Semiparametrically point-optimal hybrid rank tests for unit roots

Bo Zhou*, Ramon van den Akker, Bas J. M. Werker

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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.
Original languageEnglish
Pages (from-to)2601-2638
JournalThe Annals of Statistics
Volume47
Issue number5
DOIs
Publication statusPublished - Oct 2019

Keywords

  • Unit root test
  • semiparametric power envelope
  • limit experiment
  • LABF
  • maximal invariant
  • rank statistic
  • AUTOREGRESSIVE TIME-SERIES
  • ASYMPTOTIC INFERENCE
  • EFFICIENT TESTS
  • REGRESSIONS
  • COEFFICIENT
  • STATIONARY
  • MODELS

Cite this

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title = "Semiparametrically point-optimal hybrid rank tests for unit roots",
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.",
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author = "Bo Zhou and {van den Akker}, Ramon and Werker, {Bas J. M.}",
year = "2019",
month = "10",
doi = "10.1214/18-AOS1758",
language = "English",
volume = "47",
pages = "2601--2638",
journal = "The Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
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}

Semiparametrically point-optimal hybrid rank tests for unit roots. / Zhou, Bo; van den Akker, Ramon; Werker, Bas J. M.

In: The Annals of Statistics, Vol. 47, No. 5, 10.2019, p. 2601-2638.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Semiparametrically point-optimal hybrid rank tests for unit roots

AU - Zhou, Bo

AU - van den Akker, Ramon

AU - Werker, Bas J. M.

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N2 - 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.

AB - 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.

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KW - EFFICIENT TESTS

KW - REGRESSIONS

KW - COEFFICIENT

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