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A Higher-order interactive hidden Markov model and its applications

Author

Listed:
  • Dong-Mei Zhu

    (Southeast University)

  • Wai-Ki Ching

    (The University of Hong Kong)

  • Robert J. Elliott

    (University of Adelaide)

  • Tak-Kuen Siu

    (Macquarie University)

  • Lianmin Zhang

    (Nanjing University)

Abstract

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.

Suggested Citation

  • Dong-Mei Zhu & Wai-Ki Ching & Robert J. Elliott & Tak-Kuen Siu & Lianmin Zhang, 2017. "A Higher-order interactive hidden Markov model and its applications," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1055-1069, October.
    • Handle: RePEc:spr:orspec:v:39:y:2017:i:4:d:10.1007_s00291-017-0484-0
    DOI: 10.1007/s00291-017-0484-0
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    References listed on IDEAS

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    1. Berry, Michael W. & Browne, Murray & Langville, Amy N. & Pauca, V. Paul & Plemmons, Robert J., 2007. "Algorithms and applications for approximate nonnegative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 155-173, September.
    2. Wai-Ki Ching & Michael K. Ng, 2006. "Markov Chains: Models, Algorithms and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-29337-0, April.
    3. Kwai Leung & Yue Kwok, 2009. "Counterparty Risk for Credit Default Swaps: Markov Chain Interacting Intensities Model with Stochastic Intensity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(3), pages 169-181, September.
    4. Girardin, Eric & Joyeux, Roselyne, 2013. "Macro fundamentals as a source of stock market volatility in China: A GARCH-MIDAS approach," Economic Modelling, Elsevier, vol. 34(C), pages 59-68.
    5. Nigel J. Cutland & Ekkehard Kopp & Walter Willinger, 1993. "From Discrete to Continuous Financial Models: New Convergence Results For Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 101-123, April.
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