Testing for shifts in trend with an integrated or stationary noise component

We consider testing for structural changes in the trend function of a time series without any prior knowledge of whether the noise component is stationary or integrated. Following Perron and Yabu (2009), we consider a quasi-feasible generalized least squares procedure that uses a super-efficient estimate of the sum of the autoregressive parameters α when α = 1. This allows tests of basically the same size with stationary or integrated noise regardless of whether the break is known or unknown, provided that the Exp functional of Andrews and Ploberger (1994) is used in the latter case. To improve the finite-sample properties, we use the bias-corrected version of the estimate of α proposed by Roy and Fuller (2001). Our procedure has a power function close to that attainable if we knew the true value of α in many cases. We also discuss the extension to the case of multiple breaks.