Semiparametrically point-optimal hybrid rank tests for unit roots
Bo Zhou, Ramon van den Akker, Bas J. M. Werker
The Annals of Statistics · 2019 · Volume 47 · Issue 5
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.
Keywords
62G10, 62G20, 62M10, 62P20, LABF, Limit experiment, maximal invariant, rank statistic, semiparametric power envelope, unit root test
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