André Berchtold

The MTD Page


The Mixture Transition Distribution (MTD) model was introduced by A.E. Raftery (1985) for the modeling of high-order Markov chains. The principle of the model is to replace the global contribution of each lagged period to the present by an individual contribution from each lag to the present. This model is very parsimonious while having the capability to represent very different situations including infinite-lag models and spatial dependences.

Since 1985, the MTD model has been developed and generalized in more than 20 publications. A continuous version of the MTD model (Le, Martin & Raftery, 1996) has proven to be able to represent series presenting non-gaussian features. Main applications include the modeling of wind speed and direction, social behavior, and financial series.


Two softwares are freely available for the computation of the finite space version of the MTD model:


Key references:

Other important references about theoretical developments and applications:

Last modified: April 6, 2004. Webmaster