IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v30y2011i4p379-405.html
   My bibliography  Save this article

Bootstrap Unit Root Tests in Models with GARCH(1,1) Errors

Author

Listed:
  • Nikolay Gospodinov
  • Ye Tao

Abstract

This article proposes a bootstrap unit root test in models with GARCH(1,1) errors and establishes its asymptotic validity under mild moment and distributional restrictions. While the proposed bootstrap test for a unit root shares the power enhancing properties of its asymptotic counterpart (Ling and Li, 2003), it offers a number of important advantages. In particular, the bootstrap procedure does not require explicit estimation of nuisance parameters that enter the distribution of the test statistic and corrects the substantial size distortions of the asymptotic test that occur for strongly heteroskedastic processes. The simulation results demonstrate the excellent finite-sample properties of the bootstrap unit root test for a wide range of GARCH specifications.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:emetrv:v:30:y:2011:i:4:p:379-405
    DOI: 10.1080/07474938.2011.553538
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2011.553538
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474938.2011.553538?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. Giuseppe Cavaliere & A. M. Robert Taylor, 2009. "Bootstrap M Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 393-421.
    2. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    3. Shiqing Ling & W. K. Li & Michael McAleer, 2003. "Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence," Econometric Reviews, Taylor & Francis Journals, vol. 22(2), pages 179-202.
    4. H. Peter Boswijk, 2000. "Testing for a Unit Root with Near-Integrated Volatility," Econometric Society World Congress 2000 Contributed Papers 1101, Econometric Society.
    5. Gospodinov, Nikolay, 2008. "Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root," Journal of Econometrics, Elsevier, vol. 146(1), pages 146-161, September.
    6. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    8. Brendan K. Beare, 2018. "Unit Root Testing with Unstable Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 816-835, November.
    9. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, vol. 133(2), pages 421-441, August.
    10. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 609-641.
    11. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    12. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-618, Nov.-Dec..
    13. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
    14. Kim, Kiwhan & Schmidt, Peter, 1993. "Unit root tests with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 59(3), pages 287-300, October.
    15. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(1), pages 29-52, March.
    16. Brandan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Series Working Papers 2008-WO6, University of Oxford, Department of Economics.
    17. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    18. Valkanov, Rossen, 2005. "Functional Central Limit Theorem approximations and the distribution of the Dickey-Fuller test with strongly heteroskedastic data," Economics Letters, Elsevier, vol. 86(3), pages 427-433, March.
    19. 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.
    20. Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
    21. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    22. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
    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, 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.
    2. Reboredo, Juan C., 2012. "Do food and oil prices co-move?," Energy Policy, Elsevier, vol. 49(C), pages 456-467.
    3. 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.

    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. Gospodinov, Nikolay, 2008. "Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root," Journal of Econometrics, Elsevier, vol. 146(1), pages 146-161, September.
    2. W. K. Li & Shiqing Ling & Michael McAleer, 2001. "A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors," ISER Discussion Paper 0545, Institute of Social and Economic Research, Osaka University.
    3. 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.
    4. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1719-1760, December.
    5. Davidson, Russell & MacKinnon, James G., 2007. "Improving the reliability of bootstrap tests with the fast double bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3259-3281, April.
    6. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages 2-18, September.
    7. Alvaro Escribano & J. Ignacio Peña & Pablo Villaplana, 2011. "Modelling Electricity Prices: International Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 622-650, October.
    8. Narayan, Paresh Kumar & Liu, Ruipeng & Westerlund, Joakim, 2016. "A GARCH model for testing market efficiency," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 41(C), pages 121-138.
    9. Andrews, Donald W.K. & Guggenberger, Patrik, 2012. "Asymptotics for LS, GLS, and feasible GLS statistics in an AR(1) model with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 169(2), pages 196-210.
    10. 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.
    11. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Paper 1127, Economics Department, Queen's University.
    12. Nikolaos Kourogenis & Nikitas Pittis, 2008. "Testing for a unit root under errors with just barely infinite variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1066-1087, November.
    13. Xu, Ke-Li, 2012. "Robustifying multivariate trend tests to nonstationary volatility," Journal of Econometrics, Elsevier, vol. 169(2), pages 147-154.
    14. Till Strohsal & Enzo Weber, 2014. "Mean-variance cointegration and the expectations hypothesis," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1983-1997, November.
    15. repec:idn:journl:v:1:y:2019:i:sp1:p:1-26 is not listed on IDEAS
    16. Trenkler, Carsten, 2009. "Bootstrapping Systems Cointegration Tests With A Prior Adjustment For Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 25(1), pages 243-269, February.
    17. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Testing for co-integration in vector autoregressions with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 158(1), pages 7-24, September.
    18. Donald W. K. Andrews & Patrik Guggenberger, 2014. "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 376-381, May.
    19. Paulo M.M. Rodrigues & Antonio Rubia, 2004. "On The Small Sample Properties Of Dickey Fuller And Maximum Likelihood Unit Root Tests On Discrete-Sampled Short-Term Interest Rates," Working Papers. Serie AD 2004-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    20. Giuseppe Cavaliere & A. M. Robert Taylor, 2009. "Bootstrap M Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 393-421.
    21. Li, Yushu & Shukur, Ghazi, 2009. "Testing for Unit Root against LSTAR Model: Wavelet Improvement under GARCH Distortion," CAFO Working Papers 2009:6, Linnaeus University, Centre for Labour Market Policy Research (CAFO), School of Business and Economics.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:30:y:2011:i:4:p:379-405. 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.