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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
  • W. K. Li
  • Michael McAleer

Abstract

Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition alpha + beta

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Paper provided by Institute of Social and Economic Research, Osaka University in its series ISER Discussion Paper with number 0544.

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Date of creation: Jun 2001
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Handle: RePEc:dpr:wpaper:0544

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  1. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 473-95, August.
  2. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  3. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
  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.
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Cited by:
  1. Werner Ploberger & Peter C.B. Phillips, 2010. "Optimal Estimation under Nonstandard Conditions," Cowles Foundation Discussion Papers 1748, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. 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.
  4. 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.
  5. Matei Demetrescu, 2010. "On the Dickey–Fuller test with White standard errors," Statistical Papers, Springer, vol. 51(1), pages 11-25, January.
  6. 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.
  7. 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.
  8. 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.
  9. repec:ebl:ecbull:v:3:y:2005:i:55:p:1-12 is not listed on IDEAS
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.

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