We introduce the idea of common serial correlation features among non-stationary, cointegrated variables. That is, the time series do not only trend together in the long run, but
adjustment restores equilibrium immediately in the period following a deviation. Allowing for delayed re-equilibration, we extend the framework to codependence. The restrictions derived for VECMs exhibiting the common feature are checked by LR and GMM-type tests. Alongside, we provide corrected maximum codependence orders and discuss identification. The concept is applied to US and European interest rate data, examining the capability of the Fed and ECB to control overnight money market rates.