BEHAVIOR OF DICKEY–FULLER t-TESTS WHEN THERE IS A BREAK UNDER THE ALTERNATIVE HYPOTHESIS

Abstract

This paper analyzes the limiting behavior of Dickey–Fuller t-tests when the true generating model is stationary around a broken linear trend. The cases of a break in level and a break in slope are considered separately and found to generate qualitatively different outcomes. In the asymptotic analysis, appropriate normalizations are applied to the break sizes. This leads to theoretical results that generate interesting predictions for sample sizes and break amounts of practical interest. Simulation evidence confirms the value of this approach to an asymptotic theory.