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Joint maximum likelihood estimation of unit root testing equations and GARCH processes: Some finite-sample issues

  • Cook, Steven
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    In recent research [B. Seo, Distribution theory for unit root tests with conditional heteroskedasticity, J. Econometrics 91 (1999) 113–144] has suggested that the examination of the unit root hypothesis in series exhibiting GARCH behaviour should proceed via joint maximum likelihood (ML) estimation of the unit root testing equation and GARCH process. The results presented show the asymptotic distribution of the resulting ML t-test to be a mixture of the Dickey–Fuller and standard normal distributions. In this paper, the relevance of these asymptotic arguments is considered for the finite samples encountered in empirical research. In particular, the influences of sample size, alternative values of the parameters of the GARCH process and the use of the Bollerslev–Wooldridge covariance matrix estimator upon the finite-sample distribution of the ML t-statistic are explored. It is shown that the resulting critical values for the ML t-statistic are similar to those of the Dickey–Fuller distribution rather than the standard normal, unless a large sample size and empirically unrealistic values of the volatility parameter of the GARCH process are considered. Use of the Bollerslev–Wooldridge standard covariance matrix estimator exaggerates this finding, causing a leftward shift in the finite-sample distribution of the ML t-statistic. The results of the simulation analysis are illustrated via an application to U.S. short term interest rates.

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    Article provided by Elsevier in its journal Mathematics and Computers in Simulation (MATCOM).

    Volume (Year): 77 (2008)
    Issue (Month): 1 ()
    Pages: 109-116

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    Handle: RePEc:eee:matcom:v:77:y:2008:i:1:p:109-116
    Contact details of provider: Web page: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/

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    1. 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 245-69, July.
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    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," CIRJE F-Series CIRJE-F-207, CIRJE, Faculty of Economics, University of Tokyo.
    4. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    5. Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
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    7. Enders, Walter & Granger, C. W. J., 1998. "Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Staff General Research Papers 1388, Iowa State University, Department of Economics.
    8. Steven Cook & Neil Manning, 2003. "The power of asymmetric unit root tests under threshold and consistent-threshold estimation," Applied Economics, Taylor & Francis Journals, vol. 35(14), pages 1543-1550.
    9. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
    10. 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.
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    22. 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.
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