We bring together some recent advances in the literature on vector autoregressive moving-average models, creating a simple specification and estimation strategy for the cointegrated case. We show that in this case with fixed initial values there exists a so-called final moving-average representation. We prove that the specification strategy is consistent. The performance of the proposed method is investigated via a Monte Carlo study and a forecasting exercise for US interest rates. We find that our method performs well relative to alternative approaches for cointegrated series and methods which do not allow for moving-average terms. Copyright © 2014 John Wiley & Sons, Ltd.