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Efficient Tests for an Autoregressive Unit Root
Abstract
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.
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Metadata
- Authors
- Elliott, G., Rothenberg, T. J., & Stock, J. H.
- Venue
- Econometrica
- Publisher
- JSTOR
- Published
- 1996-07
- Volume
- 64
- Issue
- 4
- Pages
- 813
- ISSN
- 0012-9682 (ISSN-L)
- OpenAlex
- W2149292156
- Cited by
- 5,627
- References
- 0
- FWCI
- 37.70
- Type
- journal article
- Language
- en
- Open access
- closed
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