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Error correction and long-run equilibrium in continuous time. (English) Zbl 0725.62101
Summary: 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.

MSC:
62P20 Applications of statistics to economics
62M99 Inference from stochastic processes
93E11 Filtering in stochastic control theory
93E12 Identification in stochastic control theory
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