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Bootstrap M Unit Root Tests

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  • Giuseppe Cavaliere
  • A. M. Robert Taylor

Abstract

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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    Cited by:

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    2. Skrobotov, Anton, 2018. "On bootstrap implementation of likelihood ratio test for a unit root," Economics Letters, Elsevier, vol. 171(C), pages 154-158.
    3. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    4. 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.
    5. 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(2), pages 422-456, April.
    6. 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).
    7. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    8. 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.
    9. Nikolay Gospodinov & Ye Tao, 2011. "Bootstrap Unit Root Tests in Models with GARCH(1,1) Errors," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 379-405, August.
    10. Pedersen, Thomas Quistgaard & Schütte, Erik Christian Montes, 2020. "Testing for explosive bubbles in the presence of autocorrelated innovations," Journal of Empirical Finance, Elsevier, vol. 58(C), pages 207-225.
    11. Skrobotov, Anton, 2020. "Survey on structural breaks and unit root tests," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 58, pages 96-141.
    12. Zou, Nan & Politis, Dimitris N., 2019. "Linear process bootstrap unit root test," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 74-80.

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