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Window Length Selection and Signal-Noise Separation and Reconstruction in Singular Spectrum Analysis

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  • Md Atikur Rahman Khan

    ()

  • D.S. Poskitt

    ()

Abstract

In Singular Spectrum Analysis (SSA) window length is a critical tuning parameter that must be assigned by the practitioner. This paper provides a theoretical analysis of signal-noise separation and reconstruction in SSA that can serve as a guide to optimal window choice. We establish numerical bounds on the mean squared reconstruction error and present their almost sure limits under very general regularity conditions on the underlying data generating mechanism. We also provide asymptotic bounds for the mean squared separation error. Evidence obtained using simulation experiments indicates that the theoretical properties are reflected in observed behaviour, even in relatively small samples, and the results indicate how an optimal choice for the window length can be made.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2011/wp23-11.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 23/11.

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Length: 20 pages
Date of creation: Oct 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-23

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Related research

Keywords: Dimension; Embedding; Mean squared error; Reconstruction; Signal-noise separation; Window length.;

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  1. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
  2. Forni, Mario & Lippi, Marco, 2000. "The Generalized Dynamic Factor Model: Representation Theory," CEPR Discussion Papers 2509, C.E.P.R. Discussion Papers.
  3. Poskitt, Don S, 2000. "Strongly Consistent Determination of Cointegrating Rank via Canonical Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 77-90, January.
  4. Md Atikur Rahman Khan & D.S. Poskitt, 2010. "Description Length Based Signal Detection in singular Spectrum Analysis," Monash Econometrics and Business Statistics Working Papers 13/10, Monash University, Department of Econometrics and Business Statistics.
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