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Comparison of Non-Stationary Time Series in the Frequency Domain

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  • Maharaj, E.A.

Abstract

In this paper we compare two non-stationary time series using non-parametric procedures. Evolutionary spectra are estimated for the two series. Randomization tests are performed on groups of spectral estimates for both related and independent time series. Simul ation studies show that in certain cases the tests perform reasonably well. The tests are applied to observed geological and financial time series.

Suggested Citation

  • Maharaj, E.A., 2001. "Comparison of Non-Stationary Time Series in the Frequency Domain," Monash Econometrics and Business Statistics Working Papers 1/01, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2001-1
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2001/wp1-01.pdf
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    References listed on IDEAS

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    1. 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.
    2. Timmer, J. & Lauk, M. & Vach, W. & Lucking, C. H., 1999. "A test for a difference between spectral peak frequencies," Computational Statistics & Data Analysis, Elsevier, vol. 30(1), pages 45-55, March.
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    Cited by:

    1. 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.
    2. Michela Borghesi, 2020. "Metodi statistici per il confronto di serie storiche con applicazioni finanziarie," Working Papers 2020049, University of Ferrara, Department of Economics.
    3. 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.
    4. Xu Gao & Babak Shahbaba & Hernando Ombao, 2018. "Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 549-579, October.
    5. 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.
    6. Caiado, Jorge & Crato, Nuno & Peña, Daniel, 2007. "Comparison of time series with unequal length," MPRA Paper 6605, University Library of Munich, Germany.
    7. Salcedo, Gladys E. & Porto, Rogério F. & Morettin, Pedro A., 2012. "Comparing non-stationary and irregularly spaced time series," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3921-3934.
    8. 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.
    9. Holger Dette & Efstathios Paparoditis, 2009. "Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 831-857, September.
    10. 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.
    11. 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.
    12. Sonia Díaz & José Vilar, 2010. "Comparing Several Parametric and Nonparametric Approaches to Time Series Clustering: A Simulation Study," Journal of Classification, Springer;The Classification Society, vol. 27(3), pages 333-362, November.
    13. Caiado, Jorge & Crato, Nuno, 2005. "Discrimination between deterministic trend and stochastic trend processes," MPRA Paper 2076, University Library of Munich, Germany.
    14. Pierpaolo D’Urso & Livia Giovanni & Riccardo Massari & Dario Lallo, 2013. "Noise fuzzy clustering of time series by autoregressive metric," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 217-243, November.
    15. Jin, Lei, 2021. "Robust tests for time series comparison based on Laplace periodograms," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    16. Mahmoudi, Mohammad Reza & Heydari, Mohammad Hossein & Roohi, Reza, 2019. "A new method to compare the spectral densities of two independent periodically correlated time series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 160(C), pages 103-110.
    17. Caiado, Jorge & Crato, Nuno & Peña, Daniel, 2006. "An interpolated periodogram-based metric for comparison of time series with unequal lengths," MPRA Paper 2075, University Library of Munich, Germany.
    18. Dette, Holger & Paroditis, Efstathios, 2007. "Testing equality of spectral densities," Technical Reports 2007,29, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    19. 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.
    20. Mahmoudi, Mohammad Reza, 2021. "A computational technique to classify several fractional Brownian motion processes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    21. Dette, Holger & Paparoditis, Efstathios, 2008. "Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities," Technical Reports 2008,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

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    More about this item

    Keywords

    Tests; Time series; Simulation; Evolutionary Spectra;
    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
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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