Kullback-Leibler Approach to CUSUM Quickest Detection Rule for Markovian Time Series. Issue 3 (3rd July 2018) - Girardin, Valérie; Konev, Victor; Pergamenchtchikov, Serguei
Abstract: Optimality properties of decision procedures are studied for the quickest detection of a change-point of parameters in autoregressive and other Markov type sequences. The limit of the normalized conditional log-likelihood ratios is shown to exist for Markov chains satisfying the ergodic theorem of information theory. Then closed-form expressions for this limit are derived by making use of the time average rate of Kullback-Leibler divergence. The good properties of the detection procedures based on a sequential analysis approach are proven to hold thanks to geometric ergodicity properties of the observation processes. In particular, the window-limited CUSUM rule is shown to be optimal for detecting the disruption point in autoregressive models. Sparre Andersen models are specifically studied.