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Multivariate mixed normal conditional heteroskedasticity

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  • BAUWENS, Luc
  • HAFNER, Christian M.
  • ROMBOUTS, Jeroen VK

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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File URL: http://dx.doi.org/10.1016/j.csda.2006.10.012
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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 RP with number -1906.

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Handle: RePEc:cor:louvrp:-1906

Note: In : Computational Statistics & Data, 51, 3551-3566, 2007
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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. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 211-250.
  3. 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.
  4. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," Working Paper 2004-13, Federal Reserve Bank of Atlanta.
  6. 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.
  7. 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.
  8. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139.
  9. 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.
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Citations

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Cited by:
  1. Jensen, Mark J. & Maheu, John M., 2013. "Bayesian semiparametric multivariate GARCH modeling," Journal of Econometrics, Elsevier, vol. 176(1), pages 3-17.
  2. 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.
  3. BOUADDI, Mohammed & ROMBOUTS, Jeroen V.K., 2007. "Mixed exponential power asymmetric conditional heteroskedasticity," CORE Discussion Papers 2007097, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Bentarzi, M. & Hamdi, F., 2008. "Mixture periodic autoregressive conditional heteroskedastic models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 1-16, September.
  5. 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.
  6. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2008. "Asymmetric multivariate normal mixture GARCH," CFS Working Paper Series 2008/07, Center for Financial Studies (CFS).
  7. Jeroen V.K. Rombouts & Lars Stentoft, 2010. "Multivariate Option Pricing with Time Varying Volatility and Correlations," CREATES Research Papers 2010-19, School of Economics and Management, University of Aarhus.
  8. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
  9. Rossi, Eduardo & Spazzini, Filippo, 2008. "Model and distribution uncertainty in multivariate GARCH estimation: a Monte Carlo analysis," MPRA Paper 12260, University Library of Munich, Germany.
  10. Krishnakumar, Jaya & Kabili, Andi & Roko, Ilir, 2012. "Estimation of SEM with GARCH errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3153-3181.
  11. Boudt, Kris & Croux, Christophe, 2010. "Robust M-estimation of multivariate GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2459-2469, November.
  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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