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EXSSA: SSA-based reconstruction of time series via exponential smoothing of covariance eigenvalues


  • Papailias, Fotis
  • Thomakos, Dimitrios


A critical aspect of singular spectrum analysis (SSA) is the reconstruction of the original time series under various assumptions about its underlying structure. This reconstruction depends on the choice of the components from the covariance decomposition of the trajectory matrix. In most applications, this selection is based on the prior knowledge and experience of the researcher and a variety of practical rules. This paper suggests an alternative “fully automated” approach where all components of the covariance decomposition are used via exponential smoothing of the covariance eigenvalues. We illustrate the validity of the proposed approximation via simulations on different data generating processes. A second contribution of the paper is the proposal of a “forecast revision” algorithm which combines SSA with a benchmark. An empirical exercise using four key macroeconomic variables shows how this method can be used to improve the out-of-sample forecasts of any given benchmark model. Our results suggest that the proposed method has the potential to partly automate the use of SSA.

Suggested Citation

  • Papailias, Fotis & Thomakos, Dimitrios, 2017. "EXSSA: SSA-based reconstruction of time series via exponential smoothing of covariance eigenvalues," International Journal of Forecasting, Elsevier, vol. 33(1), pages 214-229.
  • Handle: RePEc:eee:intfor:v:33:y:2017:i:1:p:214-229
    DOI: 10.1016/j.ijforecast.2016.08.004

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    References listed on IDEAS

    1. Castle, Jennifer L. & Clements, Michael P. & Hendry, David F., 2015. "Robust approaches to forecasting," International Journal of Forecasting, Elsevier, vol. 31(1), pages 99-112.
    2. 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.
    3. Hendry, David F., 2006. "Robustifying forecasts from equilibrium-correction systems," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 399-426.
    4. Hirotugu Akaike, 1969. "Power spectrum estimation through autoregressive model fitting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 407-419, December.
    5. Hassani, Hossein & Heravi, Saeed & Zhigljavsky, Anatoly, 2009. "Forecasting European industrial production with singular spectrum analysis," International Journal of Forecasting, Elsevier, vol. 25(1), pages 103-118.
    6. Lisa Sella & Roberto Marchionatti, 2012. "On the cyclical variability of economic growth in Italy, 1881–1913: a critical note," Cliometrica, Journal of Historical Economics and Econometric History, Association Française de Cliométrie (AFC), vol. 6(3), pages 307-328, October.
    7. Md Atikur Rahman Khan & D. S. Poskitt, 2013. "Moment tests for window length selection in singular spectrum analysis of short– and long–memory processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 141-155, March.
    8. Lisi, Francesco & Medio, Alfredo, 1997. "Is a random walk the best exchange rate predictor?," International Journal of Forecasting, Elsevier, vol. 13(2), pages 255-267, June.
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    Cited by:

    1. António Rua & Hossein Hassani & Emmanuel Sirimal Silva & Dimitrios Thomakos, 2019. "Monthly Forecasting of GDP with Mixed Frequency Multivariate Singular Spectrum Analysis," Working Papers w201913, Banco de Portugal, Economics and Research Department.
    2. repec:eee:intfor:v:34:y:2018:i:4:p:582-597 is not listed on IDEAS


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