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Comparison of time series with unequal length

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Author Info
Caiado, Jorge
Crato, Nuno
Peña, Daniel

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Abstract

The comparison and classification of time series is an important issue in practical time series analysis. For these purposes, various methods have been proposed in the literature, but all have shortcomings, especially when the observed time series have different sample sizes. In this paper, we propose spectral domain methods for handling time series of unequal length. The methods make the spectral estimates comparable, by producing statistics at the same frequency. A first sensible approach may consist on zero-padding the shorter time series in order to increase the corresponding number of periodogram ordinates. We show that this works well provided the sample sizes are not very different, but does not give good results in case the time series lengths are very unbalanced. For this latter case, we study some periodogram-based comparison methods and construct a test. Both the methods and the test display reasonable properties for series of any lengths. Additionally and for reference, we develop a parametric comparison method. The procedures are assessed by a Monte Carlo simulation study. As an illustrative example, a periodogram method is used to compare and cluster industrial production series of some developed countries.

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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 6605.

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Date of creation: Dec 2007
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Handle: RePEc:pra:mprapa:6605

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Related research
Keywords: Cluster analysis Interpolated periodogram Reduced periodogram Spectral analysis Time series Zero-padding.

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models
C0 - Mathematical and Quantitative Methods - - General
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Maximo Camacho & Gabriel Perez-Quiros, 2004. "Are European business cycles close enough to be just one?," Computing in Economics and Finance 2004 16, Society for Computational Economics. [Downloadable!]
    Other versions:
  2. Maharaj, Elizabeth Ann, 2002. "Comparison of non-stationary time series in the frequency domain," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 131-141, July. [Downloadable!] (restricted)
  3. Pena, Daniel & Rodriguez, Julio, 2005. "Detecting nonlinearity in time series by model selection criteria," International Journal of Forecasting, Elsevier, vol. 21(4), pages 731-748. [Downloadable!] (restricted)
  4. Caiado, Jorge & Crato, Nuno & Pena, Daniel, 2006. "A periodogram-based metric for time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2668-2684, June. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Caiado, Jorge & Crato, Nuno, 2007. "A GARCH-based method for clustering of financial time series: International stock markets evidence," MPRA Paper 2074, University Library of Munich, Germany. [Downloadable!]
  2. Caiado, Jorge & Crato, Nuno & Peña, Daniel, 2007. "Is there an identity within international stock market volatilities?," MPRA Paper 2069, University Library of Munich, Germany. [Downloadable!]
  3. Caiado, Jorge & Crato, Nuno, 2008. "Identifying the evolution of stock markets stochastic structure after the euro," MPRA Paper 6609, University Library of Munich, Germany. [Downloadable!]
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