Automatic Grouping of Time Series Decomposition Components in Singular Spectrum Analysis

Abstract

Singular spectrum analysis (SSA) is a relatively new method of time series analysis. SSA is of particular interest in application to analysis of non-stationary, short and noise time series. One of the drawbacks of SSA is that both simple harmonic oscillations and complex components of analyzed time series are decomposed into more than one component, which leads to the necessity of grouping related components for further analysis. This problem was partially addressed by Alexandrov, Golyandina (2005), mainly in application to the problem of identification of harmonic oscillations. In this paper, we present a more agile and generalized algorithm for automated grouping of components, which allows grouping not only harmonic oscillations, but also components corresponding to amplitude-modulated oscillations, fading oscillations and other. The algorithm was tested on synthetic time series, com-posed of common components: harmonic, amplitude-modulated, and exponentially damped oscillations, sum of two Gaussians, and their linear combinations. Experimental results of quality of grouping were obtained, showing that the proposed algorithm gives on average 26% better grouping results than an existing algorithm.