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.

用于建模空间相关的功能变量的大量方法通常假定功能回归系数在目标区域内是恒定的。然而，在许多情况下，功能系数在局部水平上变化要现实得多。本文提出了功能框架中的校准异方差地理加权回归模型（H-GWR）。我们的模型假设方差在整个空间中变化，并且每个局部模型（在每个位置定义）给出了方差的局部估计。由于此假设取决于焦点和其余空间观测值之间选择的距离，因此我们使用后向拟合方法来校准具有参数特定距离度量的H-GWR模型。