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Comparison of time series with unequal length in the frequency domain

Author

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  • Caiado, Jorge
  • Crato, Nuno
  • Peña, Daniel

Abstract

In statistical data analysis it is often important to compare, classify, and cluster different time series. For these purposes various methods have been proposed in the literature, but they usually assume time series with the same sample size. In this paper, we propose a spectral domain method for handling time series of unequal length. The method make the spectral estimates comparable by producing statistics at the same frequency. The procedure is compared with other methods proposed in the literature by a Monte Carlo simulation study. As an illustrative example, the proposed spectral method is applied to cluster industrial production series of some developed countries.

Suggested Citation

  • Caiado, Jorge & Crato, Nuno & Peña, Daniel, 2009. "Comparison of time series with unequal length in the frequency domain," MPRA Paper 15310, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:15310
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    1. Camacho, Maximo & Perez-Quiros, Gabriel & Saiz, Lorena, 2006. "Are European business cycles close enough to be just one?," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1687-1706.
    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.
    3. 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.
    4. Peter J. Diggle & Nicholas I. Fisher, 1991. "Nonparametric Comparison of Cumulative Periodograms," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(3), pages 423-434, November.
    5. D. S. Coates & P. J. Diggle, 1986. "Tests For Comparing Two Estimated Spectral Densities," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 7-20, January.
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    Citations

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    Cited by:

    1. João A. Bastos & Jorge Caiado, 2014. "Clustering financial time series with variance ratio statistics," Quantitative Finance, Taylor & Francis Journals, vol. 14(12), pages 2121-2133, December.
    2. Jonathan Decowski & Linyuan Li, 2015. "Wavelet-Based Tests for Comparing Two Time Series with Unequal Lengths," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 189-208, March.
    3. Maharaj, Elizabeth Ann & D’Urso, Pierpaolo, 2010. "A coherence-based approach for the pattern recognition of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3516-3537.
    4. Jentsch, Carsten & Pauly, Markus, 2012. "A note on using periodogram-based distances for comparing spectral densities," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 158-164.
    5. Jorge Caiado & Nuno Crato, 2010. "Identifying common dynamic features in stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 797-807.
    6. Preuß, Philip & Hildebrandt, Thimo, 2013. "Comparing spectral densities of stationary time series with unequal sample sizes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1174-1183.
    7. Otranto, Edoardo, 2010. "Identifying financial time series with similar dynamic conditional correlation," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 1-15, January.
    8. Mahdi Massahi & Masoud Mahootchi & Alireza Arshadi Khamseh, 2020. "Development of an efficient cluster-based portfolio optimization model under realistic market conditions," Empirical Economics, Springer, vol. 59(5), pages 2423-2442, November.
    9. Lei Jin & Suojin Wang, 2016. "A New Test for Checking the Equality of the Correlation Structures of two time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 355-368, May.
    10. Carolina Euán & Hernando Ombao & Joaquín Ortega, 2018. "The Hierarchical Spectral Merger Algorithm: A New Time Series Clustering Procedure," Journal of Classification, Springer;The Classification Society, vol. 35(1), pages 71-99, April.
    11. Jin, Lei, 2011. "A data-driven test to compare two or multiple time series," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2183-2196, June.
    12. B. Lafuente-Rego & P. D’Urso & J. A. Vilar, 2020. "Robust fuzzy clustering based on quantile autocovariances," Statistical Papers, Springer, vol. 61(6), pages 2393-2448, December.
    13. Harvill, Jane L. & Ravishanker, Nalini & Ray, Bonnie K., 2013. "Bispectral-based methods for clustering time series," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 113-131.
    14. Goffinet, Etienne & Lebbah, Mustapha & Azzag, Hanane & Loïc, Giraldi & Coutant, Anthony, 2022. "Functional non-parametric latent block model: A multivariate time series clustering approach for autonomous driving validation," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    15. Jorge Caiado & Nuno Crato & Pilar Poncela, 2020. "A fragmented-periodogram approach for clustering big data time series," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 117-146, March.
    16. João A. Bastos & Jorge Caiado, 2021. "On the classification of financial data with domain agnostic features," Working Papers REM 2021/0185, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    17. Mahmoudi, Mohammad Reza, 2021. "A computational technique to classify several fractional Brownian motion processes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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    More about this item

    Keywords

    Autocorrelation function; Cluster analysis; Interpolated periodogram; Reduced periodogram; Spectral analysis; Time series; Zero-padding.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C0 - Mathematical and Quantitative Methods - - General

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