Test for a change point in Bernoulli trials with dependence

In Krauth (2003, 2004) we considered modified maximum likelihood estimates for the location of change points in Bernoulli sequences with first-order Markov dependence. Here, we address the more difficult problem of deriving in this situation a finite conditional conservative test for the existence of a change point. Our approach is based on the property of intercalary independence of Markov processes (Dufour and Torres (2000)) and on the CUSUM statistic considered in Krauth (1999, 2000) in the case of independent binomial trials.