TY  - JOUR
AU  - Elliott,Graham
AU  - Rothenberg,Thomas J.
AU  - Stock,James H.
TI  - Efficient Tests for an Autoregressive Unit Root
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 130
PY  - 1992
Y2  - December 1992
UR  - http://www.nber.org/papers/t0130
L1  - http://www.nber.org/papers/t0130.pdf
N1  - Author contact info:
Graham Elliott
Department of Economics
UC, San Diego
9500 Gilman Drive
La Jolla, CA  92093
E-Mail: gelliott@weber.ucsd.edu

James H. Stock
Department of Economics
Harvard University
Littauer Center M27
Cambridge, MA 02138
Tel: 617/496-0502
Fax: 617/495-7730
E-Mail: James_Stock@harvard.edu
AB  - 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.
ER  -