Efficient tests for an autoregressive unit root. (English) Zbl 0888.62088

Summary: The asymptotic power envelope is derived for point-optimal tests of a unit root in the autoregressive representation of a Gaussian time series under various trend specifications. We propose a family of tests whose asymptotic power functions are tangent to the power envelope at one point and are never far below the envelope. When the series has no deterministic component, some previously proposed tests are shown to be asymptotically equivalent to members of this family. When the series has an unknown mean or linear trend, commonly used tests are found to be dominated by members of the family of point-optimal invariant tests. We propose a modified version of the Dickey-Fuller \(t\) test [see D. A. Dickey and W. A. Fuller, J. Am. Stat. Assoc. 74, 427-431 (1979; Zbl 0413.62075)] which has substantially improved power when an unknown mean or trend is present. A Monte Carlo experiment indicates that the modified test works well in small samples.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P20 Applications of statistics to economics


Zbl 0413.62075
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