Generalizations of the KPSS-test for stationarity

Bart Hobijn, Philip Hans Franses, Marius Ooms

Research output: Contribution to journalArticlepeer-review

86 Scopus citations


We propose automatic generalizations of the KPSS-test for the null hypothesis of stationarity of a univariate time series. We can use these tests for the null hypotheses of trend stationarity, level stationarity and zero mean stationarity. We introduce the asymptotic null distributions and we determine consistency against relevant nonstationary alternatives. We compare the properties of the tests with those of other proposed tests for stationarity. Monte Carlo simulations support the relevance of the tests when an autoregressive process with large positive autocorrelations is likely under the null hypothesis.

Original languageEnglish (US)
Pages (from-to)483-502
Number of pages20
JournalStatistica Neerlandica
Issue number4
StatePublished - Nov 2004
Externally publishedYes


  • Bandwidth selection
  • Choi's test
  • Heteroskedasticity and autocorrelation consistent covariance estimation
  • Leybourne and McCabe's test
  • Long run variance
  • Rate of consistency
  • Stationarity test
  • Time series

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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