Abstract

Changepoint detection in hierarchical time series is complicated by additive aggregation, which changes the stochastic scale of series across hierarchy levels and can affect the behaviour of nodewise detectors. This study investigates when scale normalisation matters for Pruned Exact Linear Time (PELT) detection and whether the source used to estimate the calibration scale provides additional information. Five procedures are examined under a common Normal--PELT--MBIC specification: raw-scale PELT (M1), full-sample standardisation (M2), robust first-difference hierarchy-blind calibration (M2-R), oracle hierarchy-scale calibration (M3-O), and estimated hierarchy-scale calibration (M3-E). Targeted experiments were conducted on a balanced 31-node hierarchy with 16 bottom-level series using 1000 Monte Carlo replications. An implementation-scale experiment showed that the implemented Normal--PELT--MBIC detector was not invariant to pure multiplicative rescaling despite an unchanged theoretical signal-to-noise ratio. Under structural stability, M1 exhibited severe aggregation-dependent over-segmentation, whereas scale calibration largely controlled false detections. For a single bottom-originating change, full-sample standardisation became increasingly contaminated
as signal magnitude increased, while the first-difference hierarchy-based estimator remained closer to baseline scale. However, the resulting differences in ancestral recovery between M2 and M3-E were generally modest. Clearer M3-E advantages emerged under repeated and temporally dispersed changepoints. Contemporaneous covariance heterogeneity had limited impact on these conclusions, whereas strong serial dependence substantially degraded false-detection control for both calibrated procedures. Comparison of M3-E with M2-R showed that once baseline scale was estimated robustly, the incremental benefit of hierarchical covariance information was small in simple settings and configuration dependent elsewhere. In application to the Australian Tourism data, M3-E produced a parsimonious changepoint configuration with substantial temporal agreement with M2 and descendant support for aggregate-level detections. Therefore, scale calibration is consequential for hierarchical PELT detection, whereas the additional value of hierarchical covariance information depends on the structural and dependence configuration.