Spatial function-on-function regression

We introduce a spatial function-on-function regression model to capture spatial dependencies in functional data by integrating spatial autoregressive techniques with functional principal component analysis. The proposed model addresses a critical gap in functional regression by enabling the analysis of functional responses influenced by spatially correlated functional predictors, a common scenario in fields such as environmental sciences, epidemiology, and socioeconomic studies. The model employs a spatial functional principal component decomposition on the response and predictor, transforming the functional data into a finite-dimensional multivariate spatial autoregressive framework. This transformation allows efficient estimation and robust handling of spatial dependencies through least squares methods. In a series of extensive simulations, the proposed model consistently demonstrated superior performance in estimating both spatial autocorrelation and regression coefficient functions compared to some favorably existing traditional approaches, particularly under moderate to strong spatial effects. Application of the proposed model to North Dakota weather data further underscored its practical utility, revealing critical spatial patterns in wind chill dynamics that align with known geographic and meteorological interactions across the region. The sfofr package in (Figure presented.) provides a comprehensive implementation of the proposed estimation method, offering a user-friendly and efficient tool for researchers and practitioners to apply the methodology in real-world scenarios. Supplementary materials accompanying this paper appear on-line.