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ADMISSIBLE AND NONADMISSIBLE TESTS IN UNIT-ROOT-LIKE SITUATIONS

Published online by Cambridge University Press:  06 September 2007

Werner Ploberger
Werner Ploberger
Affiliation:
Washington University in St. Louis
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Abstract

This paper investigates the asymptotic behavior of tests in situations where the likelihood is locally asymptotically quadratic. Necessary and sufficient conditions are given for a test to be admissible. Even without these restrictive parametric assumptions, it is shown that certain common procedures—such as the augmented Dickey–Fuller test in cases where no deterministic trend is present or standard tests for restrictions on cointegrating relationships—are asymptotically inadmissible. These results confirm the existence of tests that dominate these classical tests for all parameters.I express my gratitude to the editors, H. Lütkepohl and especially Peter C.B. Phillips, for their help, which enormously exceeded the usual amount of support. Also I thank the referees for their helpful comments. Their contribution greatly improved the paper. All remaining errors are mine.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 1 , February 2008 , pp. 15 - 42
Copyright
© 2008 Cambridge University Press

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