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SSA for Forecasting, Interpolation, Filtration and Estimation

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Singular Spectrum Analysis for Time Series

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Abstract

A reasonable forecast of a time series can be performed only if the series has a structure and there are tools to identify and use this structure. Also, we should assume that the structure of the time series is preserved for the future time period over which we are going to forecast (continue) the series. The last assumption cannot be validated using the data to be forecasted. Moreover, the structure of the series can rarely be identified uniquely. Therefore, the situation of different (and even contradictory) forecasts is not impossible. Thus, it is important not only to understand and express the structure but also to assess its stability.

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References

  1. Badeau R, David B, Richard G (2004) Selecting the modeling order for the ESPRIT high resolution method: an alternative approach. In: Proceedings of the IEEE ICASSP, vol 2, pp 1025–1028

    Google Scholar 

  2. Badeau R, Richard G, David B (2008) Performance of ESPRIT for estimating mixtures of complex exponentials modulated by polynomials. IEEE Trans Signal Process 56(2):492–504

    Article  MathSciNet  Google Scholar 

  3. Barkhuijsen H, de Beer R, van Ormondt D (1987) Improved algorithm for noniterative time-domain model fitting to exponentially damped magnetic resonance signals. J Magn Reson 73:553–557

    Google Scholar 

  4. Beckers J, Rixen M (2003) EOF calculations and data filling from incomplete oceanographic data sets. Atmos Ocean Technol 20:1839–1856

    Article  Google Scholar 

  5. Bozzo E, Carniel R, Fasino D (2010) Relationship between singular spectrum analysis and Fourier analysis: theory and application to the monitoring of volcanic activity. Comput Math Appl 60(3):812–820

    Article  MathSciNet  MATH  Google Scholar 

  6. Cadzow JA (1988) Signal enhancement: a composite property mapping algorithm. IEEE Trans Acoust 36(1):49–62

    Article  MATH  Google Scholar 

  7. de Groen P (1996) An introduction to total least squares. Nieuw Archief voor Wiskunde 14:237–253

    MATH  Google Scholar 

  8. Efron B, Tibshirani R (1986) Bootstrap methods for standard errors, confidence intervals and other measures of statistical accuracy. Stat Sci 1(1):54–75

    Article  MathSciNet  Google Scholar 

  9. Gel’fond A (1971) Calculus of finite differences. Translated from the Russian. International monographs on advanced mathematics and physics. Hindustan Publishing Corp, Delhi

    Google Scholar 

  10. Golyandina N (2010) On the choice of parameters in singular spectrum analysis and related subspace-based methods. Stat Interface 3(3):259–279

    MathSciNet  MATH  Google Scholar 

  11. Golyandina N, Osipov E (2007) The “Caterpillar”-SSA method for analysis of time series with missing values. J Stat Plan Inference 137(8):2642–2653

    Article  MathSciNet  MATH  Google Scholar 

  12. Golyandina N, Nekrutkin V, Zhigljavsky A (2001) Analysis of time series structure: SSA and related techniques. Chapman &Hall/CRC, Boca Raton

    Google Scholar 

  13. Hall MJ (1998) Combinatorial theory. Wiley, New York

    MATH  Google Scholar 

  14. Harris T, Yan H (2010) Filtering and frequency interpretations of singular spectrum analysis. Physica D 239:1958–1967

    Article  MathSciNet  MATH  Google Scholar 

  15. Kondrashov D, Ghil M (2006) Spatio-temporal filling of missing points in geophysical data sets. Nonlinear Process Geophys 13(2):151–159

    Article  Google Scholar 

  16. Kumaresan R, Tufts DW (1980) Data-adaptive principal component signal processing. In: Proceedings of the IEEE conference on decision and control. Albuquerque, pp 949–954

    Google Scholar 

  17. Kumaresan R, Tufts DW (1983) Estimating the angles of arrival of multiple plane waves. IEEE Trans Aerosp Electron Syst AES-19(1):134–139

    Google Scholar 

  18. Kung SY, Arun KS, Rao DVB (1983) State-space and singular-value decomposition-based approximation methods for the harmonic retrieval problem. J Opt Soc Am 73(12):1799–1811

    Article  Google Scholar 

  19. Nekrutkin V (2010) Perturbation expansions of signal subspaces for long signals. Stat Interface 3:297–319

    MathSciNet  MATH  Google Scholar 

  20. Oppenheim AV, Schafer RW (1975) Digital signal processing. Prentice-Hall, Upper Saddle River

    Google Scholar 

  21. Pakula L (1987) Asymptotic zero distribution of orthogonal polynomials in sinusoidal frequency estimation. IEEE Trans Inf Theor 33(4):569–576

    Article  MathSciNet  MATH  Google Scholar 

  22. Pepelyshev A, Zhigljavsky A (2010) Assessing the stability of long-horizon SSA forecasting. Stat Interface 3:321–327

    MathSciNet  MATH  Google Scholar 

  23. Roy R, Kailath T (1989) ESPRIT: estimation of signal parameters via rotational invariance techniques. IEEE Trans Acoust 37:984–995

    Article  Google Scholar 

  24. Schoellhamer D (2001) Singular spectrum analysis for time series with missing data. Geophys Res Lett 28(16):3187–3190

    Article  Google Scholar 

  25. Stoica P, Moses R (1997) Introduction to spectral analysis. Prentice Hall, Englewood Cliffs

    Google Scholar 

  26. Tufts DW, Kumaresan R (1982) Estimation of frequencies of multiple sinusoids: making linear prediction perform like maximum likelihood. Proc IEEE 70(9):975–989

    Article  Google Scholar 

  27. Usevich K (2010) On signal and extraneous roots in singular spectrum analysis. Stat Interface 3(3):281–295

    MathSciNet  MATH  Google Scholar 

  28. Van Huffel S, Chen H, Decanniere C, van Hecke P (1994) Algorithm for time-domain NMR data fitting based on total least squares. J Magn Reson Ser A 110:228–237

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Mathematics, St. Petersburg University, Universitetsky pr. 28, St. Petersburg, 198504, Russia

    Nina Golyandina

  2. School of Mathematics, Cardiff University, Senghennydd Rd., CF24 4AG, Cardiff, UK

    Anatoly Zhigljavsky

Authors
  1. Nina Golyandina
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  2. Anatoly Zhigljavsky
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Correspondence to Nina Golyandina .

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Golyandina, N., Zhigljavsky, A. (2013). SSA for Forecasting, Interpolation, Filtration and Estimation. In: Singular Spectrum Analysis for Time Series. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34913-3_3

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