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Bootstrap M Unit Root Tests


  • Giuseppe Cavaliere
  • A. M. Robert Taylor


In this article we propose wild bootstrap implementations of the local generalized least squares (GLS) de-trended M and ADF unit root tests of Stock (1999), Ng and Perron (2001), and Elliott et al. (1996), respectively. The bootstrap statistics are shown to replicate the first-order asymptotic distributions of the original statistics, while numerical evidence suggests that the bootstrap tests perform well in small samples. A recolored version of our bootstrap is also proposed which can further improve upon the finite sample size properties of the procedure when the shocks are serially correlated, in particular ameliorating the significant under-size seen in the M tests against processes with autoregressive or moving average roots close to -1. The wild bootstrap is used because it has the desirable property of preserving in the resampled data the pattern of heteroskedasticity present in the original shocks, thereby allowing for cases where the series under test is driven by martingale difference innovations.

Suggested Citation

  • Giuseppe Cavaliere & A. M. Robert Taylor, 2009. "Bootstrap M Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 393-421.
  • Handle: RePEc:taf:emetrv:v:28:y:2009:i:5:p:393-421 DOI: 10.1080/07474930802467167

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    References listed on IDEAS

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    Cited by:

    1. Harvey, David I. & Leybourne, Stephen J. & Sollis, Robert & Taylor, A.M. Robert, 2016. "Tests for explosive financial bubbles in the presence of non-stationary volatility," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 548-574.
    2. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    3. Smeekes, Stephan & Taylor, A.M. Robert, 2012. "Bootstrap Union Tests For Unit Roots In The Presence Of Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 28(02), pages 422-456, April.
    4. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94 Edward Elgar Publishing.
    5. Giuseppe Cavaliere & Peter C. B. Phillips & Stephan Smeekes & A. M. Robert Taylor, 2015. "Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 34(4), pages 512-536, April.
    6. Su, Jen-Je & Cheung, Adrian (Wai-Kong) & Roca, Eduardo, 2014. "Does Purchasing Power Parity hold? New evidence from wild-bootstrapped nonlinear unit root tests in the presence of heteroskedasticity," Economic Modelling, Elsevier, vol. 36(C), pages 161-171.
    7. Smeekes S. & Urbain J.R.Y.J., 2014. "A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing," Research Memorandum 008, Maastricht University, Graduate School of Business and Economics (GSBE).
    8. Skrobotov Anton & Cavaliere Giuseppe & Taylor Robert, 2016. "Wild Bootstrap Seasonal Unit Root Tests for Time Series with Periodic Non-Stationary Volatility," Working Papers wpaper-2016-269, Gaidar Institute for Economic Policy, revised 2016.


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