A spatiotemporal weighted regression model (STWR v1.0) for analyzing local nonstationarity in space and time

Abstract. Local spatiotemporal nonstationarity occurs in various natural and socioeconomic processes. Many studies have attempted to introduce time as a new dimension into a geographically weighted regression (GWR) model, but the actual results are sometimes not satisfying or even worse than the original GWR model. The core issue here is a mechanism for weighting the effects of both temporal variation and spatial variation. In many geographical and temporal weighted regression (GTWR) models, the concept of time distance has been inappropriately treated as a time interval. Consequently, the combined effect of temporal and spatial variation is often inaccurate in the resulting spatiotemporal kernel function. This limitation restricts the configuration and performance of spatiotemporal weights in many existing GTWR models. To address this issue, we propose a new spatiotemporal weighted regression (STWR) model and the calibration method for it. A highlight of STWR is a new temporal kernel function, wherein the method for temporal weighting is based on the degree of impact from each observed point to a regression point. The degree of impact, in turn, is based on the rate of value variation of the nearby observed point during the time interval. The updated spatiotemporal kernel function is based on a weighted combination of the temporal kernel with a commonly used spatial kernel (Gaussian or bi-square) by specifying a linear function of spatial bandwidth versus time. Three simulated datasets of spatiotemporal processes were used to test the performance of GWR, GTWR, and STWR. Results show that STWR significantly improves the quality of fit and accuracy. Similar results were obtained by using real-world data for precipitation hydrogen isotopes (δ2H) in the northeastern United States. The leave-one-out cross-validation (LOOCV) test demonstrates that, compared with GWR, the total prediction error of STWR is reduced by using recent observed points. Prediction surfaces of models in this case study show that STWR is more localized than GWR. Our research validates the ability of STWR to take full advantage of all the value variation of past observed points. We hope STWR can bring fresh ideas and new capabilities for analyzing and interpreting local spatiotemporal nonstationarity in many disciplines.