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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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Author Info
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)

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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 < 1. The former has the usual unit root distribution and the latter is a functional of a bivariate Brownian motion, as in Ling and Li (1998). Several unit root tests based on LS estimators, ML estima-tors, and mixing LS and ML estimators, are constructed. Simulation results show that tests based on mixing LS and ML estimators perform better than Dickey-Fuller tests which are based on LS estimators, and that tests based on the ML estimators perform better than the mixed estimators.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-207.

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Length: 30 pages
Date of creation: Mar 2003
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Handle: RePEc:tky:fseres:2003cf207

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  2. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation, Yale University, revised Aug 1988. [Downloadable!]
  3. 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. [Downloadable!]
  4. Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Blackwell Publishing, vol. 16(3), pages 245-69, July. [Downloadable!] (restricted)
  5. Kim, Kiwhan & Schmidt, Peter, 1993. "Unit root tests with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 59(3), pages 287-300, October. [Downloadable!] (restricted)
  6. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July. [Downloadable!] (restricted)
  7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  8. 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(01), pages 129-153, March. [Downloadable!]
  9. repec:cup:etheor:v:12:y:1996:i:1:p:129-53 is not listed on IDEAS
  10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  11. Shin, Dong Wan & So, Beong Soo, 1999. "Unit Root Tests Based On Adaptive Maximum Likelihood Estimation," Econometric Theory, Cambridge University Press, vol. 15(01), pages 1-23, February. [Downloadable!]
  12. Bruce E. Hansen, 1995. "Rethinking the Univariate Approach to Unit Root Testing: Using Covariates to Increase Power," Boston College Working Papers in Economics 300., Boston College Department of Economics.
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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," Econometrics 0405004, EconWPA. [Downloadable!]
    Other versions:
  2. 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. [Downloadable!]
  3. Marco Barassi, 2005. "On KPSS with GARCH errors," Economics Bulletin, Economics Bulletin, vol. 3(55), pages 1-12. [Downloadable!]
  4. Li, Yushu & Shukur, Ghazi, 2009. "Testing for Unit Root against LSTAR Model: Wavelet Improvement under GARCH Distortion," CAFO Working Papers 2009:6, Centre for Labour Market Policy Research (CAFO), School of Management and Economics, Växjö University. [Downloadable!]
  5. Chor-yiu SIN, 2004. "Estimation and Testing for Partially Nonstationary Vector Autoregressive Models with GARCH: WLS versus QMLE," Econometric Society 2004 Australasian Meetings 92, Econometric Society. [Downloadable!]
  6. Lucchetti, Riccardo & Palomba, Giulio, 2008. "Nonlinear Adjustment in US Bond Yields: an Empirical Analysis with Conditional Heteroskedasticity," MPRA Paper 11571, University Library of Munich, Germany. [Downloadable!]
  7. Chor-yiu SIN, 2004. "Estimation and Testing for Partially Nonstationary Vector Autoregressive Models with GARCH: WLS versus QMLE," Econometric Society 2004 North American Summer Meetings 476, Econometric Society. [Downloadable!]
  8. Álvaro Escribano & Juan Ignacio Peña & Pablo Villaplana, 2002. "Modeling Electricity Prices: International Evidence," Economics Working Papers we022708, Universidad Carlos III, Departamento de Economía. [Downloadable!]
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