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Testing the existence of moments and estimating the tail index of augmented garch processes

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  • Francq, Christian
  • Zakoian, Jean-Michel

Abstract

We investigate the problem of testing finiteness of moments for a class of semi-parametric augmented GARCH models encompassing most commonly used specifications. The existence of positive-power moments of the strictly stationary solution is characterized through the Moment Generating Function (MGF) of the model, defined as the MGF of the logarithm of the random autoregressive coefficient in the volatility dynamics. We establish the asymptotic distribution of the empirical MGF, from which tests of moments are deduced. Alternative tests relying on the estimation of the Maximal Moment Exponent (MME) are studied. Power comparisons based on local alternatives and the Bahadur approach are proposed. We provide an illustration on real financial data, showing that semi-parametric estimation of the MME offers an interesting alternative to Hill's nonparametric estimator of the tail index.

Suggested Citation

  • Francq, Christian & Zakoian, Jean-Michel, 2021. "Testing the existence of moments and estimating the tail index of augmented garch processes," MPRA Paper 110511, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:110511
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    References listed on IDEAS

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    1. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024, September.
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    6. Zhang, Rongmao & Ling, Shiqing, 2015. "Asymptotic Inference For Ar Models With Heavy-Tailed G-Garch Noises," Econometric Theory, Cambridge University Press, vol. 31(4), pages 880-890, August.
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    Cited by:

    1. Christian Francq & Baye Matar Kandji & Jean-Michel Zakoian, 2022. "Inference on Multiplicative Component GARCH without any Small-Order Moment," Working Papers 2022-09, Center for Research in Economics and Statistics.
    2. David I. Harvey & Stephen J. Leybourne & Yang Zu, 2023. "Estimation of the variance function in structural break autoregressive models with non‐stationary and explosive segments," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 181-205, March.

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    More about this item

    Keywords

    APARCH model; Bahadur slopes; Hill's estimator; Local asymptotic power; Maximal moment exponent; Moment generating function;
    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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