Dynamic functional principal components
Siegfried Hörmann, Łukasz Kidziński, Marc Hallin
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2015 · Volume 77 · Issue 2
Abstract
We address the problem of dimension reduction for time series of functional data. Suchfunctional time seriesfrequently arise, for example, when a continuous time process is segmented into some smaller natural units, such as days. Then eachXtrepresents one intraday curve. We argue that functional principal component analysis, 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. Functional principal component analysis indeed is astaticprocedure which ignores the essential information that is provided by the serial dependence structure of the functional data under study. Therefore, inspired by Brillinger's theory ofdynamic principal components, we propose adynamicversion of functional principal component analysis which is based on a frequency domain approach. By means of a simulation study and an empirical illustration, we show the considerable improvement that the dynamic approach entails when compared with the usual static procedure.
Keywords
Dimension reduction, Frequency domain analysis, Functional data analysis, Functional spectral analysis, Functional time series, Karhunen–Loève expansion, Principal components
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