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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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    References listed on IDEAS

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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. Degiannakis, Stavros, 2004. "Forecasting Realized Intra-day Volatility and Value at Risk: Evidence from a Fractional Integrated Asymmetric Power ARCH Skewed-t Model," MPRA Paper 80488, University Library of Munich, Germany.
    3. Felix Chan & Dora Marinova & Michael McAleer, 2004. "Trends and volatilities in foreign patents registered in the USA," Applied Economics, Taylor & Francis Journals, vol. 36(6), pages 585-592.
    4. Timotheos Angelidis & Stavros Degiannakis, 2005. "Modeling risk for long and short trading positions," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 6(3), pages 226-238, July.
    5. 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.
    6. Maghyereh Aktham Issa & Awartani Basel, 2012. "Modeling and Forecasting Value-at-Risk in the UAE Stock Markets: The Role of Long Memory, Fat Tails and Asymmetries in Return Innovations," Review of Middle East Economics and Finance, De Gruyter, vol. 8(1), pages 1-22, August.
    7. Eunju Hwang, 2021. "Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations," Mathematics, MDPI, vol. 9(8), pages 1-10, April.
    8. Stavros Degiannakis, 2004. "Volatility forecasting: evidence from a fractional integrated asymmetric power ARCH skewed-t model," Applied Financial Economics, Taylor & Francis Journals, vol. 14(18), pages 1333-1342.
    9. 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.
    10. 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.
    11. 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(3), pages 722-729, June.
    12. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, vol. 140(2), pages 849-873, October.
    13. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    14. 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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