Frequency-Weighted Singular Spectrum Analysis for 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.