Principal components analysis and cyclostationarity

Alain Boudou and Sylvie Viguier-Pla

Journal of Multivariate Analysis, 2022, vol. 189, issue C

Abstract: In this paper, we give a definition of a cyclostationary function, which specifies and extends usual definitions of cyclostationary processes. We transform such a cyclostationary function into a series. The property of stationarity of the series lets us proceed to the Principal Components Analysis in the frequency domain. This technique requires the introduction of new notions as the conjugated of a spectral measure, the association of a set of unitary operators with a family of stationary series, and the ampliation. We illustrate this work by a simulated example, and we end by a particular case of cyclostationary function, where the Principal Components Analysis in the frequency domain is equivalent to the classical Principal Components Analysis.

Keywords: Cyclostationarity; Orthogonal projectors; Principal Components Analysis; Random measures; Spectral measures; Stationary processes; Unitary operators (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.jmva.2021.104875

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