Changpoints

Changpoints are points in a data sequence where the statistical properties of the underlying process change abruptly. They generalize regime shifts in time series and are closely related to changepoint detection, the practice of identifying such points from observed data. In practice, a changpoint may separate segments with different means, variances, autocorrelation structures, or other distributional parameters.

Commonly defined types of changpoints include mean shifts, variance shifts, changes in trend, and changes in the full distribution. Some formulations consider multiple simultaneous changes or gradual transitions, though the classical model assumes abrupt changes at discrete points in time. Changpoints can occur in univariate or multivariate series and may be temporal or spatial in nature.

Detection and estimation typically involve modeling assumptions about the data-generating process and selecting points that optimize a fit measure, often penalized likelihood or Bayesian posterior probability. Standard methods include dynamic programming, binary segmentation, and the PELT (Pruned Exact Linear Time) algorithm, as well as Bayesian hierarchical approaches and nonparametric techniques. Model choice affects sensitivity to noise and the number of changpoints detected.

Applications of changpoints span finance, climate and environmental monitoring, quality control, epidemiology, and genomics, where detecting shifts can inform risk assessment, policy, or scientific understanding. Practical challenges include choosing the number of changpoints, handling real-world noise, and distinguishing true structural change from transient fluctuations.

See also changepoint detection and time series analysis.