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Determination of the order of a Markov chain by Akaike's information criterion

Published online by Cambridge University Press:  14 July 2016

H. Tong
H. Tong*
Affiliation:
Institute of Statistical Mathematics, Tokyo
*
*At present at University of Manchester Institute of Science and Technology, Manchester, England.
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Abstract

Using Akaike's information criterion, we have presented an objective procedure for the determination of the order of an ergodic Markov chain with a finite number of states. The procedure exploits the asymptotic properties of the maximum likelihood ratio statistics and Kullback and Leibler's mean information for the discrimination between two distributions. Numerical illustrations are given, using data from Bartlett (1966), Good and Gover (1967) and some weather records.

Keywords

MARKOV CHAINS OF ORDER kAKAIKE'S INFORMATION CRITERIONKULLBACK-LEIBLER'S INFORMATIONNORMAL REAL NUMBER
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 488 - 497
Copyright
Copyright © Applied Probability Trust 1975 

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