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

Multivariate spatio-temporal data analysis methods usually assume fairly complete data, while a number of gaps often occur along time or in space. In air quality data that may be due to instrument malfunctions; moreover, not all the pollutants of interest are measured in all the monitoring stations of a network. In literature many statistical methods have been proposed for imputing short sequences of missing values, but most of them are not valid when the fraction of missing values is high. Furthermore, the limitation of the methods commonly used consists in exploiting temporal only, or spatial only, correlation of the data. The objective of this paper is to provide an approach based on spatio-temporal Functional Principal Component Analysis (FPCA), exploiting simultaneously the spatial and temporal correlations for 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 order to obtain a good reconstruction of temporal/spatial series, especially in presence of long gap sequences, comparing spatial and spatio-temporal FPCA.