Hello everyone,

Just wanted to know how to generate 500 processes of the following model:

Yt=alpha0+alpha1*Xt+Et

where Xt is an AR(1) process as: Xt=beta0+beta1*Xt-1+Ut


I have to do this for t=30, t=100 and t=500. In this case, I have to consider that Et and Ut are N(0,1), and the other parameters are alpha0=2, alpha1=0.7, beta0=1 and beta1=0.8.

I hope you can understand what I need to do.
Thanks,
Javier