Frequency-domain characterization of Singular Spectrum Analysis eigenvectors

Abstract

Singular Spectrum Analysis (SSA) is a nonparametric approach used to decompose a time series into meaningful components, related to trends, oscillations and noise. SSA can be seen as a spectral decomposition, where each term is related to an eigenvector derived from the trajectory matrix. In this context the eigenvectors can be viewed as eigenfilters. The frequency domain interpretation of SSA is a relatively recent subject. Although the analytic solution for the frequency-response of eigenfilters is already known, the periodogram is often applied for their frequency characterization. This paper presents a comparison of these methods, applied to eigenfilters' frequency characterization for time series components identification. To perform this evaluation, several tests were carried out, in both a synthetic and real data time series. In every situations the eigenfilters analytic frequency response method provided better results compared to the periodogram in terms of frequency estimates as well as their dispersion and sensitivity to variations in the SSA algorithm parameter.