Estimation in the Mixture of Markov Chains Moving With Different Speeds

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Abstract
This article considers a new mixture of time-homogeneous finite Markov chains where the mixing is on the rate of movement and develops the EM algorithm for maximum likelihood estimation of the parameters of the mixture. Continuous- and discrete-time versions of the mixture are defined, and their estimation is considered separately. The developed methods are illustrated with an application to modeling bond ratings migration. The class of mixture models proposed in this article provides a framework for modeling population heterogeneity with respect to the rate of movement. The proposed mixture subsumes the mover–stayer model, which has been widely used in applications.

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