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Principal Components Analysis of Periodically Correlated Functional Time Series
Author(s) -
Kidziński Łukasz,
Kokoszka Piotr,
Jouzdani Neda Mohammadi
Publication year - 2018
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12283
Subject(s) - mathematics , functional principal component analysis , series (stratigraphy) , hilbert space , principal component analysis , functional data analysis , time series , filter (signal processing) , algorithm , operator (biology) , simple (philosophy) , inversion (geology) , mathematical analysis , computer science , statistics , paleontology , biochemistry , chemistry , philosophy , epistemology , repressor , structural basin , transcription factor , gene , computer vision , biology
Within the framework of functional data analysis, we develop principal component analysis for periodically correlated time series of functions. We define the components of the above analysis including periodic operator‐valued filters, score processes, and the inversion formulas. We show that these objects are defined via a convergent series under a simple condition requiring summability of the Hilbert–Schmidt norms of the filter coefficients and that they possess optimality properties. We explain how the Hilbert space theory reduces to an approximate finite‐dimensional setting which is implemented in a custom‐build |R| package. A data example and a simulation study show that the new methodology is superior to existing tools if the functional time series exhibits periodic characteristics.