Abstract
Let a realization of a time series be given, which coincides with that of an autoregressive Process except for a single observation. The location of this value is assumed to be known. In order to desctibe the outlier a slippage model is used. In this paper we deal with the testing problem, Whether an outlier is present or not If some parameters x are assumed to be know, we are able to give a UMPU test (x) In the case x unknown we replace x by a suitable estimator x and obtain a test (x). Severak tests are introduced and the asymptotic distributions of the test statistics are derived. A comparison of the asymptotic power functins shows that is the best of these tests.
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