On the Robustness of Singular Spectrum Analysis for Long Time Series

This paper is devoted to the theoretical investigation of the robustness of singular spectrum analysis (SSA) if the length N of a time series tends to infinity. The latter condition distinguishes the work from quite a lot of works on the robustness of SSA. Here, we used a version of the SSA method that is intended for extraction of the signal from the sum of the signal and noise. Therefore, taking the series corresponding to the available outliers as noise, we can obtain uniform estimates for the signal-approximation errors at large N. If these estimates tend to zero as N → ∞, then the method is robust. Several examples of this approach for specific signals and outliers are considered; some of them are illustrated using computer experiments.