The paper analyzes the impact of the initial condition on the problem of testing for unit roots.
To this end, we derive a family of optimal tests that maximize a weighted average power
criterion with respect to the initial condition. We then investigate the relationship of this
optimal family to popular tests. We find that many unit root tests are closely related to specific
members of the optimal family, but the corresponding members employ very different
weightings for the initial condition. The popular Dickey‐Fuller tests, for instance, put a large …

The paper analyzes the impact of the initial condition on the problem of testing for unit roots.
To this end, we derive a family of optimal tests that maximize a weighted average power
criterion with respect to the initial condition. We then investigate the relationship of this
optimal family to popular tests. We find that many unit root tests are closely related to specific
members of the optimal family, but the corresponding members employ very different
weightings for the initial condition. The popular Dickey-Fuller tests, for instance, put a large …