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A data-driven test to compare two or multiple time series

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  • Jin, Lei

Abstract

In this paper, a data-driven test is proposed to compare two independent or dependent stationary time series, in terms of the second order dynamics. We show that the problem of time series comparison is equivalent to a goodness-of-fit test checking if a constant model is adequate. Using the same framework, the proposed test is easily extended to compare multiple time series and time series of different lengths. Different to previous methods, it is based on generalized score statistics in an estimating equation setting, with some weak and flexible conditions. An extensive simulation study illustrates the validity of the asymptotic result and finite sample properties, using the tapered periodogram. The proposed test is found to perform well for many different situations, including time series with heavy-tailed or skewed innovations. An application to damage detection using vibration data is discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:6:p:2183-2196
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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.
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    6. 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.
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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. 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. 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. S. Valère Bitseki Penda & Adélaïde Olivier, 2017. "Autoregressive functions estimation in nonlinear bifurcating autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 179-210, July.
    6. 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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