We extend the class of M-tests for a unit root analyzed by Perron and Ng (1996) and Ng and Perron (1997) to the case where a change in the trend function is allowed to occur at an unknown time. These tests M(GLS) adopt the GLS detrending approach of Dufour and King (1991) and Elliott, Rothenberg and Stock (1996) (ERS). Following Perron (1989), we consider two models: one allowing for a change in slope and the other for both a change in intercept and slope. We derive the asymptotic distribution of the tests as well as that of the feasible point optimal tests PT(GLS) suggested by ERS. The asymptotic critical values of the tests aretabulated. Also, we compute the non-centrality parameter used for the local GLS detrending that permits the tests to have 50% asymptotic power at that value. We show that the M(GLS) and PT(GLS) tests have an asymptotic power function close to the power envelope. ...

Climate change detection and attribution have been the subject of intense research and debate over at least four decades. However, direct attribution of climate change to anthropogenic activities using observed climate and forcing variables through statistical methods has remained elusive, partly caused by difficulties to correctly identify the time-series properties of these variables and by the limited availability of methods to relate nonstationary variables. This paper provides strong evidence concerning the direct attribution of observed climate change to anthropogenic greenhouse gases emissions by first investigating the univariate time-series properties of observed  global and hemispheric temperatures and forcing variables and then by proposing statistically adequate multivariate models. The results show that there is a clear anthropogenic fingerprint on both global and hemis...