Nonparametric spatio-temporal modeling: Contruction of a geographically and temporally weighted spline regression.

This research introduces a new model called Geographically Temporally and Weighted Spline Nonparametric Regression (GTWSNR), which is an extension of the Geographically Temporally Weighted Regression (GTWR) model. The GTWSNR model combines nonparametric spline regression with spatial and temporal weighting, integrating geographic information and time series on an unknown regression curve. This model provides insights into spatial influences over multiple time series observations and produces forecasting results based on the analyzed spatial data. GTWSNR is designed to address the limitations of the traditional GTWR model in handling unknown regression functions. The research aims to develop the GTWSNR model to overcome these challenges and uses the Maximum Likelihood Estimator (MLE) to estimate the model. Key contributions of this study include:•The development of the GTWSNR model as a spatiotemporal approach to address unknown regression functions using a truncated spline estimator in nonparametric regression.•The application of a weighted Maximum Likelihood Estimator (MLE) method for estimating the GTWSNR model.•The implementation of the GTWSNR model on rice productivity data from 34 provinces in Indonesia to demonstrate its effectiveness as the best model.