A Higher-order interactive hidden Markov model and its applications

Dong Mei Zhu, Wai Ki Ching, Robert J. Elliott, Tak Kuen Siu, Lianmin Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this paper, we propose a higher-order interactive hidden Markov model, which incorporates both the feedback effects of observable states on hidden states and their mutual long-term dependence. The key idea of this model is to assume the probability laws governing both the observable and hidden states can be written as a pair of higher-order stochastic difference equations. We also present an efficient procedure, a heuristic algorithm, to estimate the hidden states of the chain and the model parameters. Real applications in SSE Composite Index data and default data are given to demonstrate the effectiveness of our proposed model and corresponding estimation method.

Original languageEnglish
Pages (from-to)1055-1069
Number of pages15
JournalOR Spectrum
Issue number4
Publication statusPublished - 1 Oct 2017


  • Feedback effect
  • Hidden Markov model
  • Interactive hidden Markov model
  • Stochastic difference equations


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