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Mixed Exponential Power Asymmetric Conditional Heteroskedasticity

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  • Rombouts Jeroen V. K.

    () (HEC Montreal)

  • Bouaddi Mohammed

    () (HEC Montreal)

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 weak 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 stationary. 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 stationary processes. Results on NASDAQ index returns are similar.

Suggested Citation

  • Rombouts Jeroen V. K. & Bouaddi Mohammed, 2009. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-32, May.
  • Handle: RePEc:bpj:sndecm:v:13:y:2009:i:3:n:3
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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. 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.
    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. 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.

    More about this item

    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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