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October 2019 Semiparametrically point-optimal hybrid rank tests for unit roots
Bo Zhou, Ramon van den Akker, Bas J. M. Werker
Ann. Statist. 47(5): 2601-2638 (October 2019). DOI: 10.1214/18-AOS1758

Abstract

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.

Citation

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Bo Zhou. Ramon van den Akker. Bas J. M. Werker. "Semiparametrically point-optimal hybrid rank tests for unit roots." Ann. Statist. 47 (5) 2601 - 2638, October 2019. https://doi.org/10.1214/18-AOS1758

Information

Received: 1 March 2017; Revised: 1 June 2018; Published: October 2019
First available in Project Euclid: 3 August 2019

zbMATH: 07114923
MathSciNet: MR3988767
Digital Object Identifier: 10.1214/18-AOS1758

Subjects:
Primary: 62G10, 62G20
Secondary: 62M10, 62P20

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 5 • October 2019
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