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Multivariate normal mixture GARCH

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

Abstract

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. --

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Bibliographic Info

Paper provided by Center for Financial Studies (CFS) in its series CFS Working Paper Series with number 2006/09.

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Date of creation: 2006
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Handle: RePEc:zbw:cfswop:200609

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Related research

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

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References

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. 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.
  3. 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.
  4. BAUWENS, Luc & LAURENT, Sébastien, . "A new class of multivariate skew densities, with application to generalized autoregressive conditional heteroscedasticity models," CORE Discussion Papers RP -1793, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  6. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-16, July.
  7. 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 116-31, February.
  8. 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.
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Citations

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Cited by:
  1. 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.
  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. 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.
  4. Giorgio Canarella & Stephen M. Miller & Stephen K. Pollard, 2009. "Dynamic Stock Market Interactions between the Canadian, Mexican, and the United States Markets: The NAFTA Experience," Working Papers 0905, University of Nevada, Las Vegas , Department of Economics.

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