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Stable Mixture GARCH Models

Author

Listed:
  • Simon A. BRODA

    (University of Amsterdam)

  • Markus HAAS

    (University of Munich)

  • Jochen KRAUSE

    (University of Zurich)

  • Marc S. PAOLELLA

    (University of Zurich and Swiss Finance Insitute)

  • Sven C. STEUDE

    (University of Zurich)

Abstract

A new model class for univariate asset returns is proposed which involves the use of mixtures of stable Paretian distributions, and readily lends itself to use in a multivariate context for portfolio selection. The model nests numerous ones currently in use, and is shown to outperform all its special cases. In particular, an extensive out-of-sample risk forecasting exercise for seven major FX and equity indices confirms the superiority of the general model compared to its special cases and other competitors. An improved method (in terms of speed and accuracy) is developed for the computation of the stable Paretian density. Estimation issues related to problems associated with mixture models are discussed, and a new, general, method is proposed to successfully circumvent these. Because of the tractability of the stable Paretian characteristic function, the model is straight forwardly extended to support portfolio selection using expected shortfall as the downside risk measure by using an independent component analysis framework.

Suggested Citation

  • Simon A. BRODA & Markus HAAS & Jochen KRAUSE & Marc S. PAOLELLA & Sven C. STEUDE, 2011. "Stable Mixture GARCH Models," Swiss Finance Institute Research Paper Series 11-39, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1139
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    Cited by:

    1. Tsionas, Mike G., 2016. "Bayesian analysis of multivariate stable distributions using one-dimensional projections," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 185-193.
    2. Budanova, Sofya, 2025. "Penalized estimation of finite mixture models," Journal of Econometrics, Elsevier, vol. 249(PB).
    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. Frederik Krabbe, 2024. "Asymptotic Properties of the Maximum Likelihood Estimator for Markov-switching Observation-driven Models," Papers 2412.19555, arXiv.org, revised Dec 2025.
    5. Gong, Xu & Wen, Fenghua & Xia, X.H. & Huang, Jianbai & Pan, Bin, 2017. "Investigating the risk-return trade-off for crude oil futures using high-frequency data," Applied Energy, Elsevier, vol. 196(C), pages 152-161.
    6. Ausloos, Marcel & Jovanovic, Franck & Schinckus, Christophe, 2016. "On the “usual” misunderstandings between econophysics and finance: Some clarifications on modelling approaches and efficient market hypothesis," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 7-14.
    7. Mike G. Tsionas & Nicholas Apergis, 2023. "Another look at contagion across United States and European financial markets: Evidence from the credit default swaps markets," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(1), pages 1137-1155, January.
    8. Kai Yang & Qingqing Zhang & Xinyang Yu & Xiaogang Dong, 2023. "Bayesian inference for a mixture double autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 188-207, May.
    9. Jovanovic, Franck & Schinckus, Christophe, 2016. "Breaking down the barriers between econophysics and financial economics," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 256-266.
    10. Schinckus, Christophe, 2015. "Positivism in finance and its implication for the diversification finance research," International Review of Financial Analysis, Elsevier, vol. 40(C), pages 103-106.
    11. 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.
    12. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    13. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute.
    14. Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Time-varying mixture GARCH models and asymmetric volatility," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 602-623.
    15. Paolella, Marc S., 2017. "Asymmetric stable Paretian distribution testing," Econometrics and Statistics, Elsevier, vol. 1(C), pages 19-39.
    16. Salhi, Khaled & Deaconu, Madalina & Lejay, Antoine & Champagnat, Nicolas & Navet, Nicolas, 2016. "Regime switching model for financial data: Empirical risk analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 148-157.
    17. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci De Magistris, 2014. "Chasing Volatility. A Persistent Multiplicative Error Model With Jumps," "Marco Fanno" Working Papers 0186, Dipartimento di Scienze Economiche "Marco Fanno".
    18. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    19. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    20. Slim, Skander & Koubaa, Yosra & BenSaïda, Ahmed, 2017. "Value-at-Risk under Lévy GARCH models: Evidence from global stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 30-53.
    21. Haas, Markus & Liu, Ji-Chun, 2015. "Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112855, Verein für Socialpolitik / German Economic Association.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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