changepoint

A changepoint, in statistics, is a point in a time-ordered sequence where the statistical properties of the data change abruptly. Commonly the mean, variance, or distribution changes from one regime to another.

In a typical offline changepoint analysis, a sequence x1, ..., xn is assumed to be generated from segments with different parameters, separated by unknown changepoints. The objectives are to estimate the number of changepoints and their locations, and possibly the parameters of each segment. Online changepoint detection aims to detect changes as new data arrive.

Methods include parametric and Bayesian approaches. Parametric methods use likelihood or cost-based criteria and often rely on dynamic programming to find an optimal partition; PELT (pruned exact linear time) improves efficiency. Binary segmentation provides a fast heuristic. Bayesian methods place priors on changepoints and infer a posterior distribution over their number and positions. Nonparametric methods detect changes in distribution without strong distributional assumptions.

Changepoint models can represent abrupt mean shifts, variance changes, changes in higher moments, or full distributional shifts. Models may also incorporate periods with no change (epidemic changepoints) or gradual changes.

Applications span finance (regime switches in returns), climate science (sudden climate shifts), quality control and industrial processes, genomics (copy number variation), and neuroscience.

History and software: change-point detection has roots in quality-control and time-series analysis dating to the mid-20th century, with notable methods such as CUSUM. Modern algorithms include PELT (Killick, Fearnhead & Eckley, 2012). Software implementations exist in R (changepoint) and Python (ruptures), among others.