L ONG GAPS IN MULTIVARIATE SPATIO- TEMPORAL DATA: AN APPROACH BASED ON F UNCTIONAL DATA ANALYSIS Mariantonietta Ruggieri 1 , Antonella Plaia 1 , Francesca Di Salvo 1 1 Dipartimento di Scienze Economiche, Aziendali e Statistiche, Universit` a degli Studi di Palermo, (e-mail: mariantonietta.ruggieri@unipa.it, antonella.plaia@unipa.it, francesca.disalvo@unipa.it) ABSTRACT: The main aim of this paper is to perform Functional Principal Com- ponent Analysis (FPCA) taking into account spatio-temporal correlation structures, in order to fill in missing values in spatio-temporal multivariate data set.A spatial and a spatio-temporal variant of the classical temporal FPCA is considered; in other words, FPCA is carried out after modeling data with respect to more than one dimen- sion: space (long, lat) or space+time. Moreover, multidimensional FPCA is extended to multivariate context (more than one variable). Information on spatial or spatio- temporal structures are efficiently extracted by applying Generalized Additive Mod- els (GAMs). Both simulation studies and some performance indicators are used to validate the proposed procedure, showing that, especially in presence of long gaps, spatio-temporal FPCA provides a better reconstruction than spatial FPCA. KEYWORDS: FDA, FPCA, GAM, P-splines. 1 Introduction Over the last years, a considerable interest in modeling and describing multi- variate multidimensional data has arisen in many fields. Environmental data such as, for example, the levels of different pollutants recorded along more than one dimension, that is temporally and spatially, fall into this category. Unfortunately, measurement errors and instruments disfunction can cause high percentages of missing values and long gaps along time and/or space; it also happens that the whole network does not monitor the complete set of pollutants in each monitoring station. Therefore the problem of finding a good method to obtain the best reconstruction of the data arises. The Functional Data Anal- ysis can be considered a tool to cope with the problem of missing values: it allows to convert time series, as well as spatial series, gathered as discrete observations, into functional, reducing a great number of observations to few coefficients and preserving their temporal/spatial pattern. In a previous paper