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Dynamic Functional Principal Components

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  • Siegfried Hörmann
  • Lukasz Kidzinski
  • Marc Hallin

Abstract

In this paper, we address the problem of dimension reduction for time series of functional data (X_t:t\in \mathbb{Z}). Such functional timeseries frequently arise, e.g. when a continuous-time process is segmented into some smaller natural units, such as days. Then each X_trepresents one intraday curve. We argue that functional principal component analysis (FPCA), though a key technique in the field and a benchmark for any competitor, does not provide an adequate dimension reduction in a time-series setting. FPCA indeed is a staticprocedure which ignores the essential information provided by the serial dependence structure of the functional data under study. Therefore, inspired by Brillinger’s theory of dynamic principal components, we propose a dynamic version of FPCA, which is based on a frequency-domain approach. By means of a simulation study and an empirical illustration, we show the considerable improvement the dynamic approach entails when compared to the usual static procedure.

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Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers ECARES with number 2013/131191.

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Length: 36 p.
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Handle: RePEc:eca:wpaper:2013/131191

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