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.
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