Functional Principal Component Analysis for the explorative analysis of multisite-multivariate air pollution time series with long gaps

The knowledge of the urban air quality represents the first step to face air pollution issues. For the lastdecades many cities can rely on a network of monitoring stations recording concentration values for themain pollutants. This paper focuses on functional principal component analysis (FPCA) to investigatemultiple pollutant datasets measured over time at multiple sites within a given urban area. Our purposeis to extend what has been proposed in the literature to data that are multisite and multivariate at thesame time. The approach results to be effective to highlight some relevant statistical features of the timeseries, giving the opportunity to identify significant pollutants and to know the evolution of their variabilityalong time. The paper also deals with missing value issue. As it is known, very long gap sequences canoften occur in air quality datasets, due to long time failures not easily solvable or to data coming from amobile monitoring station. In the considered dataset, large and continuous gaps are imputed by empiricalorthogonal function procedure, after denoising raw data by functional data analysis and before performingFPCA, in order to further improve the reconstruction.