Higher-order multivariate Markov chains and their applications

Wai Ki Ching, Kwok Po NG*, Eric S. Fung

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

71 Citations (Scopus)


Markov chains are commonly used in modeling many practical systems such as queuing systems, manufacturing systems and inventory systems. They are also effective in modeling categorical data sequences. In a conventional nth order multivariate Markov chain model of s chains, and each chain has the same set of m states, the total number of parameters required to set up the model is O (mns). Such huge number of states discourages researchers or practitioners from using them directly. In this paper, we propose an nth-order multivariate Markov chain model for modeling multiple categorical data sequences such that the total number of parameters are of O (ns2 m2). The proposed model requires significantly less parameters than the conventional one. We develop efficient estimation methods for the model parameters. An application to demand predictions in inventory control is also discussed.

Original languageEnglish
Pages (from-to)492-507
Number of pages16
JournalLinear Algebra and Its Applications
Issue number2-3
Publication statusPublished - 15 Jan 2008

Scopus Subject Areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

User-Defined Keywords

  • Perron-Frobenius theorem
  • Multivariate Markov chains
  • Categorical data sequences


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