dynamic Macro Model with a loop

Dear Matlab Community

I have to calculate a dynamic Macro Model. I looks like this:

C(t)=c*Y(t-1); I(t)=b1*(C(t)-C(t-1))+b2*(C(t-1)-C(t-2)); G(t)=tau*(Y(t-1)-Y(t-2))+G_fix; Y(t)=C(t)+I(t)+G(t);

now, parameters are given: c=0.7; b1=0.5; b2=0.8; tau=0.2; and G_fix=1;

We now have to solve this model, starting in steady state. So for steady state, I have solved the model as following:

in the steady state, Y(t)=Y(t-1)=Y(t-n) so ------Y=G_fix/(1-c)------ -->C=(c*G_fix)/(1-c) -->I=0

but now, how do I calculte now a time series for 50 periods? I tried to make a foor loop but since the the Investment needs values of Y in (t-2) it never works. I'm desperately searching for an answer but I don't get it. I would be really happy if somebody could help me.

Best Rico