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GARCH Models, Tail Indexes and Error Distributions: An Empirical Investigation

Author

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  • Roman Horváth

    (Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Smetanovo nábreží 6, 111 01 Prague 1, Czech Republic
    Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodarenskou Vezi 4, 182 00, Prague, Czech Republic)

  • Boril Sopov

    (Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Smetanovo nábreží 6, 111 01 Prague 1, Czech Republic)

Abstract

We perform a large simulation study to examine the extent to which various generalized autoregressive conditional heteroskedasticity (GARCH) models capture extreme events in stock market returns. We estimate Hill's tail indexes for individual S&P 500 stock market returns ranging from 1995{2014. and compare these to the tail indexes produced by simulating GARCH models. Our results suggest that actual and simulated values differ greatly for GARCH models with normal conditional distributions, which underestimate the tail risk. By contrast, the GARCH models with Student's t conditional distributions capture the tail shape more accurately, with GARCH and GJR-GARCH being the top performers.

Suggested Citation

  • Roman Horváth & Boril Sopov, 2015. "GARCH Models, Tail Indexes and Error Distributions: An Empirical Investigation," Working Papers IES 2015/09, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised May 2015.
    • Handle: RePEc:fau:wpaper:wp2015_09
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    Cited by:

    1. Georgios Bampinas & Konstantinos Ladopoulos & Theodore Panagiotidis, 2018. "A note on the estimated GARCH coefficients from the S&P1500 universe," Applied Economics, Taylor & Francis Journals, vol. 50(34-35), pages 3647-3653, July.
    2. Guo, Xu & McAleer, Michael & Wong, Wing-Keung & Zhu, Lixing, 2017. "A Bayesian approach to excess volatility, short-term underreaction and long-term overreaction during financial crises," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 346-358.
    3. Damek, Ewa & Matsui, Muneya, 2022. "Tails of bivariate stochastic recurrence equation with triangular matrices," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 147-191.

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    More about this item

    Keywords

    GARCH; extreme events; S&P 500 study; tail index;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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