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Asymptotic and Bootstrap Tests for a Change in Autoregression Omitting Variability Estimation

  • Barbora Peštová
  • Michal PeštaEmail author
Conference paper
  • 1.1k Downloads
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

A sequence of time-ordered observations follows an autoregressive model of order one and its parameter is possibly subject to change at most once at some unknown time point. The aim is to test whether such an unknown change has occurred or not. A change-point method presented here rely on a ratio type test statistic based on the maxima of cumulative sums. The main advantage of the developed approach is that the variance of the observations neither has to be known nor estimated. Asymptotic distribution of the test statistic under the no-change null hypothesis is derived. Moreover, we prove the consistency of the test under the alternative. A bootstrap procedure is proposed in the way of a completely data-driven technique without any tuning parameters. The results are illustrated through a simulation study, which demonstrates the computational efficiency of the procedure. A practical application to real data is presented as well.

Keywords

Change point Structural change Change in autoregression Hypothesis testing Bootstrap Ratio type statistic Variance estimation free test 

Notes

Acknowledgements

Institutional support to Barbora Peštová was provided by RVO:67985807. Michal Pešta was supported by the Czech Science Foundation project No. 18-01781Y.

References

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of Computer ScienceThe Czech Academy of SciencesPragueCzech Republic
  2. 2.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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