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Unit Root Testing with Unstable Volatility

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Author Info
Brendan K. Beare () (Nuffield College, Oxford University)
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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Publisher Info
Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2008-W06.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
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/

For technical questions regarding this item, or to correct its listing, contact: (Maxine Collett).

Related research
Keywords: unit root; heteroskedasticity; nonstationary volatility.;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
    Other versions:
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  3. Phillips, Peter C B & Xiao, Zhijie, 1998. " A Primer on Unit Root Testing," Journal of Economic Surveys, Blackwell Publishing, vol. 12(5), pages 423-69, December. [Downloadable!] (restricted)
    Other versions:
  4. Peter C. B. Phillips & Ke-Li Xu, 2006. "Inference in Autoregression under Heteroskedasticity," Journal of Time Series Analysis, Blackwell Publishing, vol. 27(2), pages 289-308, 03. [Downloadable!] (restricted)
  5. Perron, Pierre & Ng, Serena, 1996. "Useful Modifications to Some Unit Root Tests with Dependent Errors and Their Local Asymptotic Properties," Review of Economic Studies, Blackwell Publishing, vol. 63(3), pages 435-63, July. [Downloadable!] (restricted)
    Other versions:
  6. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-36, July. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
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  8. Giuseppe Cavaliere & A. M. Robert Taylor, 2008. "Time-Transformed Unit Root Tests for Models with Non-Stationary Volatility," Journal of Time Series Analysis, Blackwell Publishing, vol. 29(2), pages 300-330, 03. [Downloadable!] (restricted)
  9. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 24(01), pages 43-71, February. [Downloadable!]
  10. Kim, Tae-Hwan & Leybourne, Stephen & Newbold, Paul, 2002. "Unit root tests with a break in innovation variance," Journal of Econometrics, Elsevier, vol. 109(2), pages 365-387, August. [Downloadable!] (restricted)
  11. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2009. "Heteroskedastic Time Series With A Unit Root," Econometric Theory, Cambridge University Press, vol. 25(05), pages 1228-1276, October. [Downloadable!]
  12. Giuseppe Cavaliere, 2003. "Unit root tests under time-varyng variances," Quaderni di Dipartimento 2, Department of Statistics, University of Bologna. [Downloadable!]
  13. 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, vol. 54(3), pages 257-87, August.
  14. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September. [Downloadable!] (restricted)
  15. Hamori, Shigeyuki & Tokihisa, Akira, 1997. "Testing for a unit root in the presence of a variance shift1," Economics Letters, Elsevier, vol. 57(3), pages 245-253, December. [Downloadable!] (restricted)
  16. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October. [Downloadable!] (restricted)
  17. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January. [Downloadable!] (restricted)
    Other versions:
  18. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June. [Downloadable!]
  19. H. Peter Boswijk, 2001. "Testing for a Unit Root with Near-Integrated Volatility," Tinbergen Institute Discussion Papers 01-077/4, Tinbergen Institute. [Downloadable!]
    Other versions:
  20. repec:cup:etheor:v:24:y:2007:i:01:p:43-71 is not listed on IDEAS
  21. de Jong, Robert M., 2000. "A Strong Consistency Proof For Heteroskedasticity And Autocorrelation Consistent Covariance Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 16(02), pages 262-268, April. [Downloadable!]
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