Minimizing the impact of the initial condition on testing for unit roots

The outcome of popular unit root tests depends heavily on the initial condition, i.e. on the difference between the initial observation and the deterministic component. In some applications it is difficult to rule out small or large values of the initial condition a priori, so this dependence can be quite difficult to deal with in practice. We explore a number of methods for constructing unit root tests whose properties are less affected by the initial condition. We show that no nontrivial test can remain completely unaffected, and instead derive an asymptotically efficient unit root test whose power varies relatively little as a function of the initial condition.