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Moment Tests for Window Length Selection in Singular Spectrum Analysis of Short- and Long-Memory Processes

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  • Md Atikur Rahman Khan

    ()

  • D.S. Poskitt

    ()

Abstract

In this paper we propose a new methodology for selecting the window length in Singular Spectral Analysis in which the window length is determined from the data prior to the commencement of modeling. The selection procedure is based on statistical tests designed to test the convergence of the autocovariance function. A classical time series portmanteau type statistic and two test statistics derived using a conditional moment principle are considered. The first two are applicable to short-memory processes, and the third is applicable to both short- and long-memory processes. We derive the asymptotic distribution of the statistics under fairly general regularity conditions and show that the criteria will identify true convergence with a finite window length with probability one as the sample size increases. Results obtained using Monte-Carlo simulation indicate the relevance of the asymptotic theory, even in relatively small samples, and that the conditional moment tests will choose a window length consistent with the Whitney embedding theorem. Application to observations on the Southern Oscillation Index shows how observed experimental behaviour can be reflected in features seen with real world data sets.

Suggested Citation

  • Md Atikur Rahman Khan & D.S. Poskitt, 2011. "Moment Tests for Window Length Selection in Singular Spectrum Analysis of Short- and Long-Memory Processes," Monash Econometrics and Business Statistics Working Papers 22/11, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2011-22
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp22-11.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. D. S. Poskitt, 2008. "Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 224-250, March.
    3. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
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    Cited by:

    1. 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.
    2. 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.

    More about this item

    Keywords

    Portmanteau type test; Conditional moment test; Asymptotic distribution; Linear regular process; Singular spectrum analysis; Embedding;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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