Bayesian methods for change-point detection in long-range dependent processes

We describe a Bayesian method for detecting structural changes in a long-range dependent process. In particular, we focus on changes in the long-range dependence parameter, d, and changes in the process level, μ. Markov chain Monte Carlo (MCMC) methods are used to estimate the posterior probability and size of a change at time t, along with other model parameters. A time-dependent Kalman filter approach is used to evaluate the likelihood of the fractionally integrated ARMA model characterizing the long-range dependence. The method allows for multiple change points and can be extended to the long-memory stochastic volatility case. We apply the method to three examples, to investigate a change in persistence of the yearly Nile River minima, to investigate structural changes in the series of durations between intraday trades of IBM stock on the New York Stock Exchange, and to detect structural breaks in daily stock returns for the Coca Cola Company during the 1990s.