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.

翻译：地理与时间加权回归（GTWR）模型是一种重要的局部技术，用于探索数据关系中的空间异质性以及时间依赖性，尤其是在处理实际数据时具有较高的拟合能力。本文考虑了一个由时空噪声（空间上有色、时间上分数）驱动的GTWR模型。关于协变量，我们假设它们之间存在相关性，并考虑了两种交互类型：弱交互和强交互。在这些假设下，得到了加权最小二乘估计量（WLS）及其收敛速率。为证明所研究估计量的良好性能，提供了四种不同情景的模拟研究，观察到残差在零附近以小幅波动振荡。R软件的STARMA包可获取$R^{2}$系数的变体，其值非常接近1，这意味着大部分变异性可由该模型解释。