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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.
Howell Tong (Mon,) studied this question.