Continuous Time-Varying Kriging for Spatial Prediction of Functional Data: An Environmental Application

Abstract

Spatially correlated functional data are present in a wide range of environmental disciplines and, in this context, efficient prediction of curves is a key issue. We present an approach for spatial prediction based on the functional linear pointwise model adapted to the case of spatially correlated curves. First, a smoothing process is applied to the curves by expanding the curves and the functional parameters in terms of a set of basis functions. The number of basis functions is chosen by cross-validation. Then, the spatial prediction of a curve is obtained as a pointwise linear combination of the smoothed data. The prediction problem is solved by estimating a linear model of coregionalization to set the spatial dependence among the fitted coefficients. We extend an optimization criterion used in multivariable geostatistics to the functional context. The method is illustrated by smoothing and predicting temperature curves measured at 35 Canadian weather stations.