Heteroskedastic geographically weighted regression model for functional data

Abstract

A large number of approaches for modelling spatially dependent functional variables often assume that the functional regression coefficients are constant over the region of interest. However, in many occasions it is far more realistic that functional coefficients vary at a local level. The present paper proposes a calibrated heteroskedastic geographically weighted regression model (H-GWR) in the functional framework. Our model assumes that the variance varies across the space, and that each local model (defined at each location) gives a local estimation of the variance. Since this assumption depends on the chosen distance between the focal point and the rest of spatial observations, we use a back-fitting approach to calibrate the H-GWR model with a parameter-specific distance metric. This new approach improves the model performance in terms of predictive fit, as illustrated by simulations and through the analysis of a financial real data set.