IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v32y2013i8p869-891.html
   My bibliography  Save this article

Detrending Bootstrap Unit Root Tests

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2012.690693
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474938.2012.690693?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Franz C. Palm & Stephan Smeekes & Jean‐Pierre Urbain, 2008. "Bootstrap Unit‐Root Tests: Comparison and Extensions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 371-401, March.
    2. Giuseppe Cavaliere & A. M. Robert Taylor, 2009. "Bootstrap M Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 393-421.
    3. Sul, Donggyu, 2009. "Panel unit root tests under cross section dependence with recursive mean adjustment," Economics Letters, Elsevier, vol. 105(1), pages 123-126, October.
    4. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    5. Dong Wan Shin & Beong Soo So, 2001. "recursive Mean Adjustment for Unit Root Tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(5), pages 595-612, September.
    6. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
    7. Richard, Patrick, 2009. "Modified fast double sieve bootstraps for ADF tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4490-4499, October.
    8. Patrick Richard, 2007. "ARMA Sieve bootstrap unit root tests," Cahiers de recherche 07-05, Departement d'économique de l'École de gestion à l'Université de Sherbrooke, revised Jul 2009.
    9. Zhije Xiao & Peter C.B. Phillips, 1998. "An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy," Econometrics Journal, Royal Economic Society, vol. 1(RegularPa), pages 27-43.
    10. 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.
    11. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Journal of Econometrics, Elsevier, vol. 169(2), pages 188-195.
    12. Elliott, Graham, 1999. "Efficient Tests for a Unit Root When the Initial Observation Is Drawn from Its Unconditional Distribution," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 767-783, August.
    13. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2010. "A Sieve Bootstrap Test For Cointegration In A Conditional Error Correction Model," Econometric Theory, Cambridge University Press, vol. 26(3), pages 647-681, June.
      • Arnold Zellner & Franz C. Palm, 2000. "Correction," Econometrica, Econometric Society, vol. 68(5), pages 1293-1294, September.
    14. Simon Broda & Kai Carstensen & Marc Paolella, 2009. "Assessing and Improving the Performance of Nearly Efficient Unit Root Tests in Small Samples," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 468-494.
    15. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(3), pages 587-636, June.
    16. Poskitt, D.S., 1994. "A Note on Autoregressive Modeling," Econometric Theory, Cambridge University Press, vol. 10(5), pages 884-899, December.
    17. Taylor, A M Robert, 2002. "Regression-Based Unit Root Tests with Recursive Mean Adjustment for Seasonal and Nonseasonal Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 269-281, April.
    18. Anders Rygh Swensen, 2003. "Bootstrapping unit root tests for integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 99-126, January.
    19. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    20. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    21. Swensen, Anders Rygh, 2003. "A Note On The Power Of Bootstrap Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(1), pages 32-48, February.
    22. E. J. Hannan & L. Kavalieris, 1986. "Regression, Autoregression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(1), pages 27-49, January.
    23. Perron, Pierre & Qu, Zhongjun, 2007. "A simple modification to improve the finite sample properties of Ng and Perron's unit root tests," Economics Letters, Elsevier, vol. 94(1), pages 12-19, January.
    24. Paparoditis, Efstathios & Politis, Dimitris N., 2005. "Bootstrapping Unit Root Tests for Autoregressive Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 545-553, June.
    25. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
    26. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 24(1), pages 43-71, February.
    27. Rodrigues, Paulo M.M., 2006. "Properties of recursive trend-adjusted unit root tests," Economics Letters, Elsevier, vol. 91(3), pages 413-419, June.
    28. 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.
    29. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    30. Burridge, Peter & Robert Taylor, A. M., 2004. "Bootstrapping the HEGY seasonal unit root tests," Journal of Econometrics, Elsevier, vol. 123(1), pages 67-87, November.
    31. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, vol. 71(4), pages 1269-1286, July.
    32. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    33. Parker, Cameron & Paparoditis, Efstathios & Politis, Dimitris N., 2006. "Unit root testing via the stationary bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 601-638, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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. 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.
    7. 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.
    8. 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.
    9. Li, Haiqi & Zheng, Chaowen, 2018. "Unit root quantile autoregression testing with smooth structural changes," Finance Research Letters, Elsevier, vol. 25(C), pages 83-89.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Paulo M. M. Rodrigues, 2013. "Recursive adjustment, unit root tests and structural breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 62-82, January.
    4. Franz C. Palm & Stephan Smeekes & Jean‐Pierre Urbain, 2008. "Bootstrap Unit‐Root Tests: Comparison and Extensions," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 371-401, March.
    5. Zou, Nan & Politis, Dimitris N., 2019. "Linear process bootstrap unit root test," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 74-80.
    6. Phillips, Peter C.B., 2010. "Bootstrapping I(1) data," Journal of Econometrics, Elsevier, vol. 158(2), pages 280-284, October.
    7. Hwang, Eunju & Shin, Dong Wan, 2015. "Stationary bootstrapping for semiparametric panel unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 14-25.
    8. Skrobotov Anton, 2018. "On Trend Breaks and Initial Condition in Unit Root Testing," Journal of Time Series Econometrics, De Gruyter, vol. 10(1), pages 1-15, January.
    9. Skrobotov, Anton, 2018. "On bootstrap implementation of likelihood ratio test for a unit root," Economics Letters, Elsevier, vol. 171(C), pages 154-158.
    10. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2009. "Unit Root Testing In Practice: Dealing With Uncertainty Over The Trend And Initial Condition," Econometric Theory, Cambridge University Press, vol. 25(3), pages 587-636, June.
    11. Sevan Gulesserian & Mohitosh Kejriwal, 2014. "On the power of bootstrap tests for stationarity: a Monte Carlo comparison," Empirical Economics, Springer, vol. 46(3), pages 973-998, May.
    12. David I. Harvey, & Stephen J. Leybourne, & A. M. Robert Taylor, 2007. "Testing for a unit root when uncertain about the trend [Revised to become 07/03 above]," Discussion Papers 06/03, University of Nottingham, Granger Centre for Time Series Econometrics.
    13. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Journal of Econometrics, Elsevier, vol. 169(2), pages 188-195.
    14. Samuel Brien & Michael Jansson & Morten Ørregaard Nielsen, 2022. "Nearly Efficient Likelihood Ratio Tests of a Unit Root in an Autoregressive Model of Arbitrary Order," Working Paper 1429, Economics Department, Queen's University.
    15. Richard, Patrick, 2009. "Modified fast double sieve bootstraps for ADF tests," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4490-4499, October.
    16. Sebastian Kripfganz & Daniel C. Schneider, 2020. "Response Surface Regressions for Critical Value Bounds and Approximate p‐values in Equilibrium Correction Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1456-1481, December.
    17. 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.
    18. Jürgen Wolters & Uwe Hassler, 2006. "Unit Root Testing," Springer Books, in: Olaf Hübler & Jachim Frohn (ed.), Modern Econometric Analysis, chapter 4, pages 41-56, Springer.
    19. Shelef, Amit, 2016. "A Gini-based unit root test," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 763-772.
    20. Skrobotov, Anton (Скроботов, Антон), 2015. "About Trend, the Shift and the Initial Value in Testing of the Hypothesis of a Unit Root [О Тренде, Сдвиге И Начальном Значении В Тестировании Гипотезы О Наличии Единичного Корня]," Published Papers mak6, Russian Presidential Academy of National Economy and Public Administration.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:emetrv:v:32:y:2013:i:8:p:869-891. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.