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Kurtosis analysis in GARCH models with Gram–Charlier-like innovations

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  • Vacca, Gianmarco
  • Zoia, Maria Grazia

Abstract

The approach based on polynomially-modified distributions, known as Gram–Charlier-like (GCl) expansions, has been proven effective to account for both excess kurtosis and skewness of financial data. In this paper, we examine GARCH models with innovations distributed as GCl expansions (GC-GARCH). The kurtosis gluts ascribable to both time-varying volatility and GCl distributed GARCH innovations is evaluated. Furthermore, a “kurtosis targeting” approach is devised to estimate the kurtosis of GCl innovations. This leads to GC-GARCH models tailored to fit the kurtosis requirements of financial data.

Suggested Citation

  • Vacca, Gianmarco & Zoia, Maria Grazia, 2019. "Kurtosis analysis in GARCH models with Gram–Charlier-like innovations," Economics Letters, Elsevier, vol. 183(C), pages 1-1.
    • Handle: RePEc:eee:ecolet:v:183:y:2019:i:c:33
    DOI: 10.1016/j.econlet.2019.108552
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    References listed on IDEAS

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    1. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    2. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
    3. Luca Bagnato & Valerio Potì & Maria Zoia, 2015. "The role of orthogonal polynomials in adjusting hyperpolic secant and logistic distributions to analyse financial asset returns," Statistical Papers, Springer, vol. 56(4), pages 1205-1234, November.
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    Cited by:

    1. Vacca, Gianmarco & Zoia, Maria Grazia & Bagnato, Luca, 2022. "Forecasting in GARCH models with polynomially modified innovations," International Journal of Forecasting, Elsevier, vol. 38(1), pages 117-141.
    2. Quatto, Piero & Vacca, Gianmarco & Zoia, Maria Grazia, 2021. "A new copula for modeling portfolios with skewed, leptokurtic and high-order dependent risk factors," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).

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    More about this item

    Keywords

    Orthogonal polynomials; GARCH model; Gram–Charlier-like expansions; Kurtosis;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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