A finite-sample sensitivity analysis of the Dickey–Fuller test under local-to-unity detrending

In recent research, Elliott et al. (1996) have shown the use of local-to-unity detrending via generalized least squares (GLS) to substantially increase the power of the Dickey–Fuller (1979) unit root test. In this paper the relationship between the extent of detrending undertaken, determined by the detrending parameter c, and the power of the resulting GLS-based Dickey– Fuller (DF-GLS) test is examined. Using Monte Carlo simulation it is shown that the values of c suggested by Elliott et al. (1996) on the basis of a limiting power function seldom maximize the power of the DF-GLS test for the finite samples encountered in applied research. This result is found to hold for the DF-GLS test including either an intercept or an intercept and a trend term. An empirical examination of the order of integration of the UK household savings ratio illustrates these findings, with the unit root hypothesis rejected using values of c other than that proposed by Elliott et al. (1996).