Unit root tests and structural change when the initial observation is drawn from its unconditional distribution

Following Elliott (1999; International Economic Review 40, 767-83.) and Perron and Rodríguez (2003; Journal of Econometrics 115,1-27), we develop unit root tests in the context of structural change models using GLS detrended data (Elliott, Rothenberg and Stock 1996; Econometrica 64, 813-39) when the initial observation is drawn from its unconditional distribution. We derive the limiting distributions of the M-tests (Stock, 1999 cointegration, causality and forecasting; Oxford University Press, 137-67; Perron and Ng 1996; Review of Economics Studies 63, 435-463), the ADF statistic and a feasible optimal point test from which we derive the power envelope. Asymptotic power functions are calculated and compared with the case where the initial condition is not random. Finite sample size and power simulations under various forms of error processes are performed using different lag selection methods and two different methods to select the break point. Empirical applications are also provided.