Exponential bounds for the probability of wrong determination of the order of a Markov chain by using the EDC criterion

The Efficient Determination Criterion (EDC), proposed by Zhao et al. (2001. Statist. Inference for Stochastic Processes 4, 273-282), generalizes the AIC and the BIC criteria and provides a class of consistent estimators for the order of a Markov chain. In this note, we exhibit exponential bounds for the probability of wrong determination of the order.