How to find the moment a sequence of non-Euclidean observations - transportation networks as graph Laplacians, compositional data, covariance objects - changes distribution when the sequence is periodic rather than identically distributed. Existing object-valued change point detectors assume an i.i.d. null, so rush-hour or seasonal cycles blur the change they are meant to find. The procedure here groups observations into blocks whose length equals the known period so the blocks become i.i.d. draws from a product measure, sweeps a Cramer-von Mises-type scan statistic across block splits to locate the change block, calibrates it with a permutation test with early stopping, and then localizes the change point inside the block by marginal two-sample tests plus nearest-neighbour classification - crucially without assuming the change falls on a block boundary, which forces the change block to follow a mixed measure equal to neither side. Instantiated with a detector built from the metric distribution function, the theory gives the limiting null law, asymptotic power one under local alternatives, consistency under the irregular change block, and a near-optimal localization rate, all via projection techniques for higher-order U-statistics; seeded binary segmentation extends it to multiple change points. Applied to hourly Citi Bike networks it recovers Thanksgiving 2019, the day after New Year's, and the March 2020 COVID shutdown.
A statistics methodology paper (submitted to Biometrika) that develops change point detection for sequences of non-Euclidean random objects whose distribution is periodic rather than identically dist…