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Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence

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  • Shiqing Ling

    (Department of Mathematics, Hong Kong University of Science and Technology)

  • W. K. Li

    (Department of Statistics and Actuarial Science, University of Hong Kong)

  • Michael McAleer

    (Department of Economics, University of Western Australia)

Abstract

Least squares (LS) and maximum likelihood (ML) estimation are con-sidered for unit root processes with GARCH (1, 1) errors. The asymp-totic distributions of LS and ML estimators are derived under the con-dition ƒ¿ + ƒÀ

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2003cf207
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    References listed on IDEAS

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    1. Herce, Miguel A., 1996. "Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors," Econometric Theory, Cambridge University Press, vol. 12(1), pages 129-153, March.
    2. W. K. Li & T. K. Mak, 1994. "On The Squared Residual Autocorrelations In Non‐Linear Time Series With Conditional Heteroskedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 627-636, November.
    3. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    4. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    7. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    8. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. W. K. Li & Shiqing Ling & Michael McAleer, 2001. "A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors," ISER Discussion Paper 0545, Institute of Social and Economic Research, Osaka University.
    11. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
    12. Shin, Dong Wan & So, Beong Soo, 1999. "Unit Root Tests Based On Adaptive Maximum Likelihood Estimation," Econometric Theory, Cambridge University Press, vol. 15(1), pages 1-23, February.
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