In this paper we propose a methodology to detect unit roots in time series with two different integration orders. The presented methodology considers a specific stochastic process with two parts: one of them is [an I(1) process and the order an I(0)]. In order to analyze this kind of stochastic process and we propose three sequential tests based on the standard ADF test. The first one simultaneously analyses stationarity in the two parts in to which the sample has been divided. The other two sequential tests analyze the two subsamples separately. Results show that test power changes depending on the location of the non-stationarity and on the existence of a deterministic trend in the process. Finally, this set of tests is applied to analyze the long-run interest rate of Spain and France with respect to Germany from 1994 to 2002.

Key words: Unit Roots, ADF test, sequential tests.
JEL classification: C12, C15.