I have a model of four implied exchange rates which are based on stock prices denominated in two currencies. They should all be cointegrated based on the law of one price.
Each of the series is clearly I(1) based on ADF-testing, even when adding constant/trend terms. When using Johansen's test, I attain a matrix $\Pi$ of full rank. According to text books this should imply that the underlying data is I(0) and no Error Correction Model is needed as the data is already stationary. However as mentioned, the ADF clearly stated that it is non-stationary.
I'd appreciate your comment on that. Thank you!