Testing for common cyclical features in VAR models with cointegration

We consider VAR models for variables exhibiting cointegration and comon cyclical features. While the presence of cointegration reduces the rank of the long-run multiplier matrix, other types of common features lead to rank reduction of the short-run dynamics. We distinguish between strong and weak form reduced rank structures. Strong form reduced rank structures analyzed by Engle and Kozicki (1993) arise when a linear combination of the first differenced variables corrected for the long-run effects are white noise.The weak form has an interest in its own. For instance, it is a necessary condition for the strong form. We also consider the mixed form which combined strong and weak form. We discuss the model selection issues which arise from this distinction and propose a simple approach to testing for these structures using a sequence of likelihood ratio test statistics. The finite sample behavior of the sequential approach is analyzed in a Monte Carlo experiment. Finally, we illustrate the relevance of the different form of reduced ranks with an empirical analysis of US business fluctuations over the period 1954-1996.