Change Point Detection
A change point is a time where the underlying behavior of a series shifts, such as a jump in the mean or a sudden rise in volatility. Finding these moments explains structural breaks.
What can change
- A shift in the mean level, like sales stepping up after a launch.
- A change in variance, like a market becoming more turbulent.
- A change in trend slope, where a flat line begins to climb.
How detection works
Most methods compare the data before and after a candidate split.
- Define a cost that measures how poorly one model fits a segment.
- A real change point lowers the total cost when you allow two segments instead of one.
- Search for the splits that minimize total cost plus a penalty for adding too many.
The penalty matters: without it, the method would place a change point everywhere and overfit.
Online and offline
- Offline detection scans a full recorded series after the fact.
- Online detection watches a live stream and raises an alert as soon as a shift appears.
Key idea
Change point detection locates shifts in a series by finding splits that lower total fitting cost while a penalty guards against placing too many.