Where should the null live? Surrogate tests for clustering of threshold-derived air-quality indices, with application to PM2.5 exceedances in Chile
Abstract
Air-quality and climate monitoring routinely convert native-resolution measurements into exceedance counts before testing whether high values cluster in time. A surrogate null can be imposed on the derived index or on the native series and then propagated through the same thresholding and aggregation. We show that the two placements can encode different scientific hypotheses and lead to opposite conclusions. In 31 Chilean PM2.5 monitoring stations (2018--2025), weekly clustering of days above the 50 ug m^-3 national 24-hour standard was significant at all stations under an index-level IAAFT null but at only two under a daily native-resolution null; a native generative null with seasonal marginals and short-memory Gaussian-copula dependence agreed with the native surrogate at 30 of 31 stations. Across thresholds spanning the WHO guideline (15 ug m^-3) to the Chilean episode-alert level (80 ug m^-3), index-only rejections increased from 8 of 31 to all eligible stations as monthly event probabilities became more seasonally concentrated, and equalizing monthly event probabilities at the 50 ug m^-3 level reduced index-only decisions from 29 to five. We formalize the issue as null transport through a lossy observation map: an exact aggregate-level equivalent of a native null exists if and only if the randomization kernel is lumpable with respect to that map. A within-fiber diagnostic, which perturbs native amplitudes while keeping the observed index exactly fixed, shows that this condition fails in the monitoring data: the native null distribution moved by a median of 18 times its Monte Carlo variability. Weekly clustering of PM2.5 exceedances in Chile is therefore fully compatible with seasonality plus short-memory daily persistence, and index-level surrogate rejections should not be read as evidence about daily concentration dynamics.
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BibTeX
@misc{herreramarin2026where,
title = {{Where should the null live? Surrogate tests for clustering of threshold-derived air-quality indices, with application to PM2.5 exceedances in Chile}},
author = {Mauricio Herrera-Marín},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.27769},
eprint = {2609.27769},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27769},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Where should the null live? Surrogate tests for clustering of threshold-derived air-quality indices, with application to PM2.5 exceedances in Chile
AU - Mauricio Herrera-Marín
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2609.27769
UR - https://arxiv.org/abs/2609.27769
AB - Air-quality and climate monitoring routinely convert native-resolution measurements into exceedance counts before testing whether high values cluster in time. A surrogate null can be imposed on the derived index or on the native series and then propagated through the same thresholding and aggregation. We show that the two placements can encode different scientific hypotheses and lead to opposite conclusions. In 31 Chilean PM2.5 monitoring stations (2018--2025), weekly clustering of days above the 50 ug m^-3 national 24-hour standard was significant at all stations under an index-level IAAFT null but at only two under a daily native-resolution null; a native generative null with seasonal marginals and short-memory Gaussian-copula dependence agreed with the native surrogate at 30 of 31 stations. Across thresholds spanning the WHO guideline (15 ug m^-3) to the Chilean episode-alert level (80 ug m^-3), index-only rejections increased from 8 of 31 to all eligible stations as monthly event probabilities became more seasonally concentrated, and equalizing monthly event probabilities at the 50 ug m^-3 level reduced index-only decisions from 29 to five. We formalize the issue as null transport through a lossy observation map: an exact aggregate-level equivalent of a native null exists if and only if the randomization kernel is lumpable with respect to that map. A within-fiber diagnostic, which perturbs native amplitudes while keeping the observed index exactly fixed, shows that this condition fails in the monitoring data: the native null distribution moved by a median of 18 times its Monte Carlo variability. Weekly clustering of PM2.5 exceedances in Chile is therefore fully compatible with seasonality plus short-memory daily persistence, and index-level surrogate rejections should not be read as evidence about daily concentration dynamics.
ER -