Banerjee, Dolado and Mestre (J. Time Ser. Anal. 19 (1998) 267-283) introduc
e an error-correction test for the null hypothesis of no cointegration. The
present paper supplements their work. They provide critical values for reg
ressions with and without detrending. Here it is shown that the latter are
not appropriate if the series display linear trends. This does not mean tha
t detrending is required. Correct percentiles are suggested for the case th
at series follow linear time trends but tests are based on regressions with
out detrending. They are readily available from the literature.