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Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting

  • Fuqi Chen
  • Rogemar MamonEmail author
  • Sévérien Nkurunziza
Article

Abstract

Determining accurately when regime and structural changes occur in various time-series data is critical in many social and natural sciences. We develop and show further the equivalence of two consistent estimation techniques in locating the change point under the framework of a generalised version of the one-dimensional Ornstein–Uhlenbeck process. Our methods are based on the least sum of squared error and the maximum log-likelihood approaches. The case where both the existence and the location of the change point are unknown is investigated and an informational methodology is employed to address these issues. Numerical illustrations are presented to assess the methods’ performance.

Keywords

Sequential analysis Least sum of squared errors Maximum likelihood Consistent estimator Existence of change point 

Notes

Acknowledgements

F. Chen and R. Mamon would like to acknowledge the financial support, via a Fields Postdoctoral Fellowship for F. Chen, provided by the Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada, where this research was initially conceived and partially conducted. R. Mamon wishes to express his appreciation for the hospitality of the Division of Physical Sciences and Mathematics, University of the Philippines Visayas, where certain revisions of this paper were made during his academic visit both as an Adjunct Professor and a DOST-PCIEERD Balik Scientist for the Philippine government. Both S. Nkurunziza and R. Mamon thank the Natural Sciences and Engineering Research Council of Canada for the support of their research. Likewise, all authors are grateful to Charmaine Dean (Western University’s Dean of Science) and Matt Davison (Canada Research Chair in Quantitative Finance) for their generous financial support on this research collaboration. Some valuable feedback from Charmaine Dean and Reg Kuperger are very much appreciated. Finally, the authors sincerely thank the Associate Editor and an anonymous referee for their helpful comments.

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  • Fuqi Chen
    • 1
  • Rogemar Mamon
    • 1
    • 2
    Email author
  • Sévérien Nkurunziza
    • 3
  1. 1.Department of Statistical and Actuarial SciencesUniversity of Western OntarioLondonCanada
  2. 2.Division of Physical Sciences and MathematicsUniversity of the Philippines VisayasMiag-ao, IloiloPhilippines
  3. 3.Department of Mathematics and StatisticsUniversity of WindsorWindsorCanada

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