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Testing equality of stationary autocovariances

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  • Robert Lund
  • Hany Bassily
  • Brani Vidakovic

Abstract

. This article studies tests for assessing whether two stationary and independent time series have the same dynamics – specifically, whether the autocovariances of both series coincide at all lags. Frequency domain statistics previously proposed for this purpose are reviewed. A time domain statistic is then developed and investigated. The performance of these statistics are compared. Multivariate versions of the results are constructed. The methods are applied in the analysis of temperatures and precipitations from Atlanta and Athens, Georgia. Our interest here is driven by the need to identify a good climatological reference series for a given station.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:30:y:2009:i:3:p:332-348
    DOI: 10.1111/j.1467-9892.2009.00616.x
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    References listed on IDEAS

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    1. 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.
    2. Hsiao-Yun Huang & Hernando Ombao & David S. Stoffer, 2004. "Discrimination and Classification of Nonstationary Time Series Using the SLEX Model," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 763-774, January.
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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. 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.
    3. 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.
    4. Taheriyoun, Ali Reza, 2012. "Testing the covariance function of stationary Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 606-613.
    5. Jin, Lei, 2021. "Robust tests for time series comparison based on Laplace periodograms," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    6. Andrew J. Grant & Barry G. Quinn, 2017. "Parametric Spectral Discrimination," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 838-864, November.
    7. 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.
    8. Dilip Nachane & Aditi Chaubal, 2022. "A Comparative Evaluation of Some DSP Filters vis-à-vis Commonly Used Economic Filters," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 161-190, September.
    9. Nikolay Iskrev, 2013. "On the distribution of information in the moment structure of DSGE models," 2013 Meeting Papers 339, Society for Economic Dynamics.
    10. Baek, Changryong & Gates, Katheleen M. & Leinwand, Benjamin & Pipiras, Vladas, 2021. "Two sample tests for high-dimensional autocovariances," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).

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