A unifying framework for analysing common cyclical features in cointegrated time series

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.