Skip to main content

Advertisement

SpringerLink
Log in

Combining singular spectrum analysis and PAR(p) structures to model wind speed time series

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

Singular spectrum analysis (SSA) is a technique that decomposes a time series into a set of components, such as, trend, harmonics, and residuals. Leaving out the residual components and adding up the others, the time series can be smoothed. This procedure has been used to model Brazilian electricity consumption and flow series. The PAR(p), periodic autoregressive models, has been broadly used in modelling energy series in Brazil. This paper presents an approach of this decomposition method, by fitting the PAR(p), considering its multivariate version known as multivariate SSA (MSSA). The method was applied to a vector of two wind speed series recorded at two locations in the Brazilian Northeast region. The obtained results, when compared to the univariate decomposition of each series, were far superior, showing that the spatial correlation between the two series were considered by MSSA decomposition stage.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Golyandina N, Nekrutkin V, and Zhihgljavsky A, Analysis of Time Series Structure: SSA and Reletade Techniques, Chapman & Hall/CRC, New York, 2001.

    Book  Google Scholar 

  2. Hassani H, Singular spectrum analysis: Methodology and comparison, Journal of Data Science, 2007, 5: 239–257.

    Google Scholar 

  3. Schreiber T and Grassberger P, A simple noise-reduction method for real data, Phys. Letter A, 1991, 160(5): 411–418.

    Article  MathSciNet  Google Scholar 

  4. Sivakumar B, Phoon K, Liong S, and Liaw C, A systematic approach to noise reduction in chaotic hydrological time series, Journal of Hydrology, 1999, 219: 103–135.

    Article  Google Scholar 

  5. Jayawardena A and Gurung A, Noise reduction and prediction of hydrometeorological time series: Dynamical systemas approach vs. stochastic approach, Journal of Hydrology, 2000, 228: 242–264.

    Article  Google Scholar 

  6. Elshorbagy A, Simonovic S, and Panu U, Noise reduction in chaotic hydrologic time series: Facts and doubts, Journal of Hydrology, 2002, 256: 147–265.

    Article  Google Scholar 

  7. Golyandina N and Stepanov D, SSA-based approaches to analysis and forecast of multidimensional time series, Proceedings of the Fifth Workshop on Simulation (Department of Mathematics, St. Petersburg State University), Russia, 2005.

    Google Scholar 

  8. Patterson K, Hassani H, Heravi H, and Zhigljavsky A, Multivariate singular spectrum analysis for forecasting revisions to real-time data, Journal of Applied Statistics, 2011, 38(10): 2183–2211.

    Article  MathSciNet  Google Scholar 

  9. Miranian A, Abdollahzade M, and Hassani H, Day-ahead electricity price analysis and forecasting by singular specttrum analysis, IET Generation Transmission and Distribution, 2013, 7(4): 337–346.

    Article  Google Scholar 

  10. Hassani H, Heravi S, and Zhigljavsky A, Forecasting European industrial production with singular spectrum analysis, International Journal of Forecasting, 2009, 25(1): 103–118.

    Google Scholar 

  11. Hassani H, Soofi A, and Zhigljavsky A, Predicting inflation dynamics with singular spectrum analysis, Journal of the Royal Statistical Society, 2013, 176(3): 743–760.

    Article  MathSciNet  Google Scholar 

  12. Hassani H, Heravi S, and Zhigljavsky A, Forecasting UK industrial production with multivariate singular spectrum analysis, Journal of Forecasting, 2013, 32(5): 395–408.

    Article  MathSciNet  Google Scholar 

  13. Junior L, Menezes M, Cassiano K, Pessanha J, and Souza R, Residential electricity consumption forecasting using a geometric combination approach, International Journal of Energy and Statistics, 2013, 1(2): 113–125.

    Article  Google Scholar 

  14. Cassiano K, Junior L, Souza R, Moises M, Pessanha J, and Souza R, Hydroelectric energy forecast, International Journal of Energy and Statistics, 2013, 1(3): 205–214.

    Article  Google Scholar 

  15. Qadrdan M, Ghodsi M, and Wu J, Probabilistic wind power forecasting using a single forecast, International Journal of Energy and Statistics, 2013, 1(2): 99–111.

    Article  Google Scholar 

  16. Beneki C and Silva E S, Analysisng and forecasting European union energy data, International Journal of Energy and Statistics, 2013, 1(2): 127–141.

    Article  Google Scholar 

  17. Zhang Q, Wang B, He B, Peng Y, and Pen M, Singular spectrum analysis and ARIMA hybrid model for annual runoff forecasting, Water Resour Manage, 2011, 25: 2683–2703.

    Article  Google Scholar 

  18. Golyandina N and Vlassieva E, First-order SSA-errors for long time series: Model examples of simple noisy signals, Proceedings of 6th St. Petersburg Workshop on Simulation, 2009, Vol. 1, St. Petersburg State University, 314–319.

    Google Scholar 

  19. Hassani H, Mahmoudvand R, Zokaei M, and Ghodsi M, On the separability between signal and noise in singular spectrum analysis, Fluctuation and Noise Letters, 2012, 11(2): 1250, 014.

    Article  Google Scholar 

  20. Hassani H and Thomakos D, A review on singular spectrum analysis for economic and financial time series, Statistics and Its Interface, 2010, 3: 377–397.

    Article  MATH  MathSciNet  Google Scholar 

  21. Kubrusly, Elements of Operator Theory, Birkhuser, Boston, 2001.

    Book  MATH  Google Scholar 

  22. Hassani H, Mahmoudvand R, and Zoakaei, Separability and window length in singular spectrum analysis, Comptes Rendus Mathematique, 2011, 1349: 987–990.

    Article  Google Scholar 

  23. Morettin P and Toloi L, Análise Séries Temporais, 2nd. ed. ABE, Projeto Fisher, Editora: Edgard Blucher, Sõ Paulo, 2006.

    Google Scholar 

  24. Hassani H and Mahmoudvand R, Multivariate singular spectrum analysis: A general view and new vector forecasting approach, International Journal of Energy and Statistics, 2013, 1(1): 55–83.

    Article  Google Scholar 

  25. Hipel K and McLeod A, Time Series Modelling of Water Resources and Environmental Systems, Elsevier, Amsterdam, The Netherlands, 1994.

    Google Scholar 

  26. Maceira M and Pena D, Geração de cenários sintéticos de energia e vazão para o planejamento da operação energética, Proceedings of the XVI Brazilian Symposium of Water Resources (ABRH Brazilian Association of Water Resources), Joõ Pessoa, Brazil, 2005.

    Google Scholar 

  27. Maceira M, Operação Ótima de Reservatórios com Previsão de Afluências, Master’s degree thesis, Federal University of Rio de Janeiro, Brazil, 1989.

    Google Scholar 

  28. Quenouille M, Approximate tests of correlation in time series 3, Mathematical Proceedings of the Cambridge Philosophical Society, 1949, 45(3): 483–484.

    Article  MATH  MathSciNet  Google Scholar 

  29. Brock W, Dechert W, and Scheinkman J, A Test for Independence Based On the Coreelatin Dimension, Department of Economics, university of Wisconsin at Madison, University of Houston, and University of Chicago, 1987.

    Google Scholar 

  30. Mahmoudvand R, Najari N, and Zokaei M, On the optimal parameters for reconstruction and forecasting in singular spectrum analysis, Communication in Statistics: Simulations and Computations, 2013, 42(4): 860–870.

    Article  MATH  MathSciNet  Google Scholar 

  31. Hassani H, Mahmoudvand R, and Yarmohammadi Y, Filtering and denoising in linear regression analysis, Fluctuation and Noise Letters, 2010, 9(4): 343–358.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Fluminense Federal University (UFF), Niterói, Brazil

    Moisés Lima de Menezes

  2. Electrical Engineering Department, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil

    Reinaldo Castro Souza

  3. Institute of Mathematics and Statistics, State University of Rio de Janeiro (UERJ), Rio de Janeiro, Brazil

    José Francisco Moreira Pessanha

Authors
  1. Moisés Lima de Menezes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reinaldo Castro Souza
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. José Francisco Moreira Pessanha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Moisés Lima de Menezes.

Additional information

This paper was recommended for publication by Editor WANG Shouyang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Menezes, M.L., Souza, R.C. & Pessanha, J.F.M. Combining singular spectrum analysis and PAR(p) structures to model wind speed time series. J Syst Sci Complex 27, 29–46 (2014). https://doi.org/10.1007/s11424-014-3301-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-014-3301-8

Keywords

Search

Navigation