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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 theoretical 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 a 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 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. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," Working Paper 2004-13, Federal Reserve Bank of Atlanta.
  2. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139, September.
  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. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 211-250.
  5. Denis Pelletier, 2004. "Regime Switching for Dynamic Correlations," Econometric Society 2004 North American Summer Meetings 230, Econometric Society.
  6. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. 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.
  8. 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.
  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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