Nonmonotonic power for tests of a mean shift in a time series

Ciprian M. Crainiceanu, Timothy J. Vogelsang

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


The null hypothesis-based statistics CUSUM and QS are widely used for testing parameter stability. We provide examples, extensive simulation studies and theoretical results showing that these statistics fail to detect obvious shifts in the mean of a time series. Moreover, the detection probability can decrease when the magnitude of the shift in mean increases. Estimation of nuisance parameters under the null is identified as an important cause of this counterintuitive behavior of the power function. Results indicate that tests designed for the specific alternative of a shift in mean of a time series should be preferred.

Original languageEnglish (US)
Pages (from-to)457-476
Number of pages20
JournalJournal of Statistical Computation and Simulation
Issue number6
StatePublished - Jan 1 2007


  • CUSUM test
  • Change point
  • HAC estimator
  • Serial correlation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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