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Semiparametrically point-optimal hybrid rank tests for unit roots

Zhou, B.; Van Den Akker, R.; Werker, Bas J.M.

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B. Zhou

R. Van Den Akker

Bas J.M. Werker


We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, that is, have the correct (asymptotic) size, irrespective of the true innovation density. For a correctly specified reference density, our test is point-optimal and nearly efficient. For arbitrary reference densities, we establish a Chernoff–Savage-type result, that is, our test performs as well as commonly used tests under Gaussian innovations but has improved power under other, for example, fat-tailed or skewed, innovation distributions. To avoid nonparametric estimation, we propose a simplified version of our test that exhibits the same asymptotic properties, except for the Chernoff–Savage result that we are only able to demonstrate by means of simulations.


Zhou, B., Van Den Akker, R., & Werker, B. J. (2019). Semiparametrically point-optimal hybrid rank tests for unit roots. Annals of Statistics, 47(5), 2601-2638.

Journal Article Type Article
Acceptance Date Aug 3, 2019
Online Publication Date Aug 3, 2019
Publication Date Oct 31, 2019
Deposit Date Sep 3, 2019
Publicly Available Date Nov 8, 2019
Journal Annals of Statistics
Print ISSN 0090-5364
Publisher Institute of Mathematical Statistics
Peer Reviewed Peer Reviewed
Volume 47
Issue 5
Pages 2601-2638
Public URL


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