# Simulating Co-Integrated Assets

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!

• If $\beta$ is drifting, can you still say the series are cointegrated? The standard definition of cointegration has a constant beta. (But probably it could be generalized.) – Richard Hardy Sep 10 '16 at 7:26
• While you are correct, i have found time series can be co-integrated for periods of time before a change in volatility affects the $\beta$ – FX_NINJA Sep 10 '16 at 18:47

## 1 Answer

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.