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.