Spatio-Temporal Weighted Regression Model with Fractional-Colored Noise: Parameter estimation and consistency

TL;DR

This paper introduces a spatio-temporal weighted regression model accounting for fractional-colored noise, providing parameter estimation, convergence analysis, and demonstrating strong empirical performance through simulations and R package implementation.

Contribution

It develops a novel GTWR model with fractional-colored noise and correlated covariates, along with consistent weighted least squares estimators and practical simulation validation.

Findings

Estimator shows small residual oscillations around zero.

High R-squared values indicate strong model fit.

Simulation confirms estimator's good performance.

Abstract

Geographical and Temporal Weighted Regression (GTWR) model is an important local technique for exploring spatial heterogeneity in data relationships, as well as temporal dependence due to its high fitting capacity when it comes to real data. In this article, we consider a GTWR model driven by a spatio-temporal noise, colored in space and fractional in time. Concerning the covariates, we consider that they are correlated, taking into account two interaction types between covariates, weak and strong interaction. Under these assumptions, Weighted Least Squares Estimator (WLS) is obtained, as well as its rate of convergence. In order to evidence the good performance of the estimator studied, it is provided a simulation study of four different scenarios, where it is observed that the residuals oscillate with small variation around zero. The STARMA package of the R software allows obtaining a variant of the $R^{2}$ coefficient, with values very close to 1, which means that most of the variability is explained by the model.