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Mixed Exponential Power Asymmetric Conditional Heteroskedasticity

Author

Listed:
  • Mohammed Bouaddi
  • Jeroen V.K. Rombouts
Abstract
To match the stylized facts of high frequency financial time series precisely and parsimoniously, this paper presents a finite mixture of conditional exponential power distributions where each component exhibits asymmetric conditional heteroskedasticity. We provide stationarity conditions and unconditional moments to the fourth order. We apply this new class to Dow Jones index returns. We find that a two-component mixed exponential power distribution dominates mixed normal distributions with more components, and more parameters, both in-sample and out-of-sample. In contrast to mixed normal distributions, all the conditional variance processes become stationarity. This happens because the mixed exponential power distribution allows for component-specific shape parameters so that it can better capture the tail behaviour. Therefore, the more general new class has attractive features over mixed normal distributions in our application: Less components are necessary and the conditional variances in the components are stationarity processes. Results on NASDAQ index returns are similar.

Suggested Citation

  • Mohammed Bouaddi & Jeroen V.K. Rombouts, 2007. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Cahiers de recherche 0749, CIRPEE.
    • Handle: RePEc:lvl:lacicr:0749
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    References listed on IDEAS

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    Cited by:

    1. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.
    2. Saissi Hassani, Samir & Dionne, Georges, 2023. "Using skewed exponential power mixture for VaR and CVaR forecasts to comply with market risk regulation," Working Papers 23-2, HEC Montreal, Canada Research Chair in Risk Management.
    3. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    4. Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
    5. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    6. Yin-Wong Cheung & Sang-Kuck Chung, 2011. "A Long Memory Model with Normal Mixture GARCH," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 517-539, November.
    7. Mohammed Bouaddi & Khouzeima Moutanabbir, 2022. "Systematic extreme potential gain and loss spillover across countries," Risk Management, Palgrave Macmillan, vol. 24(4), pages 327-366, December.
    8. Zhu, Dongming & Galbraith, John W., 2011. "Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 765-778, September.

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    More about this item

    Keywords

    Finite mixtures; exponential power distributions; conditional heteroskedasticity; asymmetry; heavy tails; value at risk;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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