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Wavelet-Based Tests for Comparing Two Time Series with Unequal Lengths

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  • Jonathan Decowski
  • Linyuan Li

Abstract

type="main" xml:id="jtsa12101-abs-0001"> Test procedures for assessing whether two stationary and independent time series with unequal lengths have the same spectral density (or same auto-covariance function) are investigated. A new test statistic is proposed based on the wavelet transform. It relies on empirical wavelet coefficients of the logarithm of two spectral densities' ratio. Under the null hypothesis that two spectral densities are the same, the asymptotic normal distribution of the empirical wavelet coeffcients is derived. Furthermore, these empirical wavelet coefficients are asymptotically uncorrelated. A test statistic is proposed based on these results. The performance of the new test statistic is compared to several recent test statistics, with respect to their exact levels and powers. Simulation studies show that our proposed test is very comparable to the current test statistics in most cases. The main advantage of our proposed test statistic is that it is constructed very simply and is easy to implement.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:2:p:189-208
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    File URL: http://hdl.handle.net/10.1111/jtsa.12101
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    References listed on IDEAS

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    1. 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.
    2. Robert Lund & Hany Bassily & Brani Vidakovic, 2009. "Testing equality of stationary autocovariances," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 332-348, May.
    3. 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.
    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.
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    Cited by:

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    3. Jin, Lei, 2021. "Robust tests for time series comparison based on Laplace periodograms," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    4. Andrew J. Grant & Barry G. Quinn, 2017. "Parametric Spectral Discrimination," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 838-864, November.
    5. Daniel Cirkovic & Thomas J. Fisher, 2021. "On testing for the equality of autocovariance in time series," Environmetrics, John Wiley & Sons, Ltd., vol. 32(7), November.

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