SEMIPARAMETRICALLY POINT-OPTIMAL HYBRID RANK TESTS FOR UNIT ROOTS

• 成果类型: Article
• 署名作者: Zhou, Bo; van den Akker, Ramon; Werker, Bas J. M.
• 署名单位: Hong Kong University of Science & Technology; Tilburg University; Tilburg University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1758
• 发表日期: 2019
• 页码: 2601-2638
• 关键词: autoregressive time-series; ASYMPTOTIC INFERENCE; EFFICIENT TESTS; regressions; coefficient; stationary; models

摘要

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.