Detecting Support Shift in Time Series
Abstract
We consider the detection of changes in the support of distributions generating a time series. Such changes describe modifications of the region in which observations occur, and may affect its geometry or topology. We compare support descriptors computed on two adjacent windows and retain locations where the discrepancy is sufficiently large. The procedure applies to any support functional that is Lipschitz with respect to the Hausdorff distance, including geometric quantities and several persistence-based summaries. Under a lower mass condition and suitable separation and spacing assumptions, we prove recovery of the number of change points and give bounds on their localization error. We then introduce a multiscale procedure calibrated by permutation tests, which does not require knowledge of the jump sizes, segment spacings, or regularity parameters. Finally, we establish localization lower bounds for the Hausdorff distance and related functionals. These bounds recover the dependence on the jump size up to logarithmic factors and describe the loss of localization accuracy in a weak-signal regime.
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BibTeX
@misc{henneuse2026detecting,
title = {{Detecting Support Shift in Time Series}},
author = {Hugo Henneuse},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05801015v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Detecting Support Shift in Time Series
AU - Hugo Henneuse
PY - 2026
DA - 2026/10/15
PB - HAL
UR - https://hal.science/hal-05801015v1
AB - We consider the detection of changes in the support of distributions generating a time series. Such changes describe modifications of the region in which observations occur, and may affect its geometry or topology. We compare support descriptors computed on two adjacent windows and retain locations where the discrepancy is sufficiently large. The procedure applies to any support functional that is Lipschitz with respect to the Hausdorff distance, including geometric quantities and several persistence-based summaries. Under a lower mass condition and suitable separation and spacing assumptions, we prove recovery of the number of change points and give bounds on their localization error. We then introduce a multiscale procedure calibrated by permutation tests, which does not require knowledge of the jump sizes, segment spacings, or regularity parameters. Finally, we establish localization lower bounds for the Hausdorff distance and related functionals. These bounds recover the dependence on the jump size up to logarithmic factors and describe the loss of localization accuracy in a weak-signal regime.
ER -