SE of restricted coefficients in GARCH MLE

[runner]

Dear all,

I am working with Logl object to write some Garch codes. I begin with simple ARMA(p,q)-GARCH(1,1)-Normal. I will edit it to get other garch specifications and add jump components.

With the help of prg examples available in EViews help, I wrote a prg to estimate the model with:
- Starting values for ARMA coeffs are from homoskedastic ARMA estimation
- Starting values for GARCH are alpha=0.15, beta=0.6 (as EViews set), and omega such that omega/(1-alpha-beta)=(std of ARMA resids)
- Restrict variance eqn coeffs (omega,alpha,beta) to be non-negative (I used, for instance, omega=exp(e_omega) where e_omega in (-inf,+inf))
- Set presample MA terms to zero, and variance series to estimated variance of residuals from homoskedastic ARMA

I also estimate the model with EViews built-in functions and compare results.
The prg file is attached.

I have two questions
1- Even when I try to use starting values used by EViews (eg. for ARMA coeffs EViews use 0.005), the results may be quite different between my prg and EViews estimation. Although variance eqn parameters seems to be similar, ARMA coeffs are significantly different (they even change sign). Does this reasonable? I sometimes have convergence problems, and I solved it by trying different starting values. I am also aware that EViews uses different backcasting for MA terms (using backward induction) and varince series (using exponential smoothing). Is the difference all due to backcasting, or is there any other issues to consider?
2- To restrict variance eqn coeffs, I used transformed coefficients using exponential fnc (i.e. omega=exp(e_omega)). The estimation output gives me the se of transformed coefficient (i.e., e_omega). How can I obtain se of original coeff (i.e. omega)? This is rather a theoretical question, not a programming one.

I will appreciate your comments on my problem,
Thanking in advance...