Efficient tests for unit roots with prediction errors

It is well-known that the main difference between a stationary (or trend-stationary) process and a process with a unit root is to be observed in their long-term behaviour. This paper exploits this idea and shows that nearly optimal unit-root tests can admit an interpretation based on prediction performance. This result is not only useful in understanding how efficient tests use the information, but it can also be used to construct new unit-root tests based on prediction errors. A Monte Carlo experiment for the autoregressive moving-average of order (1,1) indicates that the proposed tests have desirable size and power properties.