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 -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.
