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

TL;DR

This paper introduces two variations of singular spectrum analysis that improve the separability of time series components by using oblique inner products and derivative-based adjustments, demonstrated on simulated and real data.

Contribution

The paper proposes two novel SSA variations that weaken separability conditions through oblique inner products and derivative-based methods, enhancing component separation.

Findings

Improved component separability demonstrated on simulated data.

Effective application to real-life time series data.

Methods outperform traditional SSA in separability tasks.

Abstract

Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by SSA means the possibility of such decomposition. Two variations of SSA, which weaken the separability conditions, are proposed. Both proposed approaches consider inner products corresponding to oblique coordinate systems instead of the conventional Euclidean inner product. One of the approaches performs iterations to obtain separating inner products. The other method changes contributions of the components by involving the series derivative to avoid component mixing. Performance of the suggested methods is demonstrated on simulated and real-life data.