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Detrending Bootstrap Unit Root Tests

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  • Stephan Smeekes

Abstract

The role of detrending in bootstrap unit root tests is investigated. When bootstrapping, detrending must not only be done for the construction of the test statistic, but also in the first step of the bootstrap algorithm. It is argued that the two issues should be treated separately. Asymptotic validity of sieve bootstrap augmented Dickey--Fuller (ADF) unit root tests is shown for test statistics based on full sample and recursive ordinary least squares (OLS) and generalized least squares (GLS) detrending. It is also shown that the detrending method in the first step of the bootstrap may differ from the one used in the construction of the test statistic. A simulation study is conducted to analyze the effects of detrending on finite sample performance of the bootstrap test. It is found that full sample OLS detrending should be preferred based on power in the first step of the bootstrap algorithm, and that the decision about the detrending method used to obtain the test statistic should be based on the power properties of the corresponding asymptotic tests.

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  • Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    • Handle: RePEc:taf:emetrv:v:32:y:2013:i:8:p:869-891
    DOI: 10.1080/07474938.2012.690693
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    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. 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.
    3. Kruel, Maximiliano & Ceretta, Paulo Sergio, 2022. "Asymmetric influences on Latin American stock markets: A quantile approach," The Journal of Economic Asymmetries, Elsevier, vol. 26(C).
    4. 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.
    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. Yanglin Li, 2024. "New Unit Root Tests in the Nonlinear ESTAR Framework: The Movement and Volatility Characteristics of Crude oil and Copper Prices," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 1757-1776, May.
    7. Sergei Kharin & Zuzana Kapustova & Ivan Lichner, 2023. "Price transmission between maize and poultry product markets in the Visegrád Group countries: What is more nonlinear, egg or chicken?," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 69(12), pages 510-522.
    8. Takashi Matsuki, 2016. "Linear and nonlinear comovement in Southeast Asian local currency bond markets: a stepwise multiple testing approach," Empirical Economics, Springer, vol. 51(2), pages 591-619, September.
    9. 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.
    10. Li, Haiqi & Zheng, Chaowen, 2018. "Unit root quantile autoregression testing with smooth structural changes," Finance Research Letters, Elsevier, vol. 25(C), pages 83-89.

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