Spatio-Temporal Weighted Regression model with fractional-colored noise: Parameter estimation and consistency
Abstract
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.
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BibTeX
@article{araya2026spatiotemporal,
title = {{Spatio-Temporal Weighted Regression model with fractional-colored noise: Parameter estimation and consistency}},
author = {Héctor Araya and Lisandro J Fermín and Silfrido Gómez and Tania Roa and Soledad Torres},
journal = {Journal of Statistical Planning and Inference},
year = {2026},
month = sep,
doi = {10.1016/j.jspi.2026.106421},
eprint = {2309.11402},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05609961v2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Spatio-Temporal Weighted Regression model with fractional-colored noise: Parameter estimation and consistency
AU - Héctor Araya
AU - Lisandro J Fermín
AU - Silfrido Gómez
AU - Tania Roa
AU - Soledad Torres
PY - 2026
DA - 2026/09/21
JO - Journal of Statistical Planning and Inference
DO - 10.1016/j.jspi.2026.106421
UR - https://hal.science/hal-05609961v2
AB - 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.
SN - 0378-3758
SN - 1873-1171
ER -