Dickey Fuller tests

Can someone confirm if I understand this process correct?

  1. We start with a time series data model

  2. test if covariance stationary using the Dickey Fuller Test

  3. If unit root exists, the model is not covariance stationary which violates autocorrelation specifications

3a) to fix unit root, take the first difference of the time series and rerun dickey fuller test to confirm unit root is still not a problem

  1. if unit root does exist and two economically linked time-series models are available, test for cointergration using the Engle-Granger two-step test

  2. if passes engle-granger test, the time-series model(s) can be regressed against eachother and the resulting model could possibly be used (assuming passes all of the other multiregression tests)

Is this about right?

bump… Any comment on this topic is appreciated! About to punt quant but want the fundamentals down before I do!