I know how to simulate correlated returns, but I do not know how to simulate Co-Integrated assets. I would like to simulate a co-integrated time series where the Beta Co-Efficient is not constant, but rather has some degree of drift. An equation or model for doing so would be very helpful, thanks very much Quant SE!
I think I just figured it out, and kinda feel dumb. It appears It could be solved by multiplying one time series by the beta co-efficient, and having a random walk model the drift of the beta co-efficient, thus a stationary time series could be contrived by the two co-integrated assets.
I am not for sure however, so if I am wrong please correct me.