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Unit Root Testing with Unstable Volatility

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  • Brendan K. Beare

    ()
    (Nuffield College, Oxford University)

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    Abstract

    It is known that unit root test statistics may not have the usual asymptotic properties when the variance of innovations is unstable. In particular, persistent changes in volatility can cause the size of unit root tests to differ from the nominal level. In this paper we propose a class of modified unit root test statistics that are robust to the presence of unstable volatility. The modification is achieved by purging heteroskedasticity from the data using a kernel estimate of volatility prior to the application of standard tests. In the absence of deterministic trend components, this approach delivers test statistics that achieve standard asymptotics under the null hypothesis of a unit root. When the data are homoskedastic, the local power of unit root tests is unchanged by our modification. We use Monte Carlo simulations to compare the finite sample performance of our modified tests with that of existing methods of correcting for unstable volatility.

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    File URL: http://www.nuffield.ox.ac.uk/economics/papers/2008/w6/unitroot.pdf
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    Bibliographic Info

    Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2008-W06.

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    Length: 34 pages
    Date of creation: 05 May 2008
    Date of revision:
    Handle: RePEc:nuf:econwp:0806

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    Web page: http://www.nuff.ox.ac.uk/economics/

    Related research

    Keywords: unit root; heteroskedasticity; nonstationary volatility.;

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    References

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    1. Peter C. B. Phillips & Ke-Li Xu, 2006. "Inference in Autoregression under Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 27(2), pages 289-308, 03.
    2. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
    3. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(01), pages 43-71, February.
    4. Ke-Li Xu & Peter C.B. Phillips, 2006. "Adaptive Estimation of Autoregressive Models with Time-Varying Variances," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1585R, Cowles Foundation for Research in Economics, Yale University, revised Nov 2006.
    5. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 140(2), pages 919-947, October.
    6. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 12(5), pages 423-69, December.
    7. Perron, P. & Ng, S., 1994. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9427, Universite de Montreal, Departement de sciences economiques.
    8. H. Peter Boswijk, 2001. "Testing for a Unit Root with Near-Integrated Volatility," Tinbergen Institute Discussion Papers, Tinbergen Institute 01-077/4, Tinbergen Institute.
    9. repec:cup:etheor:v:24:y:2007:i:01:p:43-71 is not listed on IDEAS
    10. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2009. "Heteroskedastic Time Series With A Unit Root," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 25(05), pages 1228-1276, October.
    11. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics, Boston College Department of Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
    12. Peter C.B. Phillips & Chin Chin Lee, 1996. "Efficiency Gains from Quasi-Differencing Under Nonstationarity," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1134, Cowles Foundation for Research in Economics, Yale University.
    13. de Jong, Robert M., 2000. "A Strong Consistency Proof For Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimators," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(02), pages 262-268, April.
    14. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
    15. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0130, National Bureau of Economic Research, Inc.
    16. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 11(03), pages 560-586, June.
    17. repec:cup:etheor:v:24:y:2007:i:01:p:43-71_08 is not listed on IDEAS
    18. Giuseppe Cavaliere & A. M. Robert Taylor, 2008. "Time-Transformed Unit Root Tests for Models with Non-Stationary Volatility," Journal of Time Series Analysis, Wiley Blackwell, Wiley Blackwell, vol. 29(2), pages 300-330, 03.
    19. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1113-32, September.
    20. Hamori, Shigeyuki & Tokihisa, Akira, 1997. "Testing for a unit root in the presence of a variance shift1," Economics Letters, Elsevier, Elsevier, vol. 57(3), pages 245-253, December.
    21. Schmidt, Peter & Phillips, C B Peter, 1992. "LM Tests for a Unit Root in the Presence of Deterministic Trends," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, Department of Economics, University of Oxford, vol. 54(3), pages 257-87, August.
    22. Kim, Tae-Hwan & Leybourne, Stephen & Newbold, Paul, 2002. "Unit root tests with a break in innovation variance," Journal of Econometrics, Elsevier, Elsevier, vol. 109(2), pages 365-387, August.
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    Cited by:
    1. Cavaliere Giuseppe & Phillips Peter C.B. & Smeekes Stephan & Taylor A.M. Robert, 2011. "Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 056, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. Xu, Ke-Li, 2012. "Robustifying multivariate trend tests to nonstationary volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 169(2), pages 147-154.

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