ADMISSIBLE AND NONADMISSIBLE TESTS IN UNIT-ROOT-LIKE SITUATIONS

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+