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Semiparametrically point-optimal hybrid rank tests for unit roots. (English) Zbl 07114923
The main contribution of this paper is twofold. First, the authors derived the semiparametric power envelopes of unit root tests with serially correlated errors for two cases: symmetric or possibly non-symmetric innovation distributions . Their method of derivation seems to be novel and exploits the invariance structures embedded in the semiparametric unit root model. They use an application of the Asymptotic Representation Theorem (see, e.g., Theorem 15.1 in [A. W. van der Vaart, Asymptotic statistics. Cambridge: Cambridge Univ. Press (1998; Zbl 0910.62001)]) that subsequently yields the local asymptotic power envelope (Theorem 3.3).
As a second contribution, they provided two new classes of easy-to-implement unit root tests that are semiparametrically optimal in the sense that their asymptotic power curves are tangent to the associated semiparametric power envelopes.
Finally, the authors introduced a simplified version of the proposed test and they showed, in a Monte-Carlo study, that their theoretical results carry over to finite samples.
##### MSC:
 62M07 Non-Markovian processes: hypothesis testing 62G10 Nonparametric hypothesis testing 62G20 Asymptotic properties of nonparametric inference
itsmr; ITSM2000
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##### References:
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