• Unit root test;
  • heteroskedasticity;
  • ARCH;
  • GARCH;
  • covariates;
  • GLS detrending

When testing for a unit root in a time series, in spite of the well-known power problem of univariate tests, it is quite common to use only the information regarding the autoregressive behaviour contained in that series. In a series of influential papers, Elliott et al. (Efficient tests for an autoregressive unit root, Econometrica 64, 813–836, 1996), Hansen (Rethinking the univariate approach to unit root testing: using covariates to increase power, Econometric Theory 11, 1148–1171, 1995a) and Seo (Distribution theory for unit root tests with conditional heteroskedasticity, Journal of Econometrics 91, 113–144, 1999) showed that this practice can be rather costly and that the inclusion of the extraneous information contained in the near-integratedness of many economic variables, their heteroskedasticity and their correlation with other covariates can lead to substantial power gains. In this article, we show how these information sets can be combined into a single unit root test.