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Analytical quasi maximum likelihood inference in multivariate volatility models

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  • Hafner, C.M.
  • Herwartz, H.

Abstract

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.

Suggested Citation

  • Hafner, C.M. & Herwartz, H., 2003. "Analytical quasi maximum likelihood inference in multivariate volatility models," Econometric Institute Research Papers EI 2003-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1721
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    More about this item

    Keywords

    multivariate GARCH models; quasi maximum likelihood;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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