Kullback-Leibler Approach to CUSUM Quickest Detection Rule for Markovian Time Series. Issue 3 (3rd July 2018)

• Record Type: Journal Article
• Authors: Girardin, Valérie; Konev, Victor; Pergamenchtchikov, Serguei
• Is Part Of: Sequential analysis. Volume 37:Issue 3(2018)
• Page Start: 322
• Page End: 341
• Publication Date: 2018-07-03
• Subjects: Change-point detection -- CUSUM detection procedure -- Ergodic Theorem of information theory -- Kullback-Leibler divergence -- Relative entropy -- Sequential detection -- Sparre Andersen models; 62L10 -- 62L15 -- 60G40 -- 60J10 -- 62B10 -- 94A17; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2018.1548846
• Languages: English
• ISSNs: 0747-4946

Abstract

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.