Abstract
This paper analyzes the performance of multiple steps estimators of vector autoregressive multivariate conditional correlation GARCH models by means of Monte Carlo experiments. We show that if innovations are Gaussian, estimating the parameters in multiple steps is a reasonable alternative to the maximization of the full likelihood function. Our results also suggest that for the sample sizes usually encountered in financial econometrics, the differences between the volatility and correlation estimates obtained with the more efficient estimator and the multiple steps estimators are negligible. However, when innovations are distributed as a Student-t, using multiple steps estimators might not be a good idea.
- 1
Notice that the vec operator stacks the columns of a matrix while the vech operator stacks the columns of the lower triangular part of a matrix.
- 2
In order to check the robustness of the results, we have also considered different scenarios by changing the parameter values in Table 1 and repeated the Monte Carlo experiment. All the results are similar and they are not included in the paper to save space but they are available from the authors upon request.
- 3
Relative deviations are prefered to absolute ones, although conclusions do not change if absolute deviations are plotted.
- 4
In order to better interpret the numbers, true volatility is computed substituting the true parameter values by the 1-step estimates of the correct model.
Acknowledgement
We are very grateful to an anonymous referee for helpful comments. Financial support from IVIE (Instituto Valenciano de Investigaciones Económicas) to the project “Estimating Multivariate GARCH Models in Multiple Steps with an Application to Stock Markets” is gratefully acknowledged. We also acknowledge the Spanish Government for grant ECO2011-29751.
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