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Multivariate normal mixture GARCH


  • Haas, Markus
  • Mittnik, Stefan
  • Paolella, Marc S.


We present a multivariate generalization of the mixed normal GARCH model proposed in Haas, Mittnik, and Paolella (2004a). Issues of parametrization and estimation are discussed. We derive conditions for covariance stationarity and the existence of the fourth moment, and provide expressions for the dynamic correlation structure of the process. These results are also applicable to the single-component multivariate GARCH(p, q) model and simplify the results existing in the literature. In an application to stock returns, we show that the disaggregation of the conditional (co)variance process generated by our model provides substantial intuition, and we highlight a number of findings with potential significance for portfolio selection and further financial applications, such as regime-dependent correlation structures and leverage effects.

Suggested Citation

  • Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2006. "Multivariate normal mixture GARCH," CFS Working Paper Series 2006/09, Center for Financial Studies (CFS).
  • Handle: RePEc:zbw:cfswop:200609

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    References listed on IDEAS

    1. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    4. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
    5. Bauwens, Luc & Laurent, Sebastien, 2005. "A New Class of Multivariate Skew Densities, With Application to Generalized Autoregressive Conditional Heteroscedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 346-354, July.
    6. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    7. Campbell, Rachel & Koedijk, Kees & Kofman, Paul, 2002. "Increased Correlation in Bear markets: A Downside Risk Perspective," CEPR Discussion Papers 3172, C.E.P.R. Discussion Papers.
    8. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 319-342.
    9. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
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    Cited by:

    1. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2009. "Asymmetric multivariate normal mixture GARCH," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2129-2154, April.
    2. Haas, Markus & Mittnik, Stefan, 2008. "Multivariate regimeswitching GARCH with an application to international stock markets," CFS Working Paper Series 2008/08, Center for Financial Studies (CFS).
    3. Giorgio Canarella & Stephen M. Miller & Stephen K. Pollard, 2008. "Dynamic Stock Market Interactions between the Canadian, Mexican, and the United States Markets: The NAFTA Experience," Working papers 2008-49, University of Connecticut, Department of Economics.
    4. Chung, Sang-Kuck, 2009. "Bivariate mixed normal GARCH models and out-of-sample hedge performances," Finance Research Letters, Elsevier, vol. 6(3), pages 130-137, September.

    More about this item


    Conditional Volatility; Regime-dependent Correlations; Leverage Effect; Multivariate GARCH; Second-order Dependence;

    JEL classification:

    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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