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Singular spectrum analysis (SSA) as a nonparametric tool for decomposition ofan observed time series into sum of interpretable components such as trend,oscillations and noise is considered. The separability of these seriescomponents by SSA means the possibility of such decomposition. Two variationsof SSA, which weaken the separability conditions, are proposed. Both proposedapproaches consider inner products corresponding to oblique coordinate systemsinstead of the conventional Euclidean inner product. One of the approachesperforms iterations to obtain separating inner products. The other methodchanges contributions of the components by involving the series derivative toavoid component mixing. Performance of the suggested methods is demonstrated onsimulated and real-life data.

Variations of singular spectrum analysis for separability improvement: non-orthogonal decompositions of time series