This note discusses estimation and testing for the presence of common cycles in cointe-grated vector autoregressions. A simple two-stage estimator is considered where the cointegration vectors are estimated in the first stage and the remaining parameters, subject to common cycles, in the second stage. The latter stage is equivalent to using reduced rank regression in a stationary framework.
... [Show full abstract] Simple procedures for iterating on these two stages are discussed with emphasis on estimating the cointegration space conditional on the common cycles restriction. It is shown that the two-stage estimator of the parameters describing the dynamics is asymptotically Gaussian and efficient. Furthermore, an estimator of the co-feature matrix is examined and its asymptotic prop-erties are derived. Finally, two asymptotically equivalent methods for computing the likelihood ratio test for the null of s versus s g common cycles are presented along with the limiting be-havior of the tests.