Tests for unit roots and the initial condition

Ulrich K. Müller, Graham Elliott

Research output: Contribution to journalComment/debatepeer-review

128 Scopus citations


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 weight on extreme deviations of the initial observation from the deterministic component, whereas other popular tests put more weight on moderate deviations. Since the power of unit root tests varies dramatically with the initial condition, this paper explains the results of comparative power studies of unit root tests. The results allow a much deeper understanding of the merits of particular tests in specific circumstances, and a guide to choosing which statistics to use in practice.

Original languageEnglish (US)
Pages (from-to)1269-1286
Number of pages18
Issue number4
StatePublished - 2003
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Asymptotic distributions
  • Point optimal tests
  • Unit root tests
  • Weighted average power


Dive into the research topics of 'Tests for unit roots and the initial condition'. Together they form a unique fingerprint.

Cite this