Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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CHAIN DEPENDENCE AND STATIONARITY TEST FOR TRANSITION PROBABILITIES OF MARKOV CHAIN UNDER LOGISTIC REGRESSION MODEL

  • Sinha Narayan Chandra (Monitoring Cell, Finance Division, Ministry of Finance) ;
  • Islam M. Ataharul (Department of Statistics, University of Dhaka) ;
  • Ahmed Kazi Saleh (Department of Statistics, Jahangirnagar University)
  • Published : 2006.12.31
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Abstract

To identify whether the sequence of observations follows a chain dependent process and whether the chain dependent or repeated observations follow stationary process or not, alternative procedures are suggested in this paper. These test procedures are formulated on the basis of logistic regression model under the likelihood ratio test criterion and applied to the daily rainfall occurrence data of Bangladesh for selected stations. These test procedures indicate that the daily rainfall occurrences follow a chain dependent process, and the different types of transition probabilities and overall transition probabilities of Markov chain for the occurrences of rainfall follow a stationary process in the Mymensingh and Rajshahi areas, and non-stationary process in the Chittagong, Faridpur and Satkhira areas.

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References

  1. ANDERSON, T. W. AND GOODMAN, L. A. (1957). 'Statistical inference about Markov chains', The Annals of Mathematical Statistics, 28, 89-110 https://doi.org/10.1214/aoms/1177707039
  2. BARTLETT, M. S. (1951). 'The frequency goodness of fit test for probability chains', Mathematical Proceedings of the Cambridge Philosophical Society, 47, 86-95
  3. Cox, D. R. (1970). The Analysis of Binary Data, Methuen & Co., London
  4. GATES, P. AND TONG, H. (1976). 'On Markov chain modeling to some weather data', Journal of Applied Meteorology, 15, 1145-1151 https://doi.org/10.1175/1520-0450(1976)015<1145:OMCMTS>2.0.CO;2
  5. GOODMAN, L. A. (1955). 'On the statistical analysis of Markov chains (abstract)', The Annals of Mathematical Statistics, 26, 77l
  6. HOEL, P. G. (1954). 'A test for Markov chains', Biometrika, 41, 430-433 https://doi.org/10.1093/biomet/41.3-4.430
  7. ISLAM, M. A. (1994). 'Multistate survival models for transitions and reverse transitions: An application to contraceptive use data', Journal of the Royal Statistical Society, Ser. A, 157, 441-455 https://doi.org/10.2307/2983530
  8. KATZ, R. W. (1981). 'On some criteria for estimating the order of a Markov chain', Technometrics, 23, 243-249 https://doi.org/10.2307/1267787
  9. KENDALL, M. G. AND STUART, A. (1973). The advanced theory of statistics, 3rd ed., vol. 2, Griffin, London
  10. MUENZ, L. R. AND RUBINSTEIN, L. V. (1985). 'Markov models for covariate dependence of binary sequences', Biometrics, 41, 91-10l https://doi.org/10.2307/2530646
  11. SCHWARZ, G. (1978). 'Estimating the dimension of a model', The Annals of Statistics, 6, 461-464 https://doi.org/10.1214/aos/1176344136
  12. SHIBATA, R. (1976). 'Selection of the order of an autoregressive model by Akaike's information criterion', Biometrika, 63, 117-126 https://doi.org/10.1093/biomet/63.1.117
  13. SINHA, N. C. (1997). 'Probability models in forecasting rainfall with application to agriculture', Unpublished Ph.D. Thesis, Department of Statistics, Jahangirnagar University, Dhaka
  14. TONG, H. (1975). 'Determination of the order of a Markov chain by Akaike's information criterion', Journal of Applied Probability, 12,488-497 https://doi.org/10.2307/3212863