ML Estimators for SEM-GARCH Models: Relative Performance of Different Computational Algorithms
AbstractThough multivariate GARCH models are widely used in empirical research, their computational aspects still represent a major hurdle, especially when these specifications are introduced in structural models. One such extension namely the simultaneous equations model (SEM) with GARCH errors was considered by Engle and Kroner (1995). While there are many applications of the BEKK formulation proposed in the above article, the model as a whole has received little attention in the econometric literature. This paper uses analytical first and second order derivatives of the likelihood function of a SEM with GARCH errors to compute the corresponding ML estimators. We compare different gradient algorithms in a simulation framework and study the small sample behavior of alternative covariance matrix estimators. As it has been the case in several similar studies, it is found that using analytical results instead of numerical approximations yields better results.
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 294.
Date of creation: 04 Jul 2006
Date of revision:
GARCH; simultaneous equations; gradient algorithms;
Find related papers by JEL classification:
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
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