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Two EGARCH models and one fat tail

Author

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  • Michele Caivano

    (Bank of Italy)

  • Andrew Harvey

    (University of Cambridge)

Abstract

We compare two EGARCH models, which belong to a new class of models in which the dynamics are driven by the score of the conditional distribution of the observations. Models of this kind are called dynamic conditional score (DCS) models and their form facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum likelihood estimator. The EGB2 distribution is light-tailed, but with a higher kurtosis than the normal distribution. Hence it is complementary to the fat-tailed t. The EGB2-EGARCH model gives a good fit to many exchange rate return series, prompting an investigation into the misleading conclusions liable to be drawn from tail index estimates.

Suggested Citation

  • Michele Caivano & Andrew Harvey, 2014. "Two EGARCH models and one fat tail," Temi di discussione (Economic working papers) 954, Bank of Italy, Economic Research and International Relations Area.
    • Handle: RePEc:bdi:wptemi:td_954_14
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    References listed on IDEAS

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    3. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024.
    4. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    5. Matteo Luciani & Libero Monteforte, 2012. "Uncertainty and Heterogeneity in factor models forecasting," Working Papers 5, Department of the Treasury, Ministry of the Economy and of Finance.
    6. Harvey, Andrew & Sucarrat, Genaro, 2014. "EGARCH models with fat tails, skewness and leverage," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 320-338.
    7. Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-216, April.
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    9. Gabaix, Xavier & Ibragimov, Rustam, 2011. "Rank − 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 24-39.
    10. Michele Caivano & Andrew Harvey, 2014. "Time-series models with an EGB2 conditional distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 558-571, November.
    11. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    12. Ibragimov, Marat & Ibragimov, Rustam & Kattuman, Paul, 2013. "Emerging markets and heavy tails," Journal of Banking & Finance, Elsevier, vol. 37(7), pages 2546-2559.
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    Cited by:

    1. Giuseppe Ferrero & Marcello Miccoli & Sergio Santoro, 2014. "Informational Effects of Monetary Policy," Temi di discussione (Economic working papers) 982, Bank of Italy, Economic Research and International Relations Area.
    2. Taneli M�kinen, 2014. "Informed trading and stock market efficiency," Temi di discussione (Economic working papers) 992, Bank of Italy, Economic Research and International Relations Area.
    3. Andres, Philipp, 2014. "Maximum likelihood estimates for positive valued dynamic score models; The DySco package," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 34-42.

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    More about this item

    Keywords

    exchange rates; heavy tails; Hill�s estimator; score; robustness; EGB2; Student�s t; tail index;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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