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Dynamic functional principal components
Author(s) -
Hörmann Siegfried,
Kidziński Łukasz,
Hallin Marc
Publication year - 2015
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12076
Subject(s) - principal component analysis , functional principal component analysis , dimensionality reduction , functional data analysis , computer science , benchmark (surveying) , dimension (graph theory) , series (stratigraphy) , principal (computer security) , field (mathematics) , process (computing) , domain (mathematical analysis) , reduction (mathematics) , algorithm , mathematics , artificial intelligence , machine learning , paleontology , mathematical analysis , geometry , geodesy , pure mathematics , biology , geography , operating system
Summary We address the problem of dimension reduction for time series of functional data ( X t : t ∈ Z ) . Such functional time series frequently arise, for example, when a continuous time process is segmented into some smaller natural units, such as days. Then each X t represents 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 a static procedure 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 of dynamic principal components , we propose a dynamic version 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.