This paper introduces a new representation for seasonally cointegrated variables, namely the complex error correction model, which allows statistical inference to be performed by reduced rank regression. The suggested estimators and tests statistics are asymptotically equivalent to their maximum likelihood counterparts. The small sample properties are evaluated by a Monte Carlo study and an empirical example is presented to illustrate the concepts and methods.
A unifying framework in which the coexistence of differing forms of common cyclical features can be tested and imposed upon a cointegrated VAR model is provided. This is achieved by introducing a new notion of common cyclical features, described as the weak form of polynomial serial correlation, which encompasses most of the existing formulations. Statistical inference is based upon reduced-rank regression, and alternative forms of common cyclical features are detected through tests for over-identifying restrictions on the parameters of the new model. Some iterative estimation procedures are then proposed for simultaneously modelling various forms of common features. The concepts and methods of the paper are illustrated via an empirical investigation of the US business cycle indicators.
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