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Autoregressive Modelling of Markov Chains

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Statistical Modelling

Part of the book series: Lecture Notes in Statistics ((LNS,volume 104))

Abstract

The reduction of the number of parameters in high-order Markov chain already inspired several articles. In particular, Raftery (1985) proposed an autoregressive modelling which utilizes a same transition matrix for every lag. In this paper, we show that a model of the same type, but utilizing different matrices, gives best results and is not harder to estimate, even when the number of data is small.

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References

  • Berchtold, A. (1994). Modélisation autorégressive des chaînes de Markov d’ordre l. Cahiers du Département d’Econométrie, 94.07, Université de Genève.

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  • Kemeny, J.G. & Snell, J.L. (1976). Finite Markov Chains.. Springer-Verlag.

    MATH  Google Scholar 

  • Logan, J.A. (1981). A Structural Model of the Higher-Order Markov Process Incorporating Reversion Effects. The Journal of Mathematical Sociology, Vol. 8, 75–89.

    Article  MATH  Google Scholar 

  • Pegram, G.G.S. (1980). An Autoregressive Model for Multilag Markov 12 Chains. Journal of Applied Probability, Vol. 17, 350–362.

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  • Raftery, A.E. (1985). A Model for High-Order Markov Chains. Journal of the Royal Statistical Society B, Vol. 47, No 3, 528–539.

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  • Raftery, G.G.S. & Tavaré, S. (1994). Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model. Applied Statistics, Vol. 43, No 1, 179–199.

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Authors
  1. André Berchtold
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Editor information

Editors and Affiliations

  1. Institut für Statistik, Universität Innsbruck, Christoph-Probst-Platz, Innsbruck, A-6020, Austria

    Gilg U. H. Seeber  & Gabriele Steckel-Berger  & 

  2. Centre for Applied Statistics, Lancaster University Fylde College, Lancaster, LA1 4YF, England

    Brian J. Francis

  3. Institut für Statistik, Wirtschaftsuniversität, Augasse 2-6, Wien, A-1090, Austria

    Reinhold Hatzinger

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© 1995 Springer Science+Business Media New York

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Berchtold, A. (1995). Autoregressive Modelling of Markov Chains. In: Seeber, G.U.H., Francis, B.J., Hatzinger, R., Steckel-Berger, G. (eds) Statistical Modelling. Lecture Notes in Statistics, vol 104. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0789-4_3

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  • DOI: https://doi.org/10.1007/978-1-4612-0789-4_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94565-1

  • Online ISBN: 978-1-4612-0789-4

  • eBook Packages: Springer Book Archive

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