Multidimensional spatiotemporal autocorrelation analysis theory based on Multi-observation spatiotemporal Moran’s I and its application in resource allocation

This article seeks to advance the theory of multidimensional spatial autocorrelation analysis by introducing the Multi-observation spatiotemporal Moran’s I. Unlike the conventional spatiotemporal Moran’s I, which is limited to single observed data within each unit, the Multi-observation approach leverages multiple observations in each spatiotemporal unit. The index’s range is determined, facilitating spatial pattern discrimination. As spatiotemporal data becomes multidimensional, we extend the concept to the Multidimensional spatiotemporal Moran’s I through vectorization. Its distribution under diverse sample sizes is validated via Monte Carlo simulation and SW statistics, enhancing significance testing. The Multidimensional spatiotemporal Moran’s I adheres to the Wishart distribution under specific conditions. Additionally, we introduce comprehensive aggregation indicators based on the algebraic interpretation of Multidimensional spatiotemporal Moran’s I. These indicators are applied to U.S. Department of Energy monthly electricity generation data, illustrating the capacity to holistically assess multidimensional spatial characteristics. This approach further uncovers spatial correlations across dimensions, enhancing resource and energy optimization.