Comparing spatial and spatio-temporal FPCA to impute large continuous gaps in space

Multivariate spatio-temporal data analysis methods usually assume fairlycomplete data, while a number of gaps often occur along time or in space. In airquality data that may be due to instrument malfunctions; moreover, not all the pollutantsof interest are measured in all the monitoring stations of a network. In literaturemany statistical methods have been proposed for imputing short sequences ofmissing values, but most of them are not valid when the fraction of missing values ishigh. Furthermore, the limitation of the methods commonly used consists in exploitingtemporal only, or spatial only, correlation of the data. The objective of this paperis to provide an approach based on spatio-temporal Functional Principal ComponentAnalysis (FPCA), exploiting simultaneously the spatial and temporal correlationsfor multivariate data, in order to provide an accurate imputation of missing values.At this aim, the methodology proposed in a previous proposal is applied, in orderto obtain a good reconstruction of temporal/spatial series, especially in presence oflong gap sequences, comparing spatial and spatio-temporal FPCA.