A note of unit root testing in the presence of level shifts

In this note we discuss the properties of Augmented-Dickey-Fuller [ADF] unit root tests for autoregressive processes with a unit or near-unit root in the presence of multiple level shifts of large size. Due to the presence of level shifts, the ADF tests experience severe power losses. We consider new modified ADF unit root tests which require no knowledge of either the location or the number of level shifts. The tests are based on a two-step procedure where possible level shifts are initially detected using the level shift indicator estimators suggested by Chen and Tiao (1990, Journal of business and Economics Statistics) and Chen and Liu (1993, Journal of the American Statistical Association), and later removed by a novel procedure which is denoted as “de-jumping”. Using a Monte Carlo experiment we show that the new tests, although partially oversized in samples of moderate size, have much higher power than standard ADF tests.