Testing for codependence of cointegrated variables

We analyse nonstationary 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 the Moving Average (MA) and Vector Error Correction Model (VECM) representations and put forward a Generalized Method of Moments (GMM) test. In addition, for cases where the constraints can be uniquely imposed on a VECM a likelihood ratio test is proposed. We apply the concept to US and European interest rate data, examining the capability of the Federal Reserve Bank (Fed) and European Central Bank (ECB) to control overnight money market rates.