Scalable spatio-temporal autoregressive modeling by designing equivalent graph convolutional neural networks

Spatial and spatio-temporal autoregressive models (SAR and STAR) explicitly conceptualize outcomes at one location as a function of outcomes at nearby locations and characterize substantial spatial dependencies. However, their application is constrained by huge computational burdens associated with model estimation, rendering them infeasible for large-scale real-world problems. To address this challenge, we proposed a novel architecture that extends the principles of graph convolutional neural networks to integrate spatial autoregression in neural networks (SARNNs). By establishing the mathematical and algorithmic equivalence between SARNNs and SAR, our approach ensures unbiased parameter estimations while reducing computational complexity to <i>O</i>(<i>n</i>) and makes SAR models scalable. Then, we developed STARNNs, a spatio-temporal extension of SARNNs, by properly stacking SARNNs to form an architecture equivalent to STAR models. The strategy enables efficient and tractable solutions for large-scale complex STAR models. Monte Carlo simulation experiments confirm the equivalence between SAR (STAR) and SARNN (STARNN) modeling and emphasize the critical role of a specifically designed loss function that explicitly incorporates spatial autocorrelation. With STARNNs, we implemented a high-resolution global-scale STAR model to assess economic losses induced by climate change. The results underscore the importance of considering spatial propagation effects to accurately quantify the economic consequences of climate change.