, Volume 75, Issue 5, pp 673–708 | Cite as

Bootstrapping sequential change-point tests for linear regression

  • Marie Hušková
  • Claudia KirchEmail author


Bootstrap methods for sequential change-point detection procedures in linear regression models are proposed. The corresponding monitoring procedures are designed to control the overall significance level. The bootstrap critical values are updated constantly by including new observations obtained from the monitoring. The theoretical properties of these sequential bootstrap procedures are investigated, showing their asymptotic validity. Bootstrap and asymptotic methods are compared in a simulation study, showing that the studentized bootstrap tests hold the overall level better especially for small historic sample sizes while having a comparable power and run length.


Bootstrap Sequential test Change-point analysis Linear regression 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andreou E, Ghysels E (2006) Monitoring disruptions in financial markets. J Economet 135: 77–124MathSciNetCrossRefGoogle Scholar
  2. Antoch J, Hušková M (2001) Permutation tests for change point analysis. Stat Probab Lett 53: 37–46zbMATHCrossRefGoogle Scholar
  3. Aue A, Horváth L, Hušková M, Kokoszka P (2006) Change-point monitoring in linear models. Economet J 9: 373–403zbMATHCrossRefGoogle Scholar
  4. Aue A, Hörmann S, Horváth L, Hušková M (2009) Sequential testing for the stability of portfolio betas. In preparationGoogle Scholar
  5. Berkes I, Horváth L, Hušková M, Steinebach J (2004) Applications of permutations to the simulations of critical values. J Nonparametr Stat 16: 197–216MathSciNetzbMATHCrossRefGoogle Scholar
  6. Chow YS, Teicher H (1997) Probability Theory—Independence, Interchangeability, Martingales. 3. Springer, New YorkzbMATHGoogle Scholar
  7. Chu C-SJ, Stinchcombe M, White H (1996) Monitoring structural change. Econometrica 64: 1045–1065zbMATHCrossRefGoogle Scholar
  8. Fried R, Imhoff M (2004) On the online detection of monotonic trends in time series. Biom J 46: 90–102MathSciNetCrossRefGoogle Scholar
  9. Good P (2005) Permutation, Parametric, and Bootstrap Tests of Hypothesis. 3. Springer, New YorkGoogle Scholar
  10. Horváth L, Hušková M, Kokoszka P, Steinebach J (2004) Monitoring changes in linear models. J Stat Plann Inference 126: 225–251zbMATHCrossRefGoogle Scholar
  11. Hušková M (2004) Permutation principle and bootstrap in change point analysis. Fields Inst Commun 44: 273–291Google Scholar
  12. Hušková M, Koubková A (2005) Monitoring jump changes in linear models. J Stat Res 39: 59–78Google Scholar
  13. Hušková M, Koubková A (2006) Sequential procedures for detection of changes in autoregressive sequences. In: Hušková M, Lachout P (eds) Proceedings of the Prague stochstics, pp 437–447Google Scholar
  14. Kirch C (2008) Bootstrapping sequential change-point tests. Seq Anal 27: 330–349MathSciNetzbMATHCrossRefGoogle Scholar
  15. Koubková A (2008) Change detection in the slope parameter of a linear regression model. Tatra Mt Math Publ 39: 245–253MathSciNetzbMATHGoogle Scholar
  16. Steland A (2006) A bootstrap view on Dickey-Fuller control charts for AR(1) series. Aust J Stat 35: 339–346Google Scholar
  17. von Bahr B, Esseen C-G (1965) Inequalities for the r th absolute moment of a sum of random variables, 1 ≤ r ≤ 2. Ann Math Stat 36: 299–303zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of StatisticsCharles University of PraguePraha 8Czech Republic
  2. 2.Institute for StochasticsKarlsruhe Institute of Technology (KIT)KarlsruheGermany

Personalised recommendations