GMM is not usually chosen for general GARCH model. The essence for GMM is that modeller does not want to assume any distribution, just moment conditions. In general GMM is not appropriate for Forecasting (I am not very sure about this, but I will give an example later on). Similar to OLS, nonlinear least square also does not see the ditribution assumption as a must (of course when error term follows a normal one in OLS, common F and t tests become exact and convinient for statistical inference). In GARCH literature, MLE (QMLE) is the usual choice for parameter estimation. As we know that MLE requires assumption for error term. and this may be the exact reason why people model financial returns time series (high kurtosis, volatility clustering,...). In univariate GARCH models, fat-tailed distribution has been a routine choice except for some more theoretical works where relevant for the model with normal distribution has been readily available. In Eviews it is simple to choose t or GED(for v5?) as long as you are able to use Eviews. For Stochastic volatility model (SV) one can use GMM technique for parameter estimation but for volatility forecating, the power of GMM deserts us. So QMLE with Kalman fitler is the first choice for estimation and voaltility forecating. There are other methods for SV,e.g. Bayesian method and simulated maximumlikelihood method.
[此贴子已经被作者于2006-4-22 20:13:41编辑过]
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. This can be seen as a intuition. You can choose the one with highest maximum likelihood as your favourite specification for conditional variance models. 
