Comparisons of Robust Tests for Shifts in Trend with an Application to Trend Deviations of Real Exchange Rates in the Long Run

We study the finite sample properties of tests for structural changes in the trend function of a time series that do not require knowledge of the degree of persistence in the noise component. The tests of interest are the quasi-Feasible Generalized Least Squares (FGLS) procedure by Perron and Yabu (2009b) and the weighted average of the regression t -statistics by Harvey et al . (2009), both of which have the same limit distribution whether the noise component is stationary or has a unit-root. We analyse the finite sample size and power properties of these tests under a variety of Data-Generating Processes (DGPs). The results show that the Perron--Yabu test has greater power overall. With respect to the size, the Harvey--Leybourne--Taylor test exhibits larger size distortions unless a moving-average component is present. Using the Perron and Yabu procedure to test for structural changes in the trend function of long-run real exchange rates with respect to the US dollar indicates that for 17 out of 19 countries, the series have experienced a shift in trend since the late nineteenth century.