Desempeño de estimadores alternativos en modelos GARCH bivariados con muestras finitas

In this paper we investigate by Monte Carlo simulations the bias, mean square error, variance and distribution of estimators for bivariate GARCH models in small samples. The data generating process is a VAR (2) for the conditional mean together with a diagonal VEC model for the conditional variance. We evaluate the maximum likelihood estimator under alternative specifications for the conditional mean process. For comparison the OLS estimator (for the conditional mean) is also evaluated. We consider samples of 25, 50, 100 y 200 observations which are usual in economic applications. We find that the bias and variance of all estimators diminish as the sample size increases. Also, as the persistence in the mean (variance) is increased the estimators of the mean (variance) become more biased, more disperse and, hence, their mean square errors increase. For processes with high persistence in the variance the estimators of the conditional mean parameters are biased. The estimators of the variance do not follow standard known distributions and in the case of high persistence in the variance it is highly likely to obtain GARCH parameters greater than one. We finally present the results of an econometric exercise on the relationship among inflation, output growth and uncertainty for the case of Mexico.