The Mixture Transition Distribution (MTD) Model for High-Order Markov Chains and Non-Gaussian Time Series

The Mixture Transition Distribution model (MTD) was introduced by Raftery (1985) for the modeling of high-order Markov chains with a nite state space. Since then, it has been generalized and successfully applied to a range of situations including the analysis of wind direction, DNA and social behavior. Here we review the MTD model and the developments since 1985. We rst introduce the basic principle and then we present several extensions including general state spaces and spatial statistics. We then review methods for estimating the model parameters. Finally, a review of di erent types of applications shows the practical interest of the MTD model.