A Unit Root Test with Multiple Trend Breaks: A Theory and An Application to Us and Japanese Macroeconomic Time-Series

This study develops a unit root test that allows for an alternative hypothesis with multiple trend breaks of unknown dates, and proves that tests with fewer than the true number of breaks fail, incorrectly, to reject the null asymptotically. The asymptotic distributions of appropriate t-statistics under the unit root null are determined. In empirical applications, this test rejects the null for the Nelson—Plosser velocity of the USA, the postwar quarterly real output series of the USA and Japan, and Japanese real consumption, but not for real consumption of the USA. The finite-sample properties are examined with Monte Carlo experiments.