Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model

Adrian Raftery and Simon Tavaré

Journal of the Royal Statistical Society Series C, 1994, vol. 43, issue 1, 179-199

Abstract: The mixture transition distribution (MTD) model was introduced by Raftery as a parsimonious model for high order Markov chains. It is flexible, can represent a wide range of dependence patterns, can be physically motivated, fits data well and is in several ways a discrete‐valued analogue for the class of autoregressive time series models. However, estimation has presented difficulties because the parameter space is highly non‐convex, being defined by a large number of non‐linear constraints. Here we propose a computational algorithm for maximum likelihood estimation which is based on a way of reducing the large number of constraints. This also allows more structured versions of the model, e.g. those involving structural zeros, to be fitted quite easily. A way of fitting the model by using GLIM is also discussed. The algorithm is applied to a sequence of wind directions, and also to two sequences of deoxyribonucleic acid bases from introns from mouse genes. In each case, the MTD model fits better than the conventional Markov chain model, and for the wind data it provides superior out‐of‐sample predictions. A modification of the model to represent repeated patterns is proposed and a very parsimonious version of this modified model is successfully applied to data representing bird songs.

Date: 1994
References: Add references at CitEc
Citations: View citations in EconPapers (16)

Downloads: (external link)
https://doi.org/10.2307/2986120

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssc:v:43:y:1994:i:1:p:179-199

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9876

Access Statistics for this article

Journal of the Royal Statistical Society Series C is currently edited by R. Chandler and P. W. F. Smith

More articles in Journal of the Royal Statistical Society Series C from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().