Modified Stationarity Tests with Data-Dependent Model-Selection Rules.

The authors describe some simple methods for improving the performance of stationarity tests (i.e., tests that have a stationary null and a unit-root alternative). Specifically, they increase the rate of convergence of the test under the unit-root alternative from O-N9-p(T) to O-N9-p(T-N9-2), then suggest an optimal method of selecting the order of the autoregressive component in the fitted autoregressive integrated moving average model on which the test is based. Simulation evidence suggests that these modifications work well. The authors apply the modified procedure to U.S. monthly macroeconomic data and uncover new evidence of a unit root in unemployment.