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Empirical Performance of GARCH Models with Heavy-tailed Innovations

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  • Guo, Zi-Yi

Abstract

We introduce a new type of heavy-tailed distribution, the normal reciprocal inverse Gaussian distribution (NRIG), to the GARCH and Glosten-Jagannathan-Runkle (1993) GARCH models, and compare its empirical performance with two other popular types of heavy-tailed distribution, the Student’s t distribution and the normal inverse Gaussian distribution (NIG), using a variety of asset return series. Our results illustrate that there is no overwhelmingly dominant distribution in fitting the data under the GARCH framework, although the NRIG distribution performs slightly better than the other two types of distribution. For market indexes series, it is important to introduce both GJR-terms and the NRIG distribution to improve the models’ performance, but it is ambiguous for individual stock prices series. Our results also show the GJR-GARCH NRIG model has practical advantages in quantitative risk management. Finally, the convergence of numerical solutions in maximum-likelihood estimation of GARCH and GJR-GARCH models with the three types of heavy-tailed distribution is investigated.

Suggested Citation

  • Guo, Zi-Yi, 2017. "Empirical Performance of GARCH Models with Heavy-tailed Innovations," EconStor Preprints 167626, ZBW - Leibniz Information Centre for Economics.
    • Handle: RePEc:zbw:esprep:167626
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    Cited by:

    1. Guo, Zi-Yi, 2017. "Comparison of Error Correction Models and First-Difference Models in CCAR Deposits Modeling," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 17(4).
    2. Zi-Yi Guo, 2017. "Heavy-tailed Distributions and Risk Management of Equity Market Tail Events," Journal of Risk & Control, Risk Market Journals, vol. 4(1), pages 31-41.
    3. Kengo Kayaba & Yui Hirano & Naoki Ueda & Nobuki Matsui, 2018. "An investigation of fat-tailed distributions in fitting the Japanese stock market returns," International Journal of Finance, Insurance and Risk Management, International Journal of Finance, Insurance and Risk Management, vol. 8(2), pages 1399-1399.
    4. Guo, Zi-Yi, 2017. "Models with Short-Term Variations and Long-Term Dynamics in Risk Management of Commodity Derivatives," EconStor Preprints 167619, ZBW - Leibniz Information Centre for Economics.
    5. Yoon Hong & Ji-chul Lee & Guoping Ding, 2017. "Volatility Clustering, New Heavy-Tailed Distribution and the Stock Market Returns in South Korea," Journal of Applied Management and Investments, Department of Business Administration and Corporate Security, International Humanitarian University, vol. 6(3), pages 164-169, September.
    6. Guo, Zi-Yi, 2017. "Martingale Regressions for a Continuous Time Model of Exchange Rates," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 12(2), pages 40-45.
    7. Michael Day & Mark Diamond & Jeff Card & Jake Hurd & Jianping Xu, 2017. "GARCH model and fat tails of the Chinese stock market returns - New evidences," Journal of Risk & Control, Risk Market Journals, vol. 4(1), pages 43-49.

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    Keywords

    Heavy-tailed distribution; GARCH model; Model comparison; Numerical solution;
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