On the importance of the first observation in GLS detrending in unit root testing

First-differencing is generally taken to imply the loss of one observation, the first, or at least that the effect of ignoring this observation is asymptotically negligible. However, this is not always true, as in the case of GLS detrending. In order to illustrate this, the current paper considers as an example the use of GLS detrended data when testing for a unit root. The results show that the treatment of the first observation is absolutely crucial for test performance, and that ignorance causes test break-down.