Explain how to check time-series variables for cointegration and/or nonstationarity before putting them into a linear regression
The idea
Before regressing one time series on another, test each for a unit root. If neither has one, ordinary regression is fine. If only one has a unit root, the estimates and tests are unreliable. If both have unit roots, the regression is valid only if the two are cointegrated, meaning a long-term economic relationship keeps them from drifting apart and the regression errors are stationary. Test with the Engle–Granger method: apply a Dickey–Fuller test to the regression residuals, using Engle–Granger critical values. If cointegrated, the regression captures the long-run relationship. If not, the regression may be spurious. Cointegration requires both series to have unit roots.
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