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

TLDR

The mixture transition distribution (MTD) model, introduced by Raftery in 1985 for high‑order Markov chains with finite state spaces, has since been generalized and applied to wind direction, DNA sequence, and social behavior analyses. This paper reviews the MTD model and its developments since 1985. We first outline the basic principle, then discuss extensions to general state spaces and spatial statistics, and finally review methods for estimating model parameters. The review of diverse applications demonstrates the practical relevance of the MTD model.

Abstract

The mixture transition distribution model (MTD) was introduced in 1985 by Raftery for the modeling of high-order Markov chains with a finite state space. Since then it has been generalized and successfully applied to a range of situations, including the analysis of wind directions, DNA sequences and social behavior. Here we review the MTD model and the developments since 1985. We first introduce the basic principle and then we present several extensions, including general state spaces and spatial statistics. Following that, we review methods for estimating the model parameters. Finally, a review of different types of applications shows the practical interest of the MTD model.