Detecting change-points in Markov chains

Markov chains provide a flexible model for dependent random variables with applications in such disciplines as physics, environmental science and economics. In the applied study of Markov chains, it may be of interest to assess whether the transition probability matrix changes during an observed realization of the process. If such changes occur, it would be of interest to estimate the transitions where the changes take place and the probability transition matrix before and after each change. For the case when the number of changes is known, standard likelihood theory is developed to address this problem. The bootstrap is used to aid in the computation of pp-values. When the number of changes is unknown, the AIC and BIC measures are used for model selection. The proposed methods are studied empirically and are applied to example sets of data.