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Multivariate GARCH estimation via a Bregman-proximal trust-region method


  • St'ephane Chr'etien
  • Juan-Pablo Ortega


The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of the VEC family, the number of parameters involved in the model grows as a polynomial of order four on the dimensionality of the problem. Moreover, these parameters are subjected to convoluted nonlinear constraints necessary to ensure, for instance, the existence of stationary solutions and the positive semidefinite character of the conditional covariance matrices used in the model design. So far, this problem has been addressed in the literature only in low dimensional cases with strong parsimony constraints. In this paper we propose a general formulation of the estimation problem in any dimension and develop a Bregman-proximal trust-region method for its solution. The Bregman-proximal approach allows us to handle the constraints in a very efficient and natural way by staying in the primal space and the Trust-Region mechanism stabilizes and speeds up the scheme. Preliminary computational experiments are presented and confirm the very good performances of the proposed approach.

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  • St'ephane Chr'etien & Juan-Pablo Ortega, 2011. "Multivariate GARCH estimation via a Bregman-proximal trust-region method," Papers 1101.5475,
  • Handle: RePEc:arx:papers:1101.5475

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    1. 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.
    2. Y.K. Tse & Albert K.C. Tsui, 2000. "A Multivariate GARCH Model with Time-Varying Correlations," Econometrics 0004007, EconWPA.
    3. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
    4. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Manganelli, Simone & Ceci, Vladimiro & Vecchiato, Walter, 2002. "Sensitivity analysis of volatility: a new tool for risk management," Working Paper Series 0194, European Central Bank.
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