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.
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Acknowledgements
The authors would like to thank AE and tow referees for their detailed comments and suggestions. This research work is supported by Research Grants Council of Hong Kong under Grant Number 17301214 and HKU CERG Grants, HKU Strategic Research Theme on Computation and Information, National Natural Science Foundation of China Under Grant number 71501093 and 71601044, the Basic Research Foundation (Natural Science) of Jiangsu Province with Grant number BK20150566 and Fundamental Research Funds for the Central Universities with number 011814380024.
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Zhu, DM., Ching, WK., Elliott, R.J. et al. A Higher-order interactive hidden Markov model and its applications. OR Spectrum 39, 1055–1069 (2017). https://doi.org/10.1007/s00291-017-0484-0
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DOI: https://doi.org/10.1007/s00291-017-0484-0