Advertisement

Bayesian detection of structural changes

  • Nobuhisa Kashiwagi
Bayesian Procedure

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.

Key words and phrases

Bayesian inference change point predictive log likelihood Lindisfarne scribes problem regression 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akaike, H. (1977). On entropy maximization principle, Applications of Statistics (ed. P. R. Krishnaiah), 27–41, North-Holland, Amsterdam.Google Scholar
  2. Bacon, D. W. and Watts, D. G. (1971). Estimating the transition between two intersecting straight lines, Biometrika, 58, 525–534.Google Scholar
  3. 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
  4. 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
  5. 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
  6. Broemeling, L. D. and Tsurumi, H. (1987). Econometrics and Structural Change, Dekker, New York.Google Scholar
  7. Carlstein, E. (1988). Nonparametric change-point estimation, Ann. Statist., 16, 188–197.Google Scholar
  8. 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
  9. Harrison, P. J. and Stevens, C. F. (1976). Bayesian forecasting, J. Roy. Statist. Soc. Ser. B, 38, 205–247.Google Scholar
  10. Hinkley, D. V. (1969). Inference about the intersection in two-phase regression, Biometrika, 56, 495–504.Google Scholar
  11. Hinkley, D. V. (1970). Inference about the change-point in a sequence of random variables, Biometrika, 57, 1–17.Google Scholar
  12. Hinkley, D. V. (1971). Inference in two-phase regression, J. Amer. Statist. Assoc., 66, 736–743.Google Scholar
  13. James, B., James, K. L. and Siegmund, D. (1987). Tests for a change-point, Biometrika, 74, 71–83.Google Scholar
  14. Kitagawa, G. (1987). Non-Gaussian state-space modeling of nonstationary time series, J. Amer. Statist. Assoc., 82, 1032–1063.Google Scholar
  15. Kitagawa, G. and Akaike, H. (1982). A quasi Bayesian to outlier detection, Ann. Inst. Statist. Math., 34, 389–398.Google Scholar
  16. Lombard, F. (1987). Rank tests for changepoint problems, Biometrika, 74, 615–624.Google Scholar
  17. Page, E. S. (1954). Continuous inspection schemes, Biometrika, 41, 100–114.Google Scholar
  18. Pettitt, A. N. (1979). A non-parametric approach to the change-point problem, Appl. Statist., 28, 126–135.Google Scholar
  19. Poirier, D. J. (1976). The Econometrics of Structural Changes, North-Holland, Amsterdam.Google Scholar
  20. 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
  21. 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
  22. 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
  23. Silvey, S. D. (1958). The Lindisfarne scribes' problem, J. Roy. Statist. Soc. Ser. B, 20, 93–101.Google Scholar
  24. 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
  25. Smith, A. F. M. (1980). Change-point problems: approaches and applications, Trabajos Estadíst. Investigación Oper., 31, 83–98.Google Scholar
  26. Tanabe, K. and Tanaka, T. (1983). Fitting curves and surfaces by Bayesian models, Chikyu, 5, 179–186 (in Japanese).Google Scholar
  27. 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
  28. 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

Copyright information

© Kluwer Academic Publisher 1990

Authors and Affiliations

  • Nobuhisa Kashiwagi
    • 1
  1. 1.The Institute of Statistical MathematicsTokyoJapan

Personalised recommendations