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- Title
Singular Spectrum Analysis and Circulant Maximum Variance Frames.
- Authors
Bonenberger, Christopher; Ertel, Wolfgang; Schwenker, Friedhelm; Schneider, Markus
- Abstract
Singular spectrum analysis (SSA) is a powerful method that is frequently used in dynamical systems theory and time series analysis. However, the algorithm itself is only partially understood. In this paper, we tackle the problem of a thorough interpretation of the complete basic SSA algorithm. We point out the relationship between SSA and Fourier analysis (FA), linear filtering (LF), principal component analysis (PCA), and power spectrum density estimation (PSDE). The main contribution is a reformulation and comprehensive interpretation of SSA by means of a novel class of data-adaptive circulant frames. Based on this class of frames, we introduce a formalism for time series decomposition and reconstruction. This mathematical framework generalizes principle component analysis and SSA. We show that SSA, PCA, FA, LF, and PSDE can be found from special cases of the proposed frame structures. This way we are able to provide a formal description of SSA and its relationship to the aforementioned methods. Whilst previous approaches to the interpretation of SSA relied on approximations, we provide exact mathematical descriptions of the relation between the above-mentioned techniques.
- Subjects
SPECTRUM analysis; TIME series analysis; PRINCIPAL components analysis; SIGNAL frequency estimation; FOURIER analysis; POWER spectra
- Publication
Advances in Data Science & Adaptive Analysis, 2022, Vol 14, Issue 3/4, p1
- ISSN
2424-922X
- Publication type
Article
- DOI
10.1142/S2424922X22500085