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Title: Dynamic functional principal components Authors:  Marc Hallin - Universite Libre de Bruxelles (Belgium) [presenting]
Abstract: The problem of dimension reduction for functional time series is addressed. Such time series arise frequently, e.g. when a continuous time process is segmented into some smaller natural units, such as days, each observation representing one intraday curve. We argue that functional principal component analysis (FPCA), which is a key technique in the field, does not provide an adequate dimension reduction in a time series context. FPCA is a static procedure which ignores the essential serial dependence features of the data. Therefore, inspired by Brillingers theory of dynamic principal components, we propose a dynamic version of FPCA which is based on a frequency domain approach, and show that it provides the optimal dimension reduction. By means of a simulation study and an empirical illustration, we show the considerable improvement our method entails when compared to the usual (static) procedure.