Long gaps in multivariate spatio-temporal data: an approach based on functional data analysis

The main aim of this paper is to perform Functional Principal ComponentAnalysis (FPCA) taking into account spatio-temporal correlation structures,in order to fill in missing values in spatio-temporal multivariate data set. A spatialand a spatio-temporal variant of the classical temporal FPCA is considered; in otherwords, FPCA is carried out after modeling data with respect to more than one dimension:space (long, lat) or space+time. Moreover, multidimensional FPCA is extendedto multivariate context (more than one variable). Information on spatial or spatiotemporalstructures are efficiently extracted by applying Generalized Additive Models(GAMs). Both simulation studies and some performance indicators are used tovalidate the proposed procedure, showing that, especially in presence of long gaps,spatio-temporal FPCA provides a better reconstruction than spatial FPCA.