Article ID Journal Published Year Pages File Type
4603098 Linear Algebra and its Applications 2008 16 Pages PDF
Abstract

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(ns2m2). 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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory