Lag truncation and the local asymptotic distribution of the ADF test for a unit root

Emre Aylar, Stephan Smeekes, Joakim Westerlund*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

The issue of lag selection in ADF unit root testing is important, even asymptotically, for if the number of lags is not allowed to increase at a certain rate the test might not be correctly sized. However, size control is not the only concern. Indeed, simulations have repeatedly shown how increasing lag lengths tend to be associated with reductions in power, thus adding to the well-known low power problem when the alternative is local to the unit root. But while the simulation evidence is plentiful, there is as of yet almost no asymptotic results that can be used to ascertain whether lag length has any effect on the local asymptotic power of the ADF test. The purpose of the present paper is to fill this gap in the literature.
Original languageEnglish
Pages (from-to)2109-2118
Number of pages10
JournalStatistical Papers
Volume60
Issue number6
DOIs
Publication statusPublished - Dec 2019

Keywords

  • ADF test
  • Unit root testing
  • Lag selection
  • Local asymptotic power
  • AUTOREGRESSIVE ROOTS
  • SELECTION
  • MODELS

Cite this

Aylar, Emre ; Smeekes, Stephan ; Westerlund, Joakim. / Lag truncation and the local asymptotic distribution of the ADF test for a unit root. In: Statistical Papers. 2019 ; Vol. 60, No. 6. pp. 2109-2118.
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Lag truncation and the local asymptotic distribution of the ADF test for a unit root. / Aylar, Emre; Smeekes, Stephan; Westerlund, Joakim.

In: Statistical Papers, Vol. 60, No. 6, 12.2019, p. 2109-2118.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Aylar, Emre

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AU - Westerlund, Joakim

N1 - data source: no data used

PY - 2019/12

Y1 - 2019/12

N2 - The issue of lag selection in ADF unit root testing is important, even asymptotically, for if the number of lags is not allowed to increase at a certain rate the test might not be correctly sized. However, size control is not the only concern. Indeed, simulations have repeatedly shown how increasing lag lengths tend to be associated with reductions in power, thus adding to the well-known low power problem when the alternative is local to the unit root. But while the simulation evidence is plentiful, there is as of yet almost no asymptotic results that can be used to ascertain whether lag length has any effect on the local asymptotic power of the ADF test. The purpose of the present paper is to fill this gap in the literature.

AB - The issue of lag selection in ADF unit root testing is important, even asymptotically, for if the number of lags is not allowed to increase at a certain rate the test might not be correctly sized. However, size control is not the only concern. Indeed, simulations have repeatedly shown how increasing lag lengths tend to be associated with reductions in power, thus adding to the well-known low power problem when the alternative is local to the unit root. But while the simulation evidence is plentiful, there is as of yet almost no asymptotic results that can be used to ascertain whether lag length has any effect on the local asymptotic power of the ADF test. The purpose of the present paper is to fill this gap in the literature.

KW - ADF test

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KW - Lag selection

KW - Local asymptotic power

KW - AUTOREGRESSIVE ROOTS

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KW - MODELS

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