Trendsegments

Trendsegments is a concept in time series analysis referring to contiguous intervals over which the observable trend remains approximately linear or directionally consistent. The idea is to model a non-stationary trend as a sequence of simpler, piecewise trends, each represented by its own slope and intercept.

Each trend segment is defined by a start and end time, a slope, and an intercept. The piecewise trend is the concatenation of these segments, with breaks at change points where the trend direction or rate changes. Within a segment, data deviations are treated as noise around the segment's linear trend.

Trend segmentation relies on change-point detection and segmented regression. Common approaches include dynamic programming to minimize residual error with a penalty for adding segments, and other algorithms such as PELT, binary segmentation, or bottom-up/top-down methods. Model selection criteria like AIC, BIC, or cross-validation are used to determine an appropriate number of segments.

Applications include finance and economics for detecting regime changes in prices or indicators, climate science for regional trends, and marketing or web analytics for detecting changes in user behavior over time. Limitations include sensitivity to noise and outliers, risk of overfitting with too many segments, and dependence on the chosen detection method and penalty, which can affect interpretability and stability of results.