COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 882R

"Error Correction and Long Run Equilibria in Continuous Time"

Peter C.B. Phillips

June 1988
Revised July 1989

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.

JE Classification: 211

Keywords: Error correction, spectral regression, differential equations, triangular system, temporal aggregation, co-integration