The persistent movements away from long-run benchmark values in real exchange rates often observed in periods of currency ‡oat have been subject to much empirical research without resolving the underlying theoretical puzzle. This chapter demonstrates how the Cointegrated VAR approach of grouping together components of similar persistence can be used to uncover structures in the data that ultimately may help to explain theoretically the forces underlying such puzzling movements. The charaterization of the data into components which are empirically I(0), I(1) and I(2) is shown to be a powerful organizing principle, allowing us to structure the data into long-run, medium-run, and short-run behavior. Its main advantage is the ability to associate persistent movements away from fundamental benchmark values in one variable/relation with similar persistent movements somewhere else in the economy.JEL: C32, C50, F41