A problem concerned with the identification of the point in a time series at which some change occurs. Suppose that data are collected on one or more variables at a series of time points in order to examine the properties of the variables and possible relationships between them. The time of collection appears to be incidental. However, frequently this turns out to be not quite true. For example, in one case the explanation for an apparent change in the mean of a variable was found to be attributed to a tall meter reader who looked down at a dial being replaced by a short one who looked up at the same dial. Another example concerns changes in the responses to a question in an annual survey that turn out to be a consequence of a change in the survey design. In these examples, the cause of the change and hence the time that the change took place have been identified. Often, however, though it is evident that a change has taken place, it is not clear at what precise point this occurred.
Subjects: Probability and Statistics.