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Fat tails and asymmetry in financial volatility models

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  • Verhoeven, Peter
  • McAleer, Michael

Abstract

Although the generalised autoregressive conditional heteroskedasticity (GARCH) model has been quite successful in capturing important empirical aspects of financial data, particularly for the symmetric effects of volatility, it has had far less success in capturing the effects of extreme observations, outliers and skewness in returns. This paper examines the GARCH model under various non-normal error distributions in order to evaluate skewness and leptokurtosis. The empirical results show that GARCH models estimated using asymmetric leptokurtic distributions are superior to their counterparts estimated under normality, in terms of: (i) capturing skewness and leptokurtosis; (ii) the maximized log-likelihood values; and (iii) isolating the ARCH and GARCH parameter estimates from the adverse effects of outliers. Overall, the flexible asymmetric Student’s t-distribution performs best in capturing the non-normal aspects of the data.

Suggested Citation

  • Verhoeven, Peter & McAleer, Michael, 2004. "Fat tails and asymmetry in financial volatility models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(3), pages 351-361.
  • Handle: RePEc:eee:matcom:v:64:y:2004:i:3:p:351-361 DOI: 10.1016/S0378-4754(03)00101-0
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    Cited by:

    1. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, pages 46-78.
    2. Fang, WenShwo & Miller, Stephen M., 2009. "Modeling the volatility of real GDP growth: The case of Japan revisited," Japan and the World Economy, Elsevier, pages 312-324.
    3. repec:spr:comaot:v:23:y:2017:i:3:d:10.1007_s10588-016-9231-3 is not listed on IDEAS
    4. Zhao, Xin & Scarrott, Carl John & Oxley, Les & Reale, Marco, 2011. "GARCH dependence in extreme value models with Bayesian inference," Mathematics and Computers in Simulation (MATCOM), Elsevier, pages 1430-1440.
    5. Yuichi Nagahara, 2008. "A Method of Calculating the Downside Risk by Multivariate Nonnormal Distributions," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, pages 175-184.
    6. Hayette Gatfaoui, 2010. "Investigating the dependence structure between credit default swap spreads and the U.S. financial market," Annals of Finance, Springer, pages 511-535.
    7. Ke Zhu & Wai Keung Li, 2015. "A New Pearson-Type QMLE for Conditionally Heteroscedastic Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, pages 552-565.
    8. Amélie Charles, 2008. "Forecasting volatility with outliers in GARCH models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(7), pages 551-565.
    9. Meade, Nigel, 2010. "Oil prices -- Brownian motion or mean reversion? A study using a one year ahead density forecast criterion," Energy Economics, Elsevier, pages 1485-1498.
    10. Ke Zhu & Wai Keung Li, 2015. "A New Pearson-Type QMLE for Conditionally Heteroscedastic Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, pages 552-565.
    11. Fang, WenShwo & Miller, Stephen M., 2009. "Modeling the volatility of real GDP growth: The case of Japan revisited," Japan and the World Economy, Elsevier, pages 312-324.
    12. Carlos M. Fernández-Márquez & Francisco Fatas-Villafranca & Francisco J. Vázquez, 2017. "A computational consumer-driven market model: statistical properties and the underlying industry dynamics," Computational and Mathematical Organization Theory, Springer, pages 319-346.
    13. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, pages 259-284.
    14. Del Brio, Esther B. & Perote, Javier, 2012. "Gram–Charlier densities: Maximum likelihood versus the method of moments," Insurance: Mathematics and Economics, Elsevier, pages 531-537.
    15. Hayette Gatfaoui, 2010. "Investigating the dependence structure between credit default swap spreads and the U.S. financial market," Annals of Finance, Springer, pages 511-535.
    16. Javed Farrukh & Podgórski Krzysztof, 2014. "Leverage Effect for Volatility with Generalized Laplace Error," Stochastics and Quality Control, De Gruyter, pages 157-166.
    17. Park, Jeong-Soo, 2005. "A simulation-based hyperparameter selection for quantile estimation of the generalized extreme value distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, pages 227-234.
    18. Gamini Premaratne & Prabhath Jayasinghe, 2005. "Exchange rate exposure of stock returns at firm level," International Finance 0503004, EconWPA.
    19. Gatfaoui, Hayette, 2013. "Translating financial integration into correlation risk: A weekly reporting's viewpoint for the volatility behavior of stock markets," Economic Modelling, Elsevier, vol. 30(C), pages 776-791.
    20. repec:eee:ecmode:v:64:y:2017:i:c:p:48-59 is not listed on IDEAS

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