  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 leads to a time-series
decomposition. In this algorithm, a single free parameter, window length $K$,
is involved which is the FIR filter length for the time series. There are no
generally accepted criterion for the proper choice of the window length $K$.
Moreover, the proper window length depends on the specific problem which we are
interested in. Thus, it is important to monitor the spectral structure of the
SSA decomposition and its window length dependence in detail for the practical
application. In this paper, based on the filtering interpretation of SSA, it is
shown that the decomposition of the power spectrum for the original time series
is possible with the filters constructed from the eigenvectors of the
lagged-covariance matrix. With this, we can obtain insights into the spectral
structure of the SSA decomposition and it helps us for the proper choice of the
window length in the practical application of SSA.
