Change detection in Markov-modulated time series

We address the problem of online change detection of Markov-modulated time series models. For simplicity, we look at autoregressive time-series models the parameters of which are modulated by a finite-state homogeneous Markov chain. We propose a cumulative sum based statistical test to detect abrupt changes in such processes. Computation of average run length functions, in particular, mean delay in detection and mean time between false alarms are particularly difficult to obtain in closed form for such processes. Although there are ways to approximate such computation, we do not address those issues in this paper. Simulation studies illustrate the detection capability of our proposed test.