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Singular Spectrum Analysis of Univariate Time Series

In: Data Driven Model Learning for Engineers

Author

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  • Guillaume Mercère

    (Université de Poitiers)

Abstract

Before diving into statistical or numerical optimization considerations for characterizing time series parsimoniously and effectively, it is interesting to introduce a first technique, called the singular spectrum analysis (SSA), which yields the main components of a time series by resorting to applied linear algebra tools only. As shown in this chapter: The goal of SSA is to decompose a time series into a small number of interpretable components such as a trend, an oscillatory pattern, and noise. The SSA class of solutions can be used without making any statistical assumptions on the time series to be decomposed. The basic SSA solution assumes the existence of an unknown linear recurrent equation satisfied by the time series to be analyzed. The basic SSA algorithm is made of four steps and requires Hankel matrices and SVD only. SSA can be used for denoising a time series or, in a complementary way, for signal subspace extraction.

Suggested Citation

  • Guillaume Mercère, 2023. "Singular Spectrum Analysis of Univariate Time Series," Springer Books, in: Data Driven Model Learning for Engineers, chapter 0, pages 9-30, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-31636-4_2
    DOI: 10.1007/978-3-031-31636-4_2
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