Unit root tests and heavy-tailed innovations

Iliyan Georgiev, Paulo M M Rodrigues, A. M. Robert Taylor

Research output: Contribution to journalArticle

Abstract

We evaluate the impact of heavy-tailed innovations on some popular unit root tests. In the context of a near-integrated series driven by linear process shocks, we demonstrate that their limiting distributions are altered under infinite variance vis-à-vis finite variance. Reassuringly, however, simulation results suggest that the impact of heavy-tailed innovations on these tests is relatively small. We use the framework of Amsler and Schmidt () whereby the innovations have local-to-finite variances being generated as a linear combination of draws from a thin-tailed distribution (in the domain of attraction of the Gaussian distribution) and a heavy-tailed distribution (in the normal domain of attraction of a stable law). We also explore the properties of augmented Dickey-Fuller tests that employ Eicker-White standard errors, demonstrating that these can yield significant power improvements over conventional tests.

Original languageEnglish
Pages (from-to)733-768
JournalJournal Of Time Series Analysis
Volume38
Issue number5
DOIs
Publication statusPublished - Sep 2017

Keywords

  • Asymptotic local power functions
  • Eicker-White standard errors
  • Infinite variance
  • α-stable distribution

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