Testing for Shifts in Trend with an Integrated or Stationary Noise Component

This paper considers the problem of testing for structural changes in the trend function of a univariate time series without any prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. We propose a new approach that builds on the work of Perron and Yabu (2005), based on a Feasible Quasi Generalized Least Squares procedure that uses a superefficient estimate of the sum of the autoregressive parameters α when α = 1. In the case of a known break date, the resulting Wald test has a chi-square limit distribution in both the I(0) and I(1) cases. When the break date is unknown, the Exp functional of Andrews and Ploberger (1994) yields a test with nearly identical limit distributions in the two cases so that a testing procedure with nearly the same size in the I(0) and I(1) cases can be obtained. To improve the finite sample properties of the tests, we use the bias corrected version of the OLS estimate of α proposed by Roy and Fuller (2001). We show our procedure to be substantially more powerful than currently available alternatives and also to have a power function that is close to that attainable if we knew the true value of α in many cases. The extension to the case of multiple breaks is also discussed