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Automatic Signal Extraction for Stationary and Non-Stationary Time Series by Circulant SSA

Author

Listed:
  • Bógalo, Juan
  • Poncela, Pilar
  • Senra, Eva

Abstract

Singular Spectrum Analysis (SSA) is a nonparametric tecnique for signal extraction in time series based on principal components. However, it requires the intervention of the analyst to identify the frequencies associated to the extracted principal components. We propose a new variant of SSA, Circulant SSA (CSSA) that automatically makes this association. We also prove the validity of CSSA for the nonstationary case. Through several sets of simulations, we show the good properties of our approach: it is reliable, fast, automatic and produces strongly separable elementary components by frequency. Finally, we apply Circulant SSA to the Industrial Production Index of six countries. We use it to deseasonalize the series and to illustrate that it also reproduces a cycle in accordance to the dated recessions from the OECD.

Suggested Citation

  • Bógalo, Juan & Poncela, Pilar & Senra, Eva, 2017. "Automatic Signal Extraction for Stationary and Non-Stationary Time Series by Circulant SSA," MPRA Paper 76023, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:76023
    as

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    File URL: https://mpra.ub.uni-muenchen.de/76023/1/MPRA_paper_76023.pdf
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    References listed on IDEAS

    as
    1. Emmanuel Sirimal Silva & Hossein Hassani, 2015. "On the use of singular spectrum analysis for forecasting U.S. trade before, during and after the 2008 recession," International Economics, CEPII research center, issue 141, pages 34-49.
    2. Lisa Sella & Gianna Vivaldo & Andreas Groth & Michael Ghil, 2016. "Economic Cycles and Their Synchronization: A Comparison of Cyclic Modes in Three European Countries," Post-Print hal-01701122, HAL.
    3. de Carvalho, Miguel & Rodrigues, Paulo C. & Rua, António, 2012. "Tracking the US business cycle with a singular spectrum analysis," Economics Letters, Elsevier, vol. 114(1), pages 32-35.
    4. de Carvalho, Miguel & Rua, António, 2017. "Real-time nowcasting the US output gap: Singular spectrum analysis at work," International Journal of Forecasting, Elsevier, vol. 33(1), pages 185-198.
    5. Arteche, Josu & García-Enríquez, Javier, 2017. "Singular Spectrum Analysis for signal extraction in Stochastic Volatility models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 85-98.
    6. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    7. Hossein Hassani & Saeed Heravi & Anatoly Zhigljavsky, 2013. "Forecasting UK Industrial Production with Multivariate Singular Spectrum Analysis," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(5), pages 395-408, August.
    8. repec:cii:cepiie:2015-q1-141-30 is not listed on IDEAS
    9. Hossein Hassani & Abdol S. Soofi & Anatoly Zhigljavsky, 2013. "Predicting inflation dynamics with singular spectrum analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(3), pages 743-760, June.
    10. Hossein Hassani & Saeed Heravi & Gary Brown & Daniel Ayoubkhani, 2013. "Forecasting before, during, and after recession with singular spectrum analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(10), pages 2290-2302, October.
    11. repec:cii:cepiei:2015-q1-141-3 is not listed on IDEAS
    12. Lisa Sella & Gianna Vivaldo & Andreas Groth & Michael Ghil, 2016. "Economic Cycles and Their Synchronization: A Comparison of Cyclic Modes in Three European Countries," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 12(1), pages 25-48, September.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    circulant matrices; signal extraction; singular spectrum analysis; non-parametric; time series; Toeplitz matrices.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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