Codependence in Cointegrated Autoregressive Models

This paper investigates codependent cycles, i.e. transitory components that react to common stimuli in a similar, although not necessarily synchronous fashion. In a multivariate system, codependence corresponds to an impulse response function that is collinear except for a small number of initial periods. It is shown that the number of cofeature combinations that yield the scalar component models associated with codependence is severely limited by the dimension of a finite-order VAR system. The presence of cointegrating relationships imposes additional cross-equation restrictions and further limits the number of permissible cofeatures. For vector-error correction models, the distribution of FIML based LR tests is therefore different than that of the limited information tests proposed by Vahid and Engle (1997). Monte-Carlo simulations indicate that LR tests yield an increase in power relative to the alternative GMM and canonical correlations tests, while maintaining good size properties. An empirical application investigates the presence of codependence among individual components of the U.S. economy. It is found that the (Beveridge-Nelson) cycle under codepence assumptions contains significantly less high-frequency information than the unconstrained cycle.