code for garch-in-mean matlab

I need to estimate garch-in-mean with Garch(1,1) to get the estimated parameters. I have a series of returns, y, and so my 2 equations would be:

(1) Y_t+1 = a + b*Var_t(Y_t+1) + e_t+1;

(2) Var_t(Y_t+1) = w + alpha*((e_t)^2) + beta*Var_t-1(Y_t);

where:

Y is a series of returns, Var is the conditional variance of the returns, e are the residuals, a, b, w, alpha, and beta the parameters I want to estimate, and _t+1 or _t-1 are the subscripts to indicate the moment in time.

Does anyone know how to do it? I'm really lost here...

Thanks in advance.

Best, Rui

[Tyson]

Did anyone figure this out. I am hoping to add arch-M effects.