Unit root tests in the presence of uncertainty about the non-stochastic trend

A sequential procedure for determination of trend degree and testing for a unit root is introduced; its properties are investigated by Monte Carlo experiment. We implement the pseudo-GLS unit root tests of Elliott et al. (1996. Econometrica 64(4), 813–836), with lag length selected by the BIC criterion. Our procedure allows for quadratic trend, and we introduce a ‘GLS’-type test for this case. We compare the sequential procedure, in which trend degree is tested after a unit root pre-test, with a robust trend test recently developed by Vogelsang (1998. Econometrica 66(1), 123–149). The sequential procedure is advocated in preference both to informal use of the usual family of unit root tests and to alternative formal sequential methods that have been advanced in the literature. It is illustrated by application to the inventory data analysed in Hall (1994. Journal of Business and Economic Statistics 12(4), 461–470).