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

1 March 1975

journal article
research article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 12 (03) , 488-497
https://doi.org/10.1017/s0021900200048294

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

This publication has 9 references indexed in Scilit:

Statistical approach to computer control of cement rotary kilns
Automatica, 1972
Model Building for Prediction in Regression Based Upon Repeated Significance Tests
The Annals of Mathematical Statistics, 1971
Statistical predictor identification
Annals of the Institute of Statistical Mathematics, 1970
A Markov chain model for daily rainfall occurrence at Tel Aviv
Quarterly Journal of the Royal Meteorological Society, 1962
Statistical Inference about Markov Chains
The Annals of Mathematical Statistics, 1957
SOME THEOREMS AND SUFFICIENCY CONDITIONS FOR THE MAXIMUM-LIKELIHOOD ESTIMATOR OF AN UNKNOWN PARAMETER IN A SIMPLE MARKOV CHAIN
Biometrika, 1955
A TEST FOR MARKOFF CHAINS
Biometrika, 1954
The serial test for sampling numbers and other tests for randomness
Mathematical Proceedings of the Cambridge Philosophical Society, 1953
The frequency goodness of fit test for probability chains
Mathematical Proceedings of the Cambridge Philosophical Society, 1951