Elliott, Graham
[VerfasserIn]
;
Stock, James H.
[Sonstige Person, Familie und Körperschaft];
Rothenberg, Thomas J.
[Sonstige Person, Familie und Körperschaft]National Bureau of Economic Research
Erschienen:
Cambridge, Mass: National Bureau of Economic Research, December 1992
Erschienen in:NBER technical working paper series ; no. t0130
Umfang:
1 Online-Ressource
Sprache:
Englisch
DOI:
10.3386/t0130
Identifikator:
Reproduktionsnotiz:
Hardcopy version available to institutional subscribers
Entstehung:
Anmerkungen:
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Beschreibung:
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