Key result
Introducing a spectral weight factor into the singular spectrum analysis algorithm allows selective focus on specific frequency domains of time series with complicated spectral structures.
Why the study?
To naturally introduce a spectral weight factor into the singular spectrum analysis algorithm to enable selective focus on specific frequency domains of time series with complicated spectral structures.
Introduces a frequency-weighted extension to singular spectrum analysis for detailed study of time series with complicated spectral structures.
Enables spectral weighting in SSA adaptive filters; leaves open validation for cardiovascular time series.
Singular spectrum analysis (SSA) is a nonparametric spectral decomposition of a time series. A time series is exactly separated into arbitrary number of additive subsequences with the singular value decomposition. Previously, we have shown that SSA algorithm can equivalently be formulated as an optimality condition for the generation of adaptive filters. In this paper, based on our optimal-filter viewpoint, we show that the spectral weight factor can naturally be introduced into the SSA algorithm. With this extension, we can selectively focus on the specific frequency domain of the time series, and then the detailed study of the time series with complicated spectral structure becomes possible.
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Kume et al. (2022) studied this question. Frequency-Weighted Singular Spectrum Analysis was evaluated. Introducing a spectral weight factor into the singular spectrum analysis algorithm allows selective focus on specific frequency domains of time series with complicated spectral structures.
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