Estimation in the mixture transition distribution model

This paper introduces a new iterative algorithm for the estimation of the mixture transition distribution (MTD) model, which does not require the use of any specific external optimization procedure and can therefore be programmed in any computing language. Comparisons with previously published results show that this new algorithm performs at least as well as or better than other methods. The choice of initial values is also discussed. The MTD model was designed for the modeling of high-order Markov chains and has already proved to be a useful tool for the analysis of different types of time series such as wind speeds and social relationships. In this paper, we also propose to use it for the modeling of one-dimensional spatial data. An application using a DNA sequence shows that this approach can lead to better results than the classical Potts model.