The relationship between cointegration and error correction models, first suggested by Granger, is here extended and used to develop estimation procedures, tests, and empirical examples. A vector of time series is said to be cointegrated with cointegrating vector a if each element is stationary only after differencing while linear combinations a8xt are themselves stationary. A representation theorem connects the moving average , autoregressive, and error correction representations for cointegrated systems. A simple but asymptotically efficient two-step estimator is proposed and applied. Tests for cointegration are suggested and examined by Monte Carlo simulation. A series of examples are presented. Copyright 1987 by The Econometric Society.