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A new improved parsimonious multivariate Markov chain model. (English) Zbl 1277.60120

Summary: We present a new improved parsimonious multivariate Markov chain model. Moreover, we find a new convergence condition with a new variability to improve the prediction accuracy and minimize the scale of the convergence condition. Numerical experiments illustrate that the new improved parsimonious multivariate Markov chain model with the new convergence condition of the new variability performs better than the improved parsimonious multivariate Markov chain model in prediction.

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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[1] W.-K. Ching and M. K. Ng, Markov Chains: Models, Algorithms and Applications, International Series on Operations Research and Management Science, Springer, New York, NY, USA, 2006. · Zbl 1089.60003
[2] W.-K. Ching, E. S. Fung, and M. K. Ng, “A multivariate Markov chain model for categorical data sequences and its applications in demand predictions,” IMA Journal of Management Mathematics, vol. 13, no. 3, pp. 187-199, 2002. · Zbl 1040.62108
[3] W. K. Ching, E. S. Fung, and M. K. Ng, “Higher-order Markov chain models for categorical data sequences,” Naval Research Logistics, vol. 51, no. 4, pp. 557-574, 2004. · Zbl 1054.62098
[4] W. K. Ching, M. M. Ng, E. S. Fung, and T. Akutsu, “On construction of stochastic genetic networks based on gene expression sequences,” International Journal of Neural Systems, vol. 15, no. 4, pp. 297-310, 2005. · Zbl 02218493
[5] W. Ching, T. Siu, and L. Li, “An improved parsimonious multivariate Markov chain model for credit risk,” Journal of Credit Risk, vol. 5, pp. 1-25, 2009.
[6] D. W. C. Miao and B. M. Hambly, “Recursive formulas for the default probability distribution of a heterogeneous group of defauleable entities,” 2012.
[7] W.-K. Ching, M. K. Ng, and E. S. Fung, “Higher-order multivariate Markov chains and their applications,” Linear Algebra and Its Applications, vol. 428, no. 2-3, pp. 492-507, 2008. · Zbl 1144.65006
[8] C. Wang, T. Z. Huang, and C. Wen, “A simplified higher-order multivariate Markov chains model,” submitted. · Zbl 1144.65006
[9] C. Wang and T. Z. Huang, “Improved multivariate Markov chain model with the new convergence condition,” submitted. · Zbl 1144.65006
[10] T.-K. Siu, W.-K. Ching, E. S. Fung, and M. K. Ng, “On a multivariate Markov chain model for credit risk measurement,” Quantitative Finance, vol. 5, no. 6, pp. 543-556, 2005. · Zbl 1134.91485
[11] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985. · Zbl 0576.15001
[12] Z.-Y. You and C.-L. Wang, “A concept of nonlinear block diagonal dominance,” Journal of Computational and Applied Mathematics, vol. 83, no. 1, pp. 1-10, 1997. · Zbl 0886.65052
[13] C. Wang, T. Z. Huang, and W. K. Ching, “On simplified parsimonious models for higher-order multivariate Markov chains,” submitted.
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