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Bayesian change-point modeling with segmented ARMA model.

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This study introduces a Bayesian change-point model for time series segmentation, improving the detection of segment boundaries and dynamical properties. The novel method, utilizing an autoregressive moving average model, identifies more change-points than existing techniques.

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Area of Science:

  • Statistics and Data Science
  • Time Series Analysis
  • Geophysics and Earth Sciences

Background:

  • Time series segmentation is crucial for identifying structural changes and underlying dynamics in sequential data.
  • Existing methods for time series segmentation may lack the sensitivity to detect all relevant change-points.
  • Accurate segmentation is vital in fields like geophysics for interpreting subsurface rock properties.

Purpose of the Study:

  • To develop a novel Bayesian change-point model for robust time series segmentation.
  • To accurately identify segment boundary points and determine dynamical properties within each segment.
  • To enhance the detection of change-points compared to existing methodologies.

Main Methods:

  • A Bayesian change-point model is proposed, assuming data within segments follows an autoregressive moving average (ARMA) model.
  • Prior distributions are defined for change-point number, positions, segment means, and error terms.
  • The Generalized Gibbs sampler Markov chain Monte Carlo technique is employed to sample posterior probability distributions for uncertainty quantification.

Main Results:

  • The proposed model demonstrates high sensitivity in detecting change-points in time series data.
  • Application to simulated and real-world well-log data reveals a greater number of identified change-points compared to comparable methods.
  • The methodology effectively quantifies uncertainty in the location of detected change-points.

Conclusions:

  • The Bayesian change-point model offers a powerful and sensitive approach for time series segmentation.
  • This method significantly improves the identification of structural breaks and dynamical changes in sequential data.
  • The approach shows particular promise for analyzing complex geological data, such as well-log measurements.