SAR models with specific spatial coefficients and heteroskedastic innovations

This paper presents an innovative extension of spatial autoregressive (SAR) models, introducing spatial coefficients specific to each spatial region that evolve over time. The proposed estimation methodology covers both homoscedastic and heteroscedastic data, ensuring consistency and efficiency in the estimators of the parameters $\pmb{\rho}$ and $\pmb{\beta}$. The model is based on a robust theoretical framework, supported by the analysis of the asymptotic properties of the estimators, which reinforces its practical implementation. To facilitate its use, an algorithm has been developed in the R software, making it a standard tool for the analysis of complex spatial data. The proposed model proves to be more effective than other similar techniques, especially when modeling data with normal spatial structures and non-normal distributions, even when the residuals are not homoscedastic. Finally, the application of the model to homicide rates in the United States highlights its advantages in both statistical and social analysis, positioning it as a key tool for the analysis of spatial data in various disciplines.