Common dynamics in I(1) VAR systems

This paper discusses common cycles in I(1) vector autoregressive (VAR) systems, both for the first di¤erences of the process and for deviations from equilibrium. This extension is based on the equilibrium dynamics representation of I(1) systems, which is presented in this paper. Inference on the number of common features is addressed via reduced rank regression, as well as estimation of the cofeature relations and specification testing. An empirical application on five US monthly macro and financial time series illustrates the techniques presented in the paper. We find one cointegrating relation and one cofeature vector in the equilibrium dynamics formulation, implying four common trends and four common cycles in the system.