TY - JOUR
T1 - Higher-order multivariate Markov chains and their applications
AU - Ching, Wai Ki
AU - Ng, Michael K.
AU - Fung, Eric S.
N1 - Funding Information:
The research of his project is supported in part by HKU Strategic Research Theme Fund on Computational Physics and Numerical Methods, HKU CRCG Grant Nos. 10204436 and 10205105, Hung Hing Ying Physical Sciences Research Fund, RGC Grants 7017/07P, 7035/04P and 7035/05P and HKBU FRGs. ∗ Corresponding author. Tel.: +852 3411 7317; fax: +852 3411 5811. E-mail address: [email protected] (M.K. Ng).
Publisher copyright:
© 2008 Elsevier Inc. All rights reserved.
PY - 2008/1/15
Y1 - 2008/1/15
N2 - 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.
AB - 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.
KW - Perron-Frobenius theorem
KW - Multivariate Markov chains
KW - Categorical data sequences
UR - http://www.scopus.com/inward/record.url?scp=36048957576&partnerID=8YFLogxK
UR - https://www.sciencedirect.com/journal/linear-algebra-and-its-applications/vol/428/issue/2
U2 - 10.1016/j.laa.2007.05.021
DO - 10.1016/j.laa.2007.05.021
M3 - Journal article
AN - SCOPUS:36048957576
SN - 0024-3795
VL - 428
SP - 492
EP - 507
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 2-3
ER -