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Analytical quasi maximum likelihood inference in multivariate volatility models

  • Christian Hafner


  • Helmut Herwartz


Quasi maximum likelihood estimation and inference in multivariate volatility models remains a challenging computational task if, for example, the dimension is high. One of the reasons is that typically numerical procedures are used to compute the score and the Hessian, and often they are numerically unstable. We provide analytical formulae for the score and the Hessian and show in a simulation study that they clearly outperform numerical methods. As an example, we use the popular BEKK-GARCH model, for which we derive first and second order derivatives.

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Article provided by Springer in its journal Metrika.

Volume (Year): 67 (2008)
Issue (Month): 2 (March)
Pages: 219-239

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Handle: RePEc:spr:metrik:v:67:y:2008:i:2:p:219-239
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  7. Herwartz, Helmut & Neumann, Michael H., 2005. "Bootstrap inference in systems of single equation error correction models," Journal of Econometrics, Elsevier, vol. 128(1), pages 165-193, September.
  8. 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).
  9. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
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