This paper deals with error correction models (ECM's) and cointegrated systems that are formulated in continuous time. Long-run equilibrium coefficients in the continuous system are always identified in the discrete time reduced form, so that there is no aliasing problem for these parameters. The long-run relationships are also preserved under quite general data filtering. Frequency domain procedures are outlined for estimation and inference. These methods are asymptotically optimal under Gaussian assumptions and they have the advantages of simplicity of computation and generality of specification, thereby avoiding some methodological problems of dynamic specification. In addition, they facilitate the treatment of data irregularities such as mixed stock and flow data and temporally aggregated partial equilibrium formulations. Models with restricted cointegrating matrices are also considered.

Properties of maximum likelihood estimates of cointegrated systems are studied. Alternative formulations are considered, including a new triangular system error correction mechanism. We demonstrate that full system maximum likelihood brings the problem of inference within the family covered by the locally asymptotically mixed normal asymptotic theory, provided all unit roots have been eliminated by specification and data transformation. Methodological issues provide a major focus of the paper. Our results favor use of full system estimation in error correction mechanisms or subsystem methods that are asymptotically equivalent. They also point to disadvantages in the use of unrestricted VAR's formulated in levels and of certain single equation approaches to estimation of error correction mechanisms.