On the robustness of Singular Spectrum Analysis for long signals

Abstract

The paper is devoted to theoretical investigation of the robustness for Singular Spectrum Analysis (briefly, SSA) if the length N of time series tends to infinity. The last condition discerns the paper from many other works on this theme. Note that here the general theoretical approach to the asymptotic extraction of the signal series from the additively perturbed signal with the help of SSA was used. Therefore, taking the series corresponding to the outliers as the noise series, we can check wether the so-called reconstruction errors tend uniformly as N → ∞. If this convergence takes place then the method is robust. Several examples of such an approach for concrete signals and outlies are considered, some of them are illustrated by computational experiments.