Searching for additive outliers in nonstationary time series

Pierre Perron, Gabriel Rodríguez

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


Recently, Vogelsang (1999) proposed a method to detect outliers which explicitly imposes the null hypothesis of a unit root. It works in an iterative fashion to select multiple outlier in a given series. We show, via simulations, that, under the null hypothesis of no outliers, it has the right size in finite samples to detect a single outlier but, when applied in an iterative fashion to select multiple outliers, it exhibits severe size distortions towards finding an excessive number of outliers. We show that his iterative method is incorrect and derive the appropriate limiting distribution of the test at each step of the search. Whether corrected or not, we also show that the outliers need to be very large for the method to have any decent power. We propose an alternative method based on first-differenced data that has considerably more power. We also show that our method to identify outliers leads to unit root tests with more accurate finite sample size and robustness to departures from a unit root. The issues are illustrated using two US/Finland real-exchange rate series.

Original languageEnglish
Pages (from-to)193-220
Number of pages28
JournalJournal of Time Series Analysis
Issue number2
StatePublished - Mar 2003
Externally publishedYes


  • Additive outliers
  • Power. JEL: C2 C3 C5
  • Size
  • Unit root
  • Wiener process
  • t-test


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