On the approximation of high-order binary Markov chains by parsimonious models

We consider two parsimonious models of binary high-order Markov chains and discover their ability to approximate arbitrary high-order Markov chains. Two types of global measures for approximation accuracy are introduced, theoretical and experimental results are obtained for these measures and for the considered parsimonious models. New consistent statistical parameter estimator is constructed for parsimonious model based on two-layer artificial neural network.