Additive Decomposition of Power Spectrum Density in Singular Spectrum Analysis

Singular spectrum analysis (SSA) is a nonparametric and adaptive spectral decomposition of a time series. The singular value decomposition of the trajectory matrix and the anti-diagonal averaging lead to a time-series decomposition. In this paper, we propose an novel algorithm for the additive decomposition of the power spectrum density of a time series based on the filtering interpretation of SSA. This can be used to examine the spectral overlap or the admixture of the SSA decomposition. We can obtain insights into the spectral structure of the SSA decomposition which helps us for the proper choice of the window length in the practical application. The relationship to the conventional SSA decomposition of a time series is also discussed.