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A note on unit root tests with heavy-tailed GARCH errors

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  • Wang, Gaowen
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    Abstract

    In this paper, we derive the asymptotic distributions of Dickey-Fuller tests for unit root processes with GARCH(1,1) errors when the fourth moment condition is not satisfied. Particularly, the fourth moment condition on the scaled conditional errors is weakened.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4HXBGRB-1/2/2d6451eea5cf16c6d21f3e083385ab16
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 76 (2006)
    Issue (Month): 10 (May)
    Pages: 1075-1079

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    Handle: RePEc:eee:stapro:v:76:y:2006:i:10:p:1075-1079

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    Related research

    Keywords: Heavy-tailed GARCH Self-normalized sums Domain of attraction of the normal law;

    References

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Shiqing Ling & W. K. Li & Michael McAleer, 2001. "Estimation and Testing for Unit Root Processes with GARCH(1,1) Errors: Theory and Monte Carlo Evidence," ISER Discussion Paper 0544, Institute of Social and Economic Research, Osaka University.
    3. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
    4. Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, vol. 19(04), pages 541-564, August.
    5. Shiqing Ling, 2004. "Estimation and testing stationarity for double-autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78.
    6. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
    7. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    9. 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.
    10. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
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