Spectral approach to parameter-free unit root testing

Natalia Bailey, Liudas Giraitis

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

A relatively simple frequency-type testing procedure for unit root potentially contaminated by an additive stationary noise is introduced, which encompasses general settings and allows for linear trends. The proposed test for unit root versus stationarity is based on a finite number of periodograms computed at low Fourier frequencies. It is not sensitive to the selection of tuning parameters defining the range of frequencies so long as they are in the vicinity of zero. The test does not require augmentation, has parameter-free non-standard asymptotic distribution and is correctly sized. The consistency rate under the alternative of stationarity reveals the relation between the power of the test and the long-run variance of the process. The finite sample performance of the test is explored in a Monte Carlo simulation study, and its empirical application suggests rejection of the unit root hypothesis for some of the Nelson–Plosser time series.

Original languageEnglish
Pages (from-to)4-16
Number of pages13
JournalComputational Statistics and Data Analysis
Volume100
DOIs
Publication statusPublished - Aug 2016
Externally publishedYes

Keywords

  • Additive noise
  • Parameter-free distribution
  • Unit root test

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