On infimum Dickey–Fuller unit root tests allowing for a trend break under the null

Trend breaks appear to be prevalent in macroeconomic time series. Consequently, to avoid the catastrophic impact that unmodelled trend breaks have on power, it is standard empirical practice to employ unit root tests which allow for such effects. A popularly applied approach is the infimum ADF-type test. Its appeal has endured with practitioners despite results which show that the infimum ADF statistic diverges to −∞ as the sample size diverges, with the consequence that the test has an asymptotic size of unity when a break in trend is present under the unit root null hypothesis. The result for additive outlier-type breaks in trend (but not intercept) is refined and shows that divergence to −∞ occurs only when the true break fraction is smaller than 2/3. An alternative testing strategy based on the maximum of the original infimum statistic and the corresponding statistic constructed using the time-reversed sample data is considered.