A0265
Title: Factor models for high-dimensional functional time series
Authors: Shahin Tavakoli - University of Geneva (Switzerland) [presenting]
Marc Hallin - Universite Libre de Bruxelles (Belgium)
Gilles Nisol - ULB (Belgium)
Abstract: Theoretical foundations are set up for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result stating that, under mild assumptions on the covariance operator of the cross-section, we can represent each FTS as the sum of a common component driven by scalar factors loaded via functional loadings, and a mildly cross-correlated idiosyncratic component. The model and theory are developed in a general Hilbert space setting that allows for mixed panels of functional and scalar time series. We then turn to the identification of the number of factors, and the estimation of the factors, their loadings, and the common components. We provide a family of information criteria for identifying the number of factors and proving their consistency. We provide average error bounds for the estimators of the factors, loadings, and common components; the results encompass the scalar case, for which they reproduce and extend, under weaker conditions, well-established similar results. We provide numerical illustrations that corroborate the convergence rates predicted by the theory and provide a finer understanding of the interplay between $N$ and $T$ for estimation purposes. We conclude with an application to forecasting mortality curves, where we demonstrate that our approach outperforms existing methods.
