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 [image omitted], 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 [image omitted] 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 [image omitted] other than that proposed by Elliott et al. (1996).