Statistics and Its Interface

Volume 8 (2015)

Number 3

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

Pages: 277 – 294

DOI: https://dx.doi.org/10.4310/SII.2015.v8.n3.a3

Authors

Nina Golyandina (Department of Statistical Modeling, St. Petersburg State University, St. Petersburg, Russia)

Alex Shlemov (Department of Statistical Modeling, St. Petersburg State University, St. Petersburg, Russia)

Abstract

Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into the 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 a 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.

Keywords

ingular spectrum analysis, time series, time series decomposition, separability

2010 Mathematics Subject Classification

Primary 62G05, 94A12. Secondary 37M10, 60G35.

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Published 17 April 2015