An asymptotic invariance property of the common trends under linear transformations of the data

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 x t . We first show that Y t has an infinite order VAR representation in terms of its white noise prediction errors, ε y t , which are a linear process in ε x t , 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 y t , are linear functions of the common trends for X t , generated by ε x t . ustrate the findings with a small analysis of the term structure of interest rates.