Chiu yeung Lau
Structural breaks in time series are usually reported through a single estimated segmentation, possibly accompanied by confidence intervals for the selected break locations. This summary can be too narrow when several breakpoint configurations give comparable explanations of the same data. We propose a model selection confidence set (MSCS) for changepoint configurations. The method treats an entire segmentation, rather than an individual breakpoint, as the object of inference. Possible break locations are first represented by a finite candidate dictionary, which may be obtained from a high-sensitivity scan method. Conditional on this dictionary, we compare each feasible candidate segmentation with an over-inclusive reference segmentation by a quasi-likelihood ratio statistic and retain all configurations that are not significantly worse after bootstrap calibration. The framework is formulated for general piecewise stationary timeseries models equipped with a segmentwise working quasi-likelihood; autoregressive, ARMA, and volatility likelihoods are special cases. Because the quasi-likelihood ratio depends on serial dependence, nuisance regime parameters, segment lengths, and the candidate dictionary, we avoid universal chi-square calibration and instead use model-specific bootstrap critical values, either through a fitted parametric working model or a segmentwise block bootstrap. The resulting MSCS provides a model-level confidence statement, a breakpoint-count confidence profile, and inclusion-importance scores for candidate breakpoints. We establish coverage of the oracle candidate segmentation and prove that, under a signal-to-complexity condition, every retained segmentation contains all oracle breakpoints with probability tending to one. The proof is based on a quasi-likelihood-loss expansion and concentration inequalities for dependent observations.