Improvement of separability of time series in singular spectrum analysis by means of a method of independent component analysis

Abstract

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, a modification of the singular spectrum analysis (SSA) methods is considered for improvement of separability of time series components. The new method is named SSA-AMUSE, since it is based on the method AMUSE used for application of independent component analysis to signal separation. The suggested modification weakens the conditions of the so-called strong separability and thereby improves the quality of separation of time series components with comparison with similar methods. The paper contains the proof of the algorithm and also 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 the separability by SSA-AMUSE does not depend on amplitudes of the separated harmonics, while the Basic SSA method needs different amplitudes. A numerical example demonstrates an advantage of the SSA-AMUSE method in comparison with a similar modification. Refs 9. Figs 1.