Cointegration and Error Correction Mechanisms.

Starting from a multivariate Wold representation for N variables that are integrated of order 1, this paper shows that, given that the N variables have r cointegrating vectors, there is an equivalence between five alternative representations of the multivariate model: the autoregressive representation; the error-correction representation; the interim multiplier representation; the Bewley (1979) representation; and the common trend representation. Proof of the theorem uses a result based on the Smith-McMillan lemma for polynomial matrices. The paper concludes by commenting on the different representations. Copyright 1989 by Royal Economic Society.