Error Correction and Long Run Equilibrium in Continuous Time
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This paper deals with error correction models (ECM’s) and cointegrated systems that are formulated in continuous time. Problems of representation, identiﬁcation, estimation and time aggregation are discussed. It is shown that every ECM in continuous time has a discrete time equivalent model in ECM format. Moreover, both models may be written as triangular systems with stationary errors. This formulation simpliﬁes both the continuous and the discrete time ECM representations and it helps to motivate a class of optimal inference procedures. It is further shown that long run equilibria in the continuous system are always identiﬁed in the discrete time reduced form, so that there is no aliasing problem for these coeﬀicients.
Phillips, Peter C.B., "Error Correction and Long Run Equilibrium in Continuous Time" (1988). Cowles Foundation Discussion Papers. 1126.