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Testing for Unit Roots in Panel Data Using a Wavelet Ratio Method


  • Yushu Li


  • Ghazi Shukur


For testing unit root in single time series, most tests concentrate on the time domain. Recently, Fan and Gençay (Econom Theory 26:1305–1331, 2010 ) proposed a wavelet ratio test which took advantage of the information from the frequency domain by using a wavelet spectrum methodology. This test shows a better power than many time domain based unit root tests including the Dickey–Fuller (J Am Stat Assoc 74:427–431, 1979 ) type of test in the univariate time series case. On the other hand, various unit root tests in multivariate time series have appeared since the pioneering work of Levin and Lin (Unit root test in panel data: new results, University of California at San Diego, Discussion Paper, 1993 ). Among them, the Im–Pesaran–Shin (IPS) (J Econ 115(1):53–74, 1997 ) test is widely used for its straightforward implementation and robustness to heterogeneity. The IPS test is a group mean test which uses the average of the test statistics for each single series. As the test statistics in each series can be flexible, this paper will apply the wavelet ratio statistic to give a comparison with the test by using Dickey–Fuller t statistic in the single series. Simulation results show a gain in power by employing the wavelet ratio test instead of the Dickey–Fuller t statistic in the panel data case. As the IPS test is sensitive to cross sectional dependence, we further compare the robustness of both test statistics when there exists cross correctional dependence among the units in the panel data. Finally we apply a residual based wavestrapping methodology to reduce the over biased size problem brought up by the cross correlation for both test statistics. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Yushu Li & Ghazi Shukur, 2013. "Testing for Unit Roots in Panel Data Using a Wavelet Ratio Method," Computational Economics, Springer;Society for Computational Economics, vol. 41(1), pages 59-69, January.
  • Handle: RePEc:kap:compec:v:41:y:2013:i:1:p:59-69
    DOI: 10.1007/s10614-011-9302-y

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    References listed on IDEAS

    1. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    2. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    3. M. Hashem Pesaran, 2007. "A simple panel unit root test in the presence of cross-section dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(2), pages 265-312.
    4. Christophe Hurlin & Valérie Mignon, 2007. "Second Generation Panel Unit Root Tests," Working Papers halshs-00159842, HAL.
    5. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2011. "Cross-sectional dependence robust block bootstrap panel unit root tests," Journal of Econometrics, Elsevier, vol. 163(1), pages 85-104, July.
    6. Peter C. B. Phillips & Donggyu Sul, 2003. "Dynamic panel estimation and homogeneity testing under cross section dependence *," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 217-259, June.
    7. Chang, Yoosoon, 2004. "Bootstrap unit root tests in panels with cross-sectional dependency," Journal of Econometrics, Elsevier, vol. 120(2), pages 263-293, June.
    8. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    9. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1305-1331, October.
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    Cited by:

    1. Bjørn Gunnar Hansen & Yushu Li, 2017. "An Analysis of Past World Market Prices of Feed and Milk and Predictions for the Future," Agribusiness, John Wiley & Sons, Ltd., vol. 33(2), pages 175-193, April.
    2. Ali Abdul Aziz & Shukur Ghazi & Månsson Kristofer, 2020. "A wavelet-based variance ratio unit root test for a system of equations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(3), pages 1-16, June.
    3. Hyunjoo Kim Karlsson & Yushu Li & Ghazi Shukur, 2018. "The Causal Nexus between Oil Prices, Interest Rates, and Unemployment in Norway Using Wavelet Methods," Sustainability, MDPI, Open Access Journal, vol. 10(8), pages 1-1, August.


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