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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. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
    2. 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.
    3. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
    4. 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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    1. repec:ebl:ecbull:v:3:y:2005:i:55:p:1-12 is not listed on IDEAS
    2. Narayan, Paresh Kumar & Liu, Ruipeng & Westerlund, Joakim, 2016. "A GARCH model for testing market efficiency," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 41(C), pages 121-138.
    3. Lucchetti, Riccardo & Palomba, Giulio, 2009. "Nonlinear adjustment in US bond yields: An empirical model with conditional heteroskedasticity," Economic Modelling, Elsevier, vol. 26(3), pages 659-667, May.
    4. 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.
    5. Westerlund, Joakim, 2014. "On the choice of test for a unit root when the errors are conditionally heteroskedastic," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 40-53.
    6. Nikolaos Kourogenis & Nikitas Pittis, 2008. "Testing for a unit root under errors with just barely infinite variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1066-1087, November.
    7. Riccardo LUCCHETTI & Giulio PALOMBA, 2006. "Forecasting US bond yields at weekly frequency," Working Papers 261, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    8. Paulo M.M. Rodrigues & Antonio Rubia, 2004. "On The Small Sample Properties Of Dickey Fuller And Maximum Likelihood Unit Root Tests On Discrete-Sampled Short-Term Interest Rates," Working Papers. Serie AD 2004-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    9. Neil Kellard & Denise Osborn & Jerry Coakley & Christian Conrad & Menelaos Karanasos, 2015. "On the Transmission of Memory in Garch-in-Mean Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 706-720, September.
    10. Matei Demetrescu & Christoph Hanck, 2013. "Nonlinear IV panel unit root testing under structural breaks in the error variance," Statistical Papers, Springer, vol. 54(4), pages 1043-1066, November.
    11. Wang, Gaowen, 2006. "A note on unit root tests with heavy-tailed GARCH errors," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1075-1079, May.
    12. Gospodinov, Nikolay, 2008. "Asymptotic and bootstrap tests for linearity in a TAR-GARCH(1,1) model with a unit root," Journal of Econometrics, Elsevier, vol. 146(1), pages 146-161, September.
    13. Till Strohsal & Enzo Weber, 2014. "Mean-variance cointegration and the expectations hypothesis," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1983-1997, November.
    14. Berkes, István & Hörmann, Siegfried & Horváth, Lajos, 2008. "The functional central limit theorem for a family of GARCH observations with applications," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2725-2730, November.
    15. Matei Demetrescu, 2010. "On the Dickey–Fuller test with White standard errors," Statistical Papers, Springer, vol. 51(1), pages 11-25, January.
    16. 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.
    17. 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.
    18. Ploberger, Werner & Phillips, Peter C.B., 2012. "Optimal estimation under nonstandard conditions," Journal of Econometrics, Elsevier, vol. 169(2), pages 258-265.
    19. Salisu, Afees A. & Adeleke, Adegoke I., 2016. "Further application of Narayan and Liu (2015) unit root model for trending time series," Economic Modelling, Elsevier, vol. 55(C), pages 305-314.
    20. Ho, Kin-Yip & Shi, Yanlin & Zhang, Zhaoyong, 2013. "How does news sentiment impact asset volatility? Evidence from long memory and regime-switching approaches," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 436-456.
    21. 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.

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