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A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors

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  • W. K. Li
  • Shiqing Ling
  • Michael McAleer

Abstract

This paper provides a review of some recent theoretical results for time series models with GARCH errors, and is directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for stationary and nonstationary ARMA-GARCH are summarized. Various new ARCH-type models, including double threshold ARCH and GARCH, ARFIMA-GARCH, CHARMA and vector ARMA-GARCH, are also reviewed.

Suggested Citation

  • 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.
  • Handle: RePEc:dpr:wpaper:0545
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    Cited by:

    1. 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," Econometric Reviews, Taylor & Francis Journals, vol. 22(2), pages 179-202.
    2. Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University.
    3. Stavros Degiannakis & Alexandra Livada & Epaminondas Panas, 2008. "Rolling-sampled parameters of ARCH and Levy-stable models," Applied Economics, Taylor & Francis Journals, vol. 40(23), pages 3051-3067.
    4. Verhoeven, Peter & Pilgram, Berndt & McAleer, Michael & Mees, Alistair, 2002. "Non-linear modelling and forecasting of S&P 500 volatility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 59(1), pages 233-241.
    5. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June.
    6. Sandrine Lardic & Valérie Mignon, 2004. "Robert F. Engle et Clive W.J. Granger prix Nobel d'économie 2003," Revue d'économie politique, Dalloz, vol. 114(1), pages 1-15.

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