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A Simplified Higher-Order Markov Chain Model
In this paper, we present a simplified higher-order Markov chain model for multiple categorical data sequences also called as simplified higher-order multivariate Markov chain model.
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[1] W. Ching, E. Fung and M. Ng, A multivariate Markov chain model for categorical data sequences and its applications in demand prediction, IMA, Journal of Management Mathematics, 13 (2002) 187-199.
[2] W. Ching, E. Fung, and M. Ng, A Higher-order Markov model for the newsboys problem, J. Operational Research Society, 54 (2003) 291-298.
[3] W. Ching, E. Fung and M. Ng, Higher-order Markov chain models for categorical data sequences, Inter. J. Nav. Res. Logist., 51 (2004) 557-574.
[4] W. Ching, M. Ng and E. Fung, On Construction of stochastic genetic networks based on gene expression sequences, International Journal of Neural Systems, 15 (2005) 297-310.
[5] W. Ching and M. Ng, Markov chains: models, algorithms and applications, International Series on Operations Research and Management Science, 2006.
[6] W. Ching, Building higher-order Markov chain models with EXCEL, Intern. J. Mathematical Education in Science and Engineering, 35 (2004) 921-932.
[7] W. Ching, M. Ng, and E. Fung, Higher-order multivariate Markov chains and their applications, Linear Algebra and its Applications, 428 (2008) 492-507.
[8] W. Ching, T. Siu and L. Li, A improved parsimonious multivariate Markov chain model for credit risk, Journal of Credit Risk, 5 (2009) 1-25.
[9] W. Ching, H. Leung, H. Jiang, L. Sun, and T. Siu, A Markovian network model for default risk management, International Journal of Intelligent Engineering Informatics, 1 (2010) 104-124.
[10] V. Chvatal, Linear programming, Freeman, 1983.
[11] M. Davis and V. Lo, Modeling default correlation in bond portfolios, In Mastering Risk, 2 (2001) 141-151.
[12] R. Horn and C. Johnson, Matrix analysis, Cambridge University Press,
[13] M. Kijima, K. Komoribayashi and E. Suzuki, A multivariate Markov model for simulating correlated defaults, Journal of Risk, 4 (2002) 1-32.
[14] A. Raftery, A model for high-order Markov chains, J. R. Statist. Soc. B, 47 (1985) 528-539.
[15] T. Siu, W. Ching, M. Ng and E. Fung, On multivariate credibility approach for portfolio credit risk measurement, Quantitative Finance, 5 (2005) 543-556.
[16] S. Ross, Introduction to probability models, Academic Press, Amsterdam, Boston, 10th ed., 2010.
[17] D. Zhu and W. Ching, A note on the stationary property of highdimensional Markov chain models, International Journal of Pure and Applied Mathematics, 66 (2011) 321-330.
[18] Z.Y. You, L.C. Wang, A concept of nonlinear block diagnal dominance, J. Comput. Appl. Math, 83 (1997) 1-10.

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