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Visualizing State Identification in Auto-Regressive Hidden Markov (ARHMM) Models With the Forward and Backward Algorithms Using Excel

Author

Listed:
  • William. H. Laverty
  • Ivan. W. Kelly

Abstract

Earlier articles, Laverty, Miket, Kelly (2002c), Laverty and Kelly (2019) used Excel to simulate Hidden Markov models and calculate the probabilities of the unknown states using the forward and backward algorithms (Rabiner, 1989). In those articles, independence between observations in each state were assumed. In many situations, however, the assumption of independence within states cannot be made. A more appropriate model for the data in this case would be an Autoregressive Hidden Markov model which accounts for serial correlation within states. In this article, a two-state ARHMM will be simulated with the forward-backward algorithm used to calculate conditional state probabilities given the observed data.

Suggested Citation

  • William. H. Laverty & Ivan. W. Kelly, 2019. "Visualizing State Identification in Auto-Regressive Hidden Markov (ARHMM) Models With the Forward and Backward Algorithms Using Excel," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(5), pages 25-33, September.
    • Handle: RePEc:ibn:ijspjl:v:8:y:2019:i:5:p:25
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    More about this item

    Keywords

    auto-regressive Hidden Markov model; forward algorithm; backward algorithm; state probabilities; Excel;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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