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Title: Forecasting multiple functional time series: A static factor approach Authors:  Gilles Nisol - ULB (Belgium) [presenting]
Siegfried Hormann - Universite Libre de Bruxelles (Belgium)
Marc Hallin - Universite Libre de Bruxelles (Belgium)
Shahin Tavakoli - University of Warwick (United Kingdom)
Abstract: Theoretical foundations and a practical method to forecast multiple functional time series (FTS) are set. In order to do so, we generalize the static factor model to the case where cross-section units are FTS. We first derive a representation result. We show that if the $K$ first eigenvalues of the covariance operator of the cross-section of the $N$ FTS are unbounded while $N$ grows and if the $K+1$ eigenvalue is bounded, then we can represent the FTS as a sum of a common component driven by $K$ factors and an idiosyncratic component. We then set up an information criterion that chooses jointly the number $K$ of factors and the dimension on which we should project the FTS before estimating the static factor model. We suggest a method of estimation and prediction based on these projected FTS. We assess the performances of the method and information criterion through a simulation exercise. Finally, we consider a real-data application. We show that by applying our method to a cross-section of PM10 concentration curves obtained across several measurement centers in Graz, we have a better prediction accuracy than by limiting the analysis to individual FTS.