A Novel Estimation Approach for Mixture Transition Distribution Model in High-Order Markov Chains

Abstract

A transformation is proposed to convert the nonlinear constraints of the parameters in the mixture transition distribution (MTD) model into box-constraints. The proposed transformation removes the difficulties associated with the maximum likelihood estimation (MLE) process in the MTD modeling so that the MLEs of the parameters can be easily obtained via a hybrid algorithm from the evolutionary algorithms and/or quasi-Newton algorithms for global optimization. Simulation studies are conducted to demonstrate MTD modeling by the proposed novel approach through a global search algorithm in R environment. Finally, the proposed approach is used for the MTD modelings of three real data sets.

Keywords:

• Genetic algorithms
• High-order temporal dependence
• Markov chains
• Maximum likelihood estimation
• Mixture transition distribution

Mathematics Subject Classification:

• 65C40
• 62M05

Acknowledgments

The authors would like to thank anonymous referees and the Editor for the comments and suggestions which significantly improved this article.