Improvement of separability of time series in singular spectrum analysis using the method of independent component analysis

Abstract

The separation of signal components is an important problem of time-series analysis. For example, the solution of this problem allows one to extract a trend and to separate harmonic signals with different frequencies. In the paper, the modification of the singular spectrum analysis (SSA) method is considered for improving the separability of time-series components. The new method is called SSA-AMUSE, since it is based on the AMUSE method, which is used to apply independent component analysis to signal separation. The suggested modification weakens the conditions of the so-called strong separability and, thus, improves the quality of the separation of time-series components by comparing similar methods. The paper contains proof of the algorithm, as well as the conditions of separability for the considered modification. Besides the exact separability, the asymptotic separability is also considered. The separability conditions are applied to the case of two harmonic time series. It appears that separability by SSA-AMUSE does not depend on the amplitudes of the separated harmonics, while the Basic SSA method requires different amplitudes. A numerical example demonstrates the advantage of the SSA-AMUSE method compared with a similar modification.