Comparing the Markov Order Estimators AIC, BIC and EDC

In the framework of nested hypotheses testing, several alternatives for estimating the order of a Markov chain have been proposed. The AIC, Akaike's entropy-based information criterion, constitutes the best known tool for model identification and has had a fundamental impact in statistical model selection. In spite of the AIC's relevance, several authors have pointed out its inconsistency that may lead to overestimation of the true order. To overcome this inconsistency, the Bayesian information criterion, BIC, was proposed by introducing in the penalty term the sample size that led to a consistent estimator for large samples. A more general approach is exhibited by the EDC, efficient determination criterion, that encompass both AIC and BIC estimates. Under proper setting, the EDC, besides being a strongly consistent estimate, is an optimal estimator. These approaches are briefly presented and compared by numerical simulation. The presented results may support decisions related to estimator's choice.