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Higher-order multivariate Markov chains and their applications. (English) Zbl 1144.65006
High order multivariate Markov chains are frequently used in modelling, especially for the catagorical data sequences. To reduce the number of the estimated parameters, in some stationary cases, the authors provide a conditional minimum-maximum algorithm associated with the frequency estimation to identify the modelling parameters to meet the practical use. An application to sales demand prediction is discussed.
MSC:
65C40Computational Markov chains (numerical analysis)
60J22Computational methods in Markov chains
References:
[1]Buzacott, J.; Shanthikumar, J.: Stochastic models of manufacturing systems, (1993)
[2]Ching, W.: Iterative methods for queuing and manufacturing systems, (2001)
[3]Ching, W.; Fung, E.; Ng, M.: A multivariate Markov chain model for categorical data sequences and its applications in demand predictions, IMA J. Manage. math. 13, 87-199 (2002) · Zbl 1040.62108 · doi:10.1093/imaman/13.3.187
[4]Ching, W.; Fung, E.; Ng, M.: A higher-order Markov model for the newsboy’s problem, J. operat. Res. soc. 54, 291-298 (2003) · Zbl 1171.90539 · doi:10.1057/palgrave.jors.2601491
[5]Ching, W.; Fung, E.; Ng, M.: Higher-order Markov chain models for categorical data sequences, Int. J. Nav. res. Logist. 51, 557-574 (2004) · Zbl 1054.62098 · doi:10.1002/nav.20017
[6]Ching, W.; Ng, M.: Advances in data mining and modeling, (2003)
[7]Ching, W.; Yuen, W.; Loh, A.: An inventory model with returns and lateral transshipments, J. operat. Res. soc. 54, 636-641 (2003) · Zbl 1095.90503 · doi:10.1057/palgrave.jors.2601521
[8]Ching, W.; Fung, E.; Ng, M.; Akutsu, T.: On construction of stochastic genetic networks based on gene expression sequences, Int. J. Neural syst. 15, 297-310 (2005)
[9]Chvátal, V.: Linear programming, (1983) · Zbl 0537.90067
[10]Fang, S.; Puthenpura, S.: Linear optimization and extension, (1993) · Zbl 0799.90080
[11]Fleischmann, M.: Quantitative models for reverse, logistics, Lecture notes in economics and mathematical system 501 (2001)
[12]Horn, R.; Johnson, C.: Matrix analysis, (1985)
[13]Macdonald, I.; Zucchini, W.: Hidden Markov and other models for discrete-valued time series, (1997)
[14]Nahmias, S.: Production and operation analysis, (1997)
[15]Raftery, A.: A model for high-order Markov chains, J.R. statist. Soc. B 47, 528-539 (1985) · Zbl 0593.62091
[16]Sharma, O.: Markovian queues, (1995)
[17]Siu, T.; Ching, W.; Ng, M.; Fung, E.: On multivariate credibility approach for portfolio credit risk measurement, Quantitative finance 5, 543-556 (2005)