We analyze non-stationary time series that do not only trend together in the long run, but restore the equilibrium immediately in the period following a deviation. While this represents a common serial correlation feature, the framework is extended to codependence, allowing for delayed adjustment. We show which restrictions are implied for VECMs and lay out a likelihood ratio test. In addition, due to identification problems in codependent VECMs a GMM test approach is proposed. We apply the concept to US and European interest rate data, examining the capability of the Fed and ECB to control overnight money market rates.