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Bootstrap union tests for unit roots in the presence of nonstationary volatility

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  • Smeekes, S.

    (Quantitative Economics)

  • Taylor, A.M.R.

Abstract

Three important issues surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data; uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not, and the possible presence of nonstationary volatility in the data. Assuming homoskedasticity, Harvey, Leybourne, and Taylor (2011, Journal of Econometrics, forthcoming) propose decision rules based on a four-way union of rejections of quasi-differenced (QD) and ordinary least squares (OLS) detrended tests, both with and without a linear trend, to deal with the first two problems. In this paper we first discuss, again under homoskedasticity, how these union tests may be validly bootstrapped using the sieve bootstrap principle combined with either the independent and identically distributed (i.i.d.) or wild bootstrap resampling schemes. This serves to highlight the complications that arise when attempting to bootstrap the union tests. We then demonstrate that in the presence of nonstationary volatility the union test statistics have limit distributions that depend on the form of the volatility process, making tests based on the standard asymptotic critical values or, indeed, the i.i.d. bootstrap principle invalid. We show that wild bootstrap union tests are, however, asymptotically valid in the presence of nonstationary volatility. The wild bootstrap union tests therefore allow for a joint treatment of all three of the aforementioned issues in practice.
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  • Smeekes, S. & Taylor, A.M.R., 2010. "Bootstrap union tests for unit roots in the presence of nonstationary volatility," Research Memorandum 015, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2010015
    DOI: 10.26481/umamet.2010015
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    Cited by:

    1. Skrobotov, Anton, 2018. "On bootstrap implementation of likelihood ratio test for a unit root," Economics Letters, Elsevier, vol. 171(C), pages 154-158.
    2. Ghoshray, Atanu, 2021. "Are coffee farmers worse off in the long run?," 95th Annual Conference, March 29-30, 2021, Warwick, UK (Hybrid) 311084, Agricultural Economics Society - AES.
    3. Smeekes, S., 2011. "Bootstrap sequential tests to determine the stationary units in a panel," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    4. Addison, Tony & Ghoshray, Atanu, 2023. "Discerning trends in international metal prices in the presence of nonstationary volatility," Resource and Energy Economics, Elsevier, vol. 71(C).
    5. 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).
    6. 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.
    7. Andre M. Marques & Gilberto Tadeu Lima, 2021. "Testing for Granger Causality in Quantiles Between the Wage Share and Capacity Utilization," Working Papers, Department of Economics 2021_03, University of São Paulo (FEA-USP).
    8. Ghoshray, Atanu, 2022. "Trends and persistence of farm-gate coffee prices around the world," 96th Annual Conference, April 4-6, 2022, K U Leuven, Belgium 321166, Agricultural Economics Society - AES.
    9. Marina Friedrich & Luca Margaritella & Stephan Smeekes, 2023. "High-Dimensional Causality for Climatic Attribution," Papers 2302.03996, arXiv.org.
    10. Maican, Florin G. & Sweeney, Richard J., 2013. "Rejection Probabilities for a Battery of Unit-Root Tests," Working Papers in Economics 568, University of Gothenburg, Department of Economics.
    11. Marques, André M. & Lima, Gilberto Tadeu, 2022. "Testing for Granger causality in quantiles between the wage share in income and productive capacity utilization," Structural Change and Economic Dynamics, Elsevier, vol. 62(C), pages 290-312.
    12. 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.
    13. Mahdavi, Saeid & Westerlund, Joakim, 2018. "Subnational government tax revenue capacity and effort convergence: New evidence from sequential unit root tests," Economic Modelling, Elsevier, vol. 73(C), pages 174-183.
    14. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Stephan Smeekes, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 398-415, May.
    15. Yicong Lin & Mingxuan Song, 2023. "Robust bootstrap inference for linear time-varying coefficient models: Some Monte Carlo evidence," Tinbergen Institute Discussion Papers 23-049/III, Tinbergen Institute.

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