If the data has passed stationary tests and does not exhibit unit root problems, then the assumptions of many time series models have been met. In such cases, there might not be a need to test for cointegration, as cointegration is often explored when dealing with non-stationary time series. Am I wrong?
Cointegration analysis requires data to be integrated of at least order one (be nonstationary). If data are stationary (integrated of order zero) there is no need to apply cointegration analysis because the data cannot be cointegrated. This is because cointegration means that the linear combination of variables has an order of integration below that of the variables themselves. For example, if Y~I(0) and X~I(0) their linear combination cannot have an order of integration below 0 and they therefore cannot be cointegrated. Nevertheless, the model involving only stationary variables may still exhibit autocorrelation and need a dynamic specification (including lags of variables) that has a static long run solution (essentially obtained by removing time subscripts). However, this long run (equilibrium) solution will not be a cointegrating equation.
I can add my 2 cents to Chris Stewart's excellent answer. If a time series has no unit-root, it can still be trend non-stationary. In this case, the series needs to be "detrend". Alternatively, one can use the Dickey-Fuller regression to test for unit-root vs. tend vs. stationarity.
@Chris Stewart : Huge thanks for superb answer 👍
@Francis W Ahking : Looks like 2 grand add of answer for me 🙂 many thanks 👍
If the data has passed stationary tests and does not exhibit unit root problems, then the assumptions of many time series models have been met. In such cases, there might not be a need to test for cointegration.