Journal of Applied Mathematics

A New Improved Parsimonious Multivariate Markov Chain Model

Chao Wang and Ting-Zhu Huang

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 902972, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807845

Digital Object Identifier
doi:10.1155/2013/902972

Mathematical Reviews number (MathSciNet)
MR3032191

Zentralblatt MATH identifier
1277.60120

Citation

Wang, Chao; Huang, Ting-Zhu. A New Improved Parsimonious Multivariate Markov Chain Model. J. Appl. Math. 2013 (2013), Article ID 902972, 10 pages. doi:10.1155/2013/902972. https://projecteuclid.org/euclid.jam/1394807845


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References

  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • D. W. C. Miao and B. M. Hambly, “Recursive formulas for the default probability distribution of a heterogeneous group of defauleable entities,” 2012.
  • 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.
  • C. Wang, T. Z. Huang, and C. Wen, “A simplified higher-orderčommentComment on ref. [8?]: Please update the information of these references [8,9,14?], if possible. multivariate Markov chains model,” submitted.
  • C. Wang and T. Z. Huang, “Improved multivariate Markov chain model with the new convergence condition,” submitted.
  • 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.
  • R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
  • 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.
  • C. Wang, T. Z. Huang, and W. K. Ching, “On simplified parsimonious models for higher-order multivariate Markov chains,” submitted.