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Bayesian methods for change‐point detection in long‐range dependent processes

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  • Bonnie K. Ray
  • Ruey S. Tsay

Abstract

. We describe a Bayesian method for detecting structural changes in a long‐range dependent process. In particular, we focus on changes in the long‐range dependence parameter, d, and changes in the process level, μ. Markov chain Monte Carlo (MCMC) methods are used to estimate the posterior probability and size of a change at time t, along with other model parameters. A time‐dependent Kalman filter approach is used to evaluate the likelihood of the fractionally integrated ARMA model characterizing the long‐range dependence. The method allows for multiple change points and can be extended to the long‐memory stochastic volatility case. We apply the method to three examples, to investigate a change in persistence of the yearly Nile River minima, to investigate structural changes in the series of durations between intraday trades of IBM stock on the New York Stock Exchange, and to detect structural breaks in daily stock returns for the Coca Cola Company during the 1990s.

Suggested Citation

  • Bonnie K. Ray & Ruey S. Tsay, 2002. "Bayesian methods for change‐point detection in long‐range dependent processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(6), pages 687-705, November.
    • Handle: RePEc:bla:jtsera:v:23:y:2002:i:6:p:687-705
    DOI: 10.1111/1467-9892.00286
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    Cited by:

    1. Beran, Jan, 2007. "On parameter estimation for locally stationary long-memory processes," CoFE Discussion Papers 07/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    2. Luisa Bisaglia & Matteo Grigoletto, 2018. "A new time-varying model for forecasting long-memory series," Papers 1812.07295, arXiv.org.
    3. Phillips, Nathaniel D. & Neth, Hansjörg & Woike, Jan K. & Gaissmaier, Wolfgang, 2017. "FFTrees: A toolbox to create, visualize, and evaluate fast-and-frugal decision trees," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 12(4), pages 344-368.
    4. Luisa Bisaglia & Matteo Grigoletto, 2021. "A new time-varying model for forecasting long-memory series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 139-155, March.
    5. Jiawen Xu & Pierre Perron, 2015. "Forecasting in the presence of in and out of sample breaks," Boston University - Department of Economics - Working Papers Series wp2015-012, Boston University - Department of Economics.
    6. Cathy W. S. Chen & Bonny Lee, 2021. "Bayesian inference of multiple structural change models with asymmetric GARCH errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 1053-1078, September.

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