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Multivariate mixed normal conditional heteroskedasticity

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  • BAUWENS, Luc
  • HAFNER, Christian
  • ROMBOUTS, Jeroen

Abstract

We propose a new multivariate volatility model where the conditional distribution of a vector time series is given by a mixture of multivariate normal distributions. Each of these distributions is allowed to have a time-varying covariance matrix. The process can be globally covariance- stationary even though some components are not covariance-stationary. We derive some theo- retical properties of the model such as the unconditional covariance matrix and autocorrelations of squared returns. The complexity of the model requires a powerful estimation algorithm. In a simulation study we compare estimation by maximum likelihood with the EM algorithm and Bayesian estimation with a Gibbs sampler. Finally, we apply the model to daily U.S. stock returns.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2006012.

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Date of creation: 00 Feb 2006
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Handle: RePEc:cor:louvco:2006012

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Related research

Keywords: multivariate volatility; finite mixture; EM algorithm; Bayesian inference;

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References

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  1. Denis Pelletier, 2004. "Regime Switching for Dynamic Correlations," Econometric Society 2004 North American Summer Meetings 230, Econometric Society.
  2. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," Working Paper 2004-13, Federal Reserve Bank of Atlanta.
  3. 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.
  4. C. S. Wong & W. K. Li, 2000. "On a mixture autoregressive model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 95-115.
  5. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
  6. Christian M. Hafner, 2003. "Fourth Moment Structure of Multivariate GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(1), pages 26-54.
  7. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139.
  8. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 211-250.
  9. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
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Citations

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Cited by:
  1. Jeroen V.K. Rombouts & Lars Stentoft, 2010. "Multivariate Option Pricing with Time Varying Volatility and Correlations," Cahiers de recherche 1020, CIRPEE.
  2. Mohammed Bouaddi & Jeroen V.K. Rombouts, 2007. "Mixed Exponential Power Asymmetric Conditional Heteroskedasticity," Cahiers de recherche 07-15, HEC Montréal, Institut d'économie appliquée.
  3. Rossi, E. & Spazzini, F., 2010. "Model and distribution uncertainty in multivariate GARCH estimation: A Monte Carlo analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2786-2800, November.
  4. Mark J. Jensen & John M. Maheu, 2012. "Bayesian Semiparametric Multivariate GARCH Modeling," Working Paper Series 48_12, The Rimini Centre for Economic Analysis.
  5. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
  6. Yin-Wong Cheung & Sang-Kuck Chung, 2011. "A Long Memory Model with Normal Mixture GARCH," Computational Economics, Society for Computational Economics, vol. 38(4), pages 517-539, November.
  7. 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.
  8. 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.
  9. Bentarzi, M. & Hamdi, F., 2008. "Mixture periodic autoregressive conditional heteroskedastic models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 1-16, September.
  10. Boudt, Kris & Croux, Christophe, 2010. "Robust M-estimation of multivariate GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2459-2469, November.
  11. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3153-3181.
  12. 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.

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