• DOI:10.3386/T0130
• Corpus ID: 122699512

Efficient Tests for an Autoregressive Unit Root

@article{Elliott1992EfficientTF,
  title={Efficient Tests for an Autoregressive Unit Root},
  author={Graham Elliott and Thomas J. Rothenberg and James H. Stock},
  journal={Econometrics eJournal},
  year={1992}
}

• G. Elliott, T. Rothenberg, J. Stock
• Published 1 December 1992
• Mathematics
• Econometrics eJournal

This paper derives the asymptotic power envelope for tests of a unit autoregressive root for various trend specifications and stationary Gaussian autoregressive disturbances. A family of tests is proposed, members of which are asymptotically similar under a general 1(1) null (allowing nonnormality and general dependence) and which achieve the Gaussian power envelope. One of these tests, which is asymptotically point optimal at a power of 50%, is found (numerically) to be approximately uniformly most powerful (UMP) in the case of a constant deterministic term, and approximately uniformly most powerful invariant (UMPI) in the case of a linear trend, although strictly no UMP or UMPI test exists. We also examine a modification, suggested by the expression for the power envelope, of the Dickey-Fuller (1979) t-statistic; this test is also found to be approximately UMP (constant deterministic term case) and UMPI (time trend case). The power improvement of both new tests is large: in the demeaned case, the Pitman efficiency of the proposed tests relative to the standard Dickey-Fuller t-test is 1.9 at a power of 50%. A Monte Carlo experiment indicates that both proposed tests, particularly the modified Dickey-Fuller t-test, exhibit good power and small size distortions in finite samples with dependent errors.