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Singular Spectrum Analysis for Time Series

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International Encyclopedia of Statistical Science

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Singular spectrum analysis (SSA) is a technique of time series analysis and forecasting. It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA aims at decomposing the original series into a sum of a small number of interpretable components such as a slowly varying trend, oscillatory components and a “structureless” noise. It is based on the singular-value decomposition of a specific matrix constructed upon time series. Neither a parametric model nor stationarity-type conditions have to be assumed for the time series; this makes SSA a model-free technique.

The commencement of SSA is usually associated with publication of the papers (Broomhead and King 1986a, b) by Broomhead and King. Nowadays SSA is becoming more and more popular, especially in applications. There are several hundred papers published on methodological aspects and applications of SSA, see Golyandina et al. (2001), Vautard...

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References and Further Reading

  • Allen MR, Smith LA (1996) Monte Carlo SSA: detecting irregular oscillations in the presence of colored noise. J Clim 9:3373–3404

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  • Broomhead DS, King GP (1986a) Extracting qualitative dynamics from experimental data. Physica D 20:217–236

    MathSciNet  MATH  Google Scholar 

  • Broomhead DS, King GP (1986b) On the qualitative analysis of experimental dynamical systems. In: Sarkar S (ed) Nonlinear phenomena and chaos. Adam Hilger, Bristol, pp 113–144

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  • Cadzow JA (1988) Signal enhancement a composite property mapping algorithm. IEEE Trans Acoust Speech Signal Process 36: 4962

    Google Scholar 

  • Golub G, van Loan C (1996) Matrix computations. Johns Hopkins University Press, London

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  • Golyandina N, Osipov E (2007) The Caterpillar-SSA method for analysis of time series with missing values. J Stat Plan Infer 137:2642–2653

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  • Golyandina N, Nekrutkin V, Zhigljavsky A (2001) Analysis of time series structure: SSA and related techniques. Chapman & Hall/CRC Press, New York/London

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  • Hassani H, Zhigljavsky A, Patterson K, Soofi A (2010) A comprehensive causality test based on the singular spectrum analysis, causality in science. In: McKay Illary P, Russo F, Williamson J (eds) Causality in Sciences, Oxford University Press

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  • Kondrashov D, Ghil M (2006) Spatio-temporal filling of missing points in geophysical data sets. Nonlinear Proc Geoph 13: 151–159

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  • Markovsky I, Willems JC, Van Huffel S, De Moor B (2006) Exact and approximate modeling of linear systems: a behavioral approach. SIAM, Philadelphia

    Google Scholar 

  • Moskvina V, Schmidt KM (2003) Approximate projectors in singular spectrum analysis. SIAM J Matrix Anal Appl 24:932–942

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  • Moskvina VG, Zhigljavsky A (2003) An algorithm based on singular spectrum analysis for change-point detection. Commun Stat Simul Comput 32:319–352

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  • Van Huffel S (1993) Enhanced resolution based on minimum variance estimation and exponential data modeling. Signal process 33:333–355

    Google Scholar 

  • Vautard R, Ghil M (1989) Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D 35:395–424

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  • Vautard R, Yiou P, Ghil M (1992) Singular spectrum analysis: a toolkit for short, noisy and chaotic series. Physica D 58:95–126

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  • Zhigljavsky A (ed) (2010) Statistics and its interface, special issue on the singular spectrun analysis for time series. Springer, New York

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics, Cardiff University, Cardiff, UK

    Anatoly Zhigljavsky

Authors
  1. Anatoly Zhigljavsky
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Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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© 2011 Springer-Verlag Berlin Heidelberg

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Zhigljavsky, A. (2011). Singular Spectrum Analysis for Time Series. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_521

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