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Non-Parametric Change-Point Estimation using String Matching Algorithms

Author

Listed:
  • Oliver Johnson

    (University of Bristol)

  • Dino Sejdinovic

    (University College London)

  • James Cruise

    (Heriot-Watt University Edinburgh Campus)

  • Robert Piechocki

    (University of Bristol)

  • Ayalvadi Ganesh

    (University of Bristol)

Abstract

Given the output of a data source taking values in a finite alphabet, we wish to estimate change-points, that is times when the statistical properties of the source change. Motivated by ideas of match lengths in information theory, we introduce a novel non-parametric estimator which we call CRECHE (CRossings Enumeration CHange Estimator). We present simulation evidence that this estimator performs well, both for simulated sources and for real data formed by concatenating text sources. For example, we show that we can accurately estimate the point at which a source changes from a Markov chain to an IID source with the same stationary distribution. Our estimator requires no assumptions about the form of the source distribution, and avoids the need to estimate its probabilities. Further, establishing a fluid limit and using martingale arguments.

Suggested Citation

  • Oliver Johnson & Dino Sejdinovic & James Cruise & Robert Piechocki & Ayalvadi Ganesh, 2014. "Non-Parametric Change-Point Estimation using String Matching Algorithms," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 987-1008, December.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:4:d:10.1007_s11009-013-9359-2
    DOI: 10.1007/s11009-013-9359-2
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    References listed on IDEAS

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    1. Alex Riba & Josep Ginebra, 2005. "Change-point estimation in a multinomial sequence and homogeneity of literary style," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(1), pages 61-74.
    2. Aggarwal, Reena & Inclan, Carla & Leal, Ricardo, 1999. "Volatility in Emerging Stock Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 33-55, March.
    3. Giron, Javier & Ginebra, Josep & Riba, Alex, 2005. "Bayesian Analysis of a Multinomial Sequence and Homogeneity of Literary Style," The American Statistician, American Statistical Association, vol. 59, pages 19-30, February.
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