Spatio—Temporal Weighted Regression model with fractional-colored noise: Parameter estimation and consistency

The Geographically and Temporally Weighted Regression (GTWR) model is a well-established local technique for analyzing spatial heterogeneity and temporal dependence in georeferenced data. It is recognized for its ability to represent real-world settings. In this study, we expand upon the GTWR model by incorporating spatio-temporal noise that is colored in space and fractional in time. Under this formulation, we derive the Weighted Least Squares (WLS) estimator and formally establish its convergence rate. To evaluate the performance of the WLS estimator, we implemented a simulation study with five defined scenarios. The simulation results indicate that the model residuals exhibit small variations around zero, which suggests the accuracy of the estimator. Finally, we applied the estimator to real data on the incidence of respiratory diseases. Analyzing the residuals in this empirical application allows us to evaluate the ability of the model to capture the spatio-temporal structure of the data.