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The robustness of modified unit root tests in the presence of GARCH


  • Steven Cook


The research of Kim and Schmidt (J. Economet., 1993, 59, 287-300) is extended to examine the properties of modified Dickey-Fuller unit root tests in the presence of generalized autoregressive conditional heteroskedasticity (GARCH). Using Monte Carlo simulation, the properties of the tests are examined for a range of GARCH processes over alternative sample sizes. Oversizing is observed for all tests, with the extent of size distortion driven by the volatility, rather than the persistence, of the underlying GARCH process. While the original Dickey-Fuller test is found to exhibit greater size distortion than the modified tests, the modified tests are found to be substantially oversized when the GARCH process exhibits a high degree of volatility, even for large samples.

Suggested Citation

  • Steven Cook, 2006. "The robustness of modified unit root tests in the presence of GARCH," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 359-363.
  • Handle: RePEc:taf:quantf:v:6:y:2006:i:4:p:359-363 DOI: 10.1080/14697680600702045

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    References listed on IDEAS

    1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-927, July.
    2. Kim, Kiwhan & Schmidt, Peter, 1993. "Unit root tests with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 59(3), pages 287-300, October.
    3. Leybourne, S J, 1995. "Testing for Unit Roots Using Forward and Reverse Dickey-Fuller Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 57(4), pages 559-571, November.
    4. Stephen Leybourne & Tae-Hwan Kim & Paul Newbold, 2005. "Examination of Some More Powerful Modifications of the Dickey-Fuller Test," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 355-369, May.
    5. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    6. Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-269, July.
    7. 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.
    8. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    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.
    11. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
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    Cited by:

    1. Georgios P. Kouretas & Mark E. Wohar, 2012. "The dynamics of inflation: a study of a large number of countries," Applied Economics, Taylor & Francis Journals, vol. 44(16), pages 2001-2026, June.
    2. repec:eee:touman:v:31:y:2010:i:6:p:846-854 is not listed on IDEAS
    3. Steven Cook, 2009. "A re-examination of the stationarity of inflation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(6), pages 1047-1053.
    4. Cook, Steven, 2008. "Joint maximum likelihood estimation of unit root testing equations and GARCH processes: Some finite-sample issues," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 109-116.
    5. Li, Yushu & Shukur, Ghazi, 2009. "Testing for Unit Root against LSTAR model – wavelet improvements under GARCH distortion," Working Paper Series in Economics and Institutions of Innovation 184, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    6. Divino, Jose Angelo & McAleer, Michael, 2010. "Modelling and forecasting daily international mass tourism to Peru," Tourism Management, Elsevier, vol. 31(6), pages 846-854.
    7. Giovanni Razzu & Carl Singleton, 2013. "Are Business Cycles Gender Neutral?," Economics & Management Discussion Papers em-dp2013-07, Henley Business School, Reading University.
    8. Hans KREMERS & Andreas LOESCHEL, "undated". "The Strategic Implications of Setting Border Tax Adjustments," EcoMod2010 259600097, EcoMod.

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    GARCH; Unit root tests; Size distortion;


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