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.

中文翻译：

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马尔可夫时间序列的 CUSUM 最快检测规则的 Kullback-Leibler 方法

摘要 研究了决策过程的最优特性，以最快地检测自回归序列和其他马尔可夫类型序列中的参数变化点。对于满足信息论遍历定理的马尔可夫链，证明存在归一化条件对数似然比的极限。然后利用 Kullback-Leibler 散度的时间平均率推导出该极限的闭式表达式。由于观察过程的几何遍历特性，基于顺序分析方法的检测程序的良好特性被证明是成立的。特别是，窗口限制的 CUSUM 规则被证明是检测自回归模型中的中断点的最佳选择。专门研究了 Sparre Andersen 模型。