Abstract Detecting a change as fast as possible in an observed stochastic process is an important task. In this article, an online procedure is presented to detect changes in the parameter of general discrete-time parametric stochastic processes. As examples, regression models, autoregressive processes, and Galton–Watson processes are investigated. The test is called cumulative sum (CUSUM) type because it is based on the cumulated sums of the estimates of certain martingale difference sequences belonging to the process. In case of a single change alternative hypothesis, the procedure is examined in terms of consistency. Due to the online manner, the time of change can also be estimated.

中文翻译：

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参数离散时间随机过程的在线变化检测测试

摘要 在观察到的随机过程中尽可能快地检测变化是一项重要的任务。在本文中，提出了一种在线程序来检测一般离散时间参数随机过程的参数变化。作为示例，研究了回归模型、自回归过程和 Galton-Watson 过程。该测试称为累积和 (CUSUM) 类型，因为它基于属于该过程的某些鞅差分序列的估计值的累积和。在单一变化替代假设的情况下，根据一致性检查程序。由于是在线方式，还可以估计变化的时间。