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Tests of Markov Order and Homogeneity in a Markov Chain


  • Jonsson, Robert

    () (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)


A three-state non-homogeneous Markov chain (MC) of order m>=0, denoted M(m), was previously introduced by the author. The model was used to analyze work resumption among sick-listed patients. It was demonstrated that wrong assumptions about the Markov order m and about homogeneity can seriously invalidate predictions of future health states. In this paper focus is on tests (estimation) of m and of homogeneity. When testing for Markov order it is suggested to test M(m) against M(m+1) with m sequentially chosen as 0, 1, 2,…, until the null hypothesis can’t be rejected. Two test statistics are used, one based on the Maximum Likelihood ratio (MLR) and one based on a chi-square criterion. Also more formal test strategies based on Akaike’s and Baye’s information criteria are considered. Tests of homogeneity are based on MLR statistics. The performance of the tests is evaluated in simulation studies. The tests are applied to rehabilitation data where it is concluded that the rehabilitation process develops according to a non-homogeneous Markov chain of order 2, possibly changing to a homogeneous chain of order 1 towards the end of the period.

Suggested Citation

  • Jonsson, Robert, 2011. "Tests of Markov Order and Homogeneity in a Markov Chain," Research Reports 2011:7, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
  • Handle: RePEc:hhs:gunsru:2011_007

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    References listed on IDEAS

    1. P. J. Avery & D. A. Henderson, 1999. "Fitting Markov chain models to discrete state series such as DNA sequences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 53-61.
    2. J. P. Hughes & P Guttorp & S. P. Charles, 1999. "A non-homogeneous hidden Markov model for precipitation occurrence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 15-30.
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    Cited by:

    1. Jonsson, Robert, 2011. "A Markov Chain Model for Analysing the Progression of Patient’s Health States," Research Reports 2011:6, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.

    More about this item


    Likelihood ratio; Test power; Bias of tests;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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