Filtering and frequency interpretations of Singular Spectrum Analysis

New filtering and spectral interpretations of Singular Spectrum Analysis (SSA) are provided. It is shown that the variables reconstructed from diagonal averaging of reduced-rank approximations to the trajectory matrix can be obtained from a noncausal convolution filter with zero-phase characteristics. The reconstructed variables are readily constructed using a two-pass filtering algorithm that is well known in the signal processing literature. When the number of rows in the trajectory matrix is much larger than number of columns, many results reported in the signal processing literature can be used to derive the properties of the resulting filters and their spectra. New features of the reconstructed series are revealed using these results. Two examples are used to illustrate the results derived in this paper.