Sequential Monitoring

Up to this point we have been concerned with what is usually referred to as “retrospective” or “off-line” change point detection and estimation, in which the goal is to conduct change point analysis retrospectively on an observed series. In this chapter, we shift our focus to sequential or “online” change point detection methods. These aim to detect a change point in the data generating process, relative to a stable training or historical sample, as quickly as possible as we continue to obtain data sequentially. We begin by developing the framework of such sequential detection procedures in the context of a simple mean change in Sect. 6.1, which we then extend to linear and time series models in Sects. 6.2 and 6.3. A key consideration throughout is the distribution of the stopping time, which is the amount of time required in order to detect a change point in the data generating process. The asymptotic distribution of stopping times are investigated in Sect. 6.4.