I would like to know how the Dynare calculate the “aproximated theoretical moments”. When the routine finish, I type “mean(y_e)”, but the result is different from the “aproximated theoretical moments”. I know when I ask for mean(y_e), the Dynare claculate the mean about y_e, and not y. But, how could I calculate this on command window? Is it possible to calculate the serial correlation of this original series, like y? Thanks!

For the computation of theoretical moments, see the manual.
For the simulated mean, you must compute the mean of the simulated series, i.e. you need to specify the periods option. My guess is that the y_e you are looking at is the IRF of y to a shock to e. It is different from the unconditional simulations. When the periods statement is there, you should have a variable named y in the workspace, whose mean you can compute.