Skip to main content
Log in

Bayesian detection of structural changes

  • Bayesian Procedure
  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Abstract

A Bayesian solution is given to the problem of making inferences about an unknown number of structural changes in a sequence of observations. Inferences are based on the posterior distribution of the number of change points and on the posterior probabilities of possible change points. Detailed analyses are given for binomial data and some regression problems, and numerical illustrations are provided. In addition, an approximation procedure to compute the posterior probabilities is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Akaike, H. (1977). On entropy maximization principle, Applications of Statistics (ed. P. R. Krishnaiah), 27–41, North-Holland, Amsterdam.

    Google Scholar 

  • Bacon, D. W. and Watts, D. G. (1971). Estimating the transition between two intersecting straight lines, Biometrika, 58, 525–534.

    Google Scholar 

  • Bhattacharya, G. K. and Johnson, R. A. (1968). Nonparametric tests for shift at an unknown time point, Ann. Math. Statist., 39, 1731–1743.

    Google Scholar 

  • Booth, N. B. and Smith, A. F. M. (1982). A Bayesian approach to retrospective identification of change-points, J. Econometrics, 19, 7–22.

    Google Scholar 

  • Box, G. E. P. and Tiao, G. C. (1965). A change in level of a non-stationary time series, Biometrika, 52, 181–192.

    Google Scholar 

  • Broemeling, L. D. and Tsurumi, H. (1987). Econometrics and Structural Change, Dekker, New York.

    Google Scholar 

  • Carlstein, E. (1988). Nonparametric change-point estimation, Ann. Statist., 16, 188–197.

    Google Scholar 

  • Chernoff, H. and Zacks, S. (1964). Estimating the current mean of a normal distribution which is subjected to changes in time, Ann. Math. Statist., 35, 999–1018.

    Google Scholar 

  • Harrison, P. J. and Stevens, C. F. (1976). Bayesian forecasting, J. Roy. Statist. Soc. Ser. B, 38, 205–247.

    Google Scholar 

  • Hinkley, D. V. (1969). Inference about the intersection in two-phase regression, Biometrika, 56, 495–504.

    Google Scholar 

  • Hinkley, D. V. (1970). Inference about the change-point in a sequence of random variables, Biometrika, 57, 1–17.

    Google Scholar 

  • Hinkley, D. V. (1971). Inference in two-phase regression, J. Amer. Statist. Assoc., 66, 736–743.

    Google Scholar 

  • James, B., James, K. L. and Siegmund, D. (1987). Tests for a change-point, Biometrika, 74, 71–83.

    Google Scholar 

  • Kitagawa, G. (1987). Non-Gaussian state-space modeling of nonstationary time series, J. Amer. Statist. Assoc., 82, 1032–1063.

    Google Scholar 

  • Kitagawa, G. and Akaike, H. (1982). A quasi Bayesian to outlier detection, Ann. Inst. Statist. Math., 34, 389–398.

    Google Scholar 

  • Lombard, F. (1987). Rank tests for changepoint problems, Biometrika, 74, 615–624.

    Google Scholar 

  • Page, E. S. (1954). Continuous inspection schemes, Biometrika, 41, 100–114.

    Google Scholar 

  • Pettitt, A. N. (1979). A non-parametric approach to the change-point problem, Appl. Statist., 28, 126–135.

    Google Scholar 

  • Poirier, D. J. (1976). The Econometrics of Structural Changes, North-Holland, Amsterdam.

    Google Scholar 

  • Quandt, R. E. (1958). The estimation of the parameters of a linear regression system obeying two separate regimes, J. Amer. Statist. Assoc., 53, 873–880.

    Google Scholar 

  • Quandt, R. E. (1960). Tests of the hypothesis that a linear regression system obeys two separate regimes. J. Amer. Statist. Assoc., 55, 324–330.

    Google Scholar 

  • Schechtman, E. and Wolfe, D. A. (1985). Multiple change points problem—nonparametric procedures for estimation of the points of change, Comm. Statist. B—Simulation Comput., 14, 615–631.

    Google Scholar 

  • Silvey, S. D. (1958). The Lindisfarne scribes' problem, J. Roy. Statist. Soc. Ser. B, 20, 93–101.

    Google Scholar 

  • Smith, A. F. M. (1975). A Bayesian approach to inference about a change-point in a sequence of random variables, Biometrika, 62, 407–416.

    Google Scholar 

  • Smith, A. F. M. (1980). Change-point problems: approaches and applications, Trabajos Estadíst. Investigación Oper., 31, 83–98.

    Google Scholar 

  • Tanabe, K. and Tanaka, T. (1983). Fitting curves and surfaces by Bayesian models, Chikyu, 5, 179–186 (in Japanese).

    Google Scholar 

  • Tsurumi, H., Wago, H. and Ilmakunnas, P. (1986). Gradual switching multivariate regression models with stochastic cross-equational constraints and an application to the KLEM translog production model, J. Econometrics, 31, 235–253.

    Google Scholar 

  • Zacks, S. (1983). Survey of classical and Bayesian approaches to the change-point problem: fixed sample and sequential procedures of testing and estimation, Recent Advances in Statistics (eds. M. H. Rizvi, J. S. Rustagi and D. O. Siegmund), 245–269, Academic Press, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Kashiwagi, N. Bayesian detection of structural changes. Ann Inst Stat Math 43, 77–93 (1991). https://doi.org/10.1007/BF00116470

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00116470

Key words and phrases

Navigation