This paper studies efficient detrending in cointegrating regression and dev
elops modified tests for cointegration that use efficient detrending proced
ures. Asymptotics for these tests are derived. Monte Carlo experiments are
conducted to evaluate the detrending procedures in finite samples and to co
mpare tests for cointegration based on different detrending procedures. The
limit theory allows for increasingly remote initial condition effects as t
he sample size goes to infinity.