Usually, real-time change-point detection uses the sliding window algorithm.
Assume that the data follows a distribution, but has different parameters θ in different segments. In the two following hypotheses about the parameter,
H 0:θ = θ 0
H 1:θ = θ 1
the reference part has parameter θ 0 and the testing part in the sliding window has parameter θ 1, with the following notation:
The decision rule for testing the sliding window is:
If S j k < h 0, choose H 0.
If S j k ≥ h 0, choose H 1.