Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, <italic>Econometric Theory</italic> 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the relationships between the variables; therefore, they are important for applied work. Tests for linear restrictions on the coefficients of both the ECM and the pure VAR representation are considered under the present assumptions. It is found that they have limiting x<sup>2</sup> distributions. Tests are also derived under the assumption that the number of restrictions goes to infinity with the sample size.
