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

Author

Listed:
  • 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.

Suggested Citation

  • 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.
    • Handle: RePEc:msh:ebswps:2011-23
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp23-11.pdf
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    References listed on IDEAS

    as
    1. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    2. 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.
    3. 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.
    4. 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.
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    Cited by:

    1. Hossein Hassani & Zara Ghodsi & Rangan Gupta & Mawuli Segnon, 2017. "Forecasting Home Sales in the Four Census Regions and the Aggregate US Economy Using Singular Spectrum Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 83-97, January.
    2. Franz Ruch & Dirk Bester, 2013. "Towards a Measure of Core Inflation using Singular Spectrum Analysis," South African Journal of Economics, Economic Society of South Africa, vol. 81(3), pages 307-329, September.

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    More about this item

    Keywords

    Dimension; Embedding; Mean squared error; Reconstruction; Signal-noise separation; Window length.;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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