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Description Length Based Signal Detection in singular Spectrum Analysis

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  • Md Atikur Rahman Khan

    ()

  • D.S. Poskitt

    ()

Abstract

This paper provides an information theoretic analysis of the signal-noise separation problem in Singular Spectrum Analysis. We present a signal-plus-noise model based on the Karhunen-Loève expansion and use this model to motivate the construction of a minimum description length criterion that can be employed to select both the window length and the signal. We show that under very general regularity conditions the criterion will identify the true signal dimension with probability one as the sample size increases, and will choose the smallest window length consistent with the Whitney embedding theorem. Empirical results obtained using simulated and real world data sets indicate that the asymptotic theory is reflected in observed behaviour, even in relatively small samples.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2010/wp13-10.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 13/10.

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Length: 35 pages
Date of creation: 24 May 2010
Date of revision:
Handle: RePEc:msh:ebswps:2010-13

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Related research

Keywords: Karhunen-Loève expansion; minimum description length; signal-plus-noise model; Singular Spectrum Analysis; embedding;

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References

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  1. 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.
  2. Hansen M. H & Yu B., 2001. "Model Selection and the Principle of Minimum Description Length," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 746-774, June.
  3. D. S. Poskitt & Arivalzahan Sengarapillai, 2009. "Description Length and Dimensionality Reduction in Functional Data Analysis," Monash Econometrics and Business Statistics Working Papers 13/09, Monash University, Department of Econometrics and Business Statistics.
  4. D.S. Poskitt & Jing Zhang, 2004. "Estimating Components in Finite Mixtures and Hidden Markov Models," Monash Econometrics and Business Statistics Working Papers 10/04, Monash University, Department of Econometrics and Business Statistics.
  5. Hassani, Hossein, 2007. "Singular Spectrum Analysis: Methodology and Comparison," MPRA Paper 4991, University Library of Munich, Germany.
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Citations

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Cited by:
  1. Md Atikur Rahman Khan & D.S. Poskitt, 2011. "Window Length Selection and Signal-Noise Separation and Reconstruction in Singular Spectrum Analysis," Monash Econometrics and Business Statistics Working Papers 23/11, Monash University, Department of Econometrics and Business Statistics.
  2. 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, 03.
  3. M. Atikur Rahman Khan & D.S. Poskitt, 2014. "On The Theory and Practice of Singular Spectrum Analysis Forecasting," Monash Econometrics and Business Statistics Working Papers 3/14, Monash University, Department of Econometrics and Business Statistics.

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