Asymptotic theory of statistics form unit root test regressions when the alternative is a breaking-trend-stationary model

Abstract

We derive test regressions whose structure provides a link between tests for a unit root and tests on the nullity of the parameters associated with the regression's trend function. These test regressions turn out to be equivalent to those proposed by Perron (1989). Using these regression equations, we extend Perron's (1989) asymptotic results by deriving limiting distributions of the deterministic components for all the models considered. The asymptotic representations of these distributions show that there is no conflict between testing for unit roots and for structural breaks: acceptance of a unit root rules out acceptance of a structural break, as modelled by a dummy variable.