases. As flow attributes may follow a long-tail distribution, we conduct Monte Carlo simulations to evaluate the statistical significance of the results. We assess the FSTI using synthetic datasets and Chinese population mobility datasets, and compare some results with those of recent flow-related methods. Additionally, we perform a sensitivity analysis to select a suitable temporal threshold. The results show that the FSTI can be used to effectively detect spatiotemporal variations in the autocorrelation degree and type.