At the univariate level, ARCH(1) = GARCH(1,0) is always dominated by GARCH(1,1).

EGARCH has no underlying stochastic process that leads to its specification, no mathematical regularity conditions, including invertibility, no valid likelihood function, and hence no asymptotic properties of consistency and asymptotic normality of the QMLE of the parameters.

In short, it is unwise to use EGARCH.

Thanks a lot for your reply.

To Julian:

My pleasure.

I wish you well in your ongoing research.

There are several selection criteria to adopt whenever one is faced with making a decision among different good contending models. You may want to to consider these models' performances on the basis of the amount of information lost in the estimation process using the available Information criteria - AIC, SIC or BIC, etc. You may also want to consider available forecast error measures like RMSE, MAE, MAPE, etc. In STATA you have the Information criterion option and the log likelihood statistic. These two can suffice for making a decision with regards to which model will be data justified. The model with the least statistic in each case is taken as the most preferred.

Usually its the statistical criteria of AIC and SIC that is applied in this case.

try to use there informations criteria like AIC, SIC, BIC, etc.