It is well known that if X_{t} is a nonstationary process and Y_{t} is a linear function of X_{t}, then cointegration of Y_{t} implies cointegration of X_{t}. We want to find an analogous result for common trends if X_{t} is generated by a finite order VAR with i.i.d. (0,Ω_{x}) errors ε_{xt}. We first show that Y_{t} has an infinite order VAR representation in terms of its white noise prediction errors, ε_{yt}, which are a linear process in ε_{xt}, the prediction error for X_{t}. We then apply this result to show that the limit of the common trends for Y_{t} generated by ε_{yt}, are linear functions of the common trends for X_{t}, generated by ε_{xt}.
We illustrate the findings with a small analysis of the term structure of interest rates.