Efficient Tests for an Autoregressive Unit Root

Graham Elliott, Thomas J. Rothenberg, James H. Stock

NBER Technical Working Paper No. 130
Issued in December 1992
NBER Program(s):Economic Fluctuations and Growth

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.

download in pdf format
   (2595 K)

email paper

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/t0130

Published: Elliott, Graham, Thomas J. Rothenberg and James H. Stock. "Efficient Tests For An Autoregressive Unit Root," Econometrica, 1996, v64(4,Jul), 813-836.

Users who downloaded this paper also downloaded* these:
Staiger and Stock t0151 Instrumental Variables Regression with Weak Instruments
Campbell and Perron Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots
Campbell and Perron t0100 Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots
Schwert t0073 Tests For Unit Roots: A Monte Carlo Investigation
Diebold and Kilian w6928 Unit Root Tests Are Useful for Selecting Forecasting Models
NBER Videos

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us