A time series paradox: Unit root tests perform poorly when data are cointegrated

- Presence of a unit root in individual time series is required for cointegration.
- Cointegration makes standard unit root tests more likely to reject a unit root null.
- The paradox arises because cointegration induces a moving average (MA) component.
- The cointegration-induced MA component causes unit root tests to be oversized.

Cointegration among times series paradoxically makes it more likely that a unit test will reject the unit root null hypothesis on the individual series. This occurs because at least one series in the system has a negative moving average component.