Semiparametrically point-optimal hybrid rank tests for unit roots. (English) Zbl 1469.62330
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.
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.
Reviewer: Romeo Negrea (Timişoara)
MSC:
| 62M07 | Non-Markovian processes: hypothesis testing |
| 62G10 | Nonparametric hypothesis testing |
| 62G20 | Asymptotic properties of nonparametric inference |
Keywords:
unit root test; semiparametric power envelope; limit experiment; LABF; maximal invariant; rank statisticCitations:
Zbl 0910.62001References:
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