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Diagnosing the distribution of GARCH innovations

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  • Sun, Pengfei
  • Zhou, Chen

Abstract

The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, designed to model volatility clustering, exhibits heavy-tailedness regardless of the distribution of its innovation term. When applying the model to financial time series, the distribution of innovations plays an important role for risk measurement and option pricing. We investigate methods on diagnosing the distribution of GARCH innovations. For GARCH processes that are close to integrated-GARCH (IGARCH), we show that the method based on estimated innovations is not reliable, whereas an alternative approach based on analyzing the tail index of a GARCH series performs better. The alternative method leads to a formal test on the distribution of GARCH innovations.

Suggested Citation

  • Sun, Pengfei & Zhou, Chen, 2014. "Diagnosing the distribution of GARCH innovations," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 287-303.
    • Handle: RePEc:eee:empfin:v:29:y:2014:i:c:p:287-303
    DOI: 10.1016/j.jempfin.2014.08.005
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    9. León, Ángel & Ñíguez, Trino-Manuel, 2020. "Modeling asset returns under time-varying semi-nonparametric distributions," Journal of Banking & Finance, Elsevier, vol. 118(C).
    10. Horváth, Roman & Šopov, Boril, 2016. "GARCH models, tail indexes and error distributions: An empirical investigation," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 1-15.
    11. Herwartz, Helmut, 2017. "Stock return prediction under GARCH — An empirical assessment," International Journal of Forecasting, Elsevier, vol. 33(3), pages 569-580.
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    15. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Effective energy commodity risk management: Econometric modeling of price volatility," Economic Analysis and Policy, Elsevier, vol. 63(C), pages 234-250.
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    19. BenSaïda, Ahmed, 2015. "The frequency of regime switching in financial market volatility," Journal of Empirical Finance, Elsevier, vol. 32(C), pages 63-79.

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    More about this item

    Keywords

    GARCH(1; 1); Extreme value theory; Hill estimator; Dynamic risk management;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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