GRACE: A General, Exact Changepoint Calculus
Abstract
We introduce GRACE (the General Regime-Aware Changepoint Estimator), a general, globally exact multiple-changepoint detection and estimation framework in which arbitrary numbers of model parameters may change at or persist across estimated changepoint locations, and all permissible changepoint types and patterns of parameter sharing compete within a single ℓ0-penalized optimization. The analyst specifies which types of changepoints are permitted and which parameters each type must preserve, without specifying which changes actually occur, where they occur, or in what order. GRACE jointly estimates the number and locations of changepoints, the type of change at each location, the model fitted between changepoints, and all continuous parameters. As a direct consequence, GRACE can estimate models in which the slope persists across a mean shift. The generality of the framework is achieved through an exact dynamic-programming recursion that retains the accumulated fitting cost conditional on whichever parameters a subsequent change may preserve, tracking multiple parameters jointly when necessary. We establish the global exactness of the recursion and develop functional, penalty-based, and objective-bound pruning rules that eliminate candidates without sacrificing optimality. Ordinary optimal partitioning, FPOP, and CPOP are recovered as special cases, while piecewise-polynomial and seasonal models illustrate the broader range of permissible segment structures and transitions. The resulting framework supports heterogeneous changepoint types, parameter sharing across segments, and substantial parallel computation within a unified approach to exact changepoint estimation.
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BibTeX
@misc{grantham2026grace,
title = {{GRACE: A General, Exact Changepoint Calculus}},
author = {Michael Grantham},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.28831},
eprint = {2609.28831},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28831},
}
RIS
TY - UNPB
TI - GRACE: A General, Exact Changepoint Calculus
AU - Michael Grantham
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2609.28831
UR - https://arxiv.org/abs/2609.28831
AB - We introduce GRACE (the General Regime-Aware Changepoint Estimator), a general, globally exact multiple-changepoint detection and estimation framework in which arbitrary numbers of model parameters may change at or persist across estimated changepoint locations, and all permissible changepoint types and patterns of parameter sharing compete within a single ℓ_0-penalized optimization. The analyst specifies which types of changepoints are permitted and which parameters each type must preserve, without specifying which changes actually occur, where they occur, or in what order. GRACE jointly estimates the number and locations of changepoints, the type of change at each location, the model fitted between changepoints, and all continuous parameters. As a direct consequence, GRACE can estimate models in which the slope persists across a mean shift. The generality of the framework is achieved through an exact dynamic-programming recursion that retains the accumulated fitting cost conditional on whichever parameters a subsequent change may preserve, tracking multiple parameters jointly when necessary. We establish the global exactness of the recursion and develop functional, penalty-based, and objective-bound pruning rules that eliminate candidates without sacrificing optimality. Ordinary optimal partitioning, FPOP, and CPOP are recovered as special cases, while piecewise-polynomial and seasonal models illustrate the broader range of permissible segment structures and transitions. The resulting framework supports heterogeneous changepoint types, parameter sharing across segments, and substantial parallel computation within a unified approach to exact changepoint estimation.
ER -