Distribution-Free Changepoint Inference for Rainfall Patterns
Abstract
Long records of rainfall contain critical information about the temporal organization of precipitation within a year, including wet and dry spells. Detecting when this temporal pattern changes is central to climate-impact assessment and environmental monitoring.A common data structure features observations from m locations over T years. For location i and year t, the record is a vector of daily measurements Xi,t = (Xi,t,1, ..., Xi,t,D)⊤, with D = 365. The goal is to identify an unknown year t0 when the temporal rainfall pattern changes across the region. Because changes in the intra-annual pattern affect the frequency-domain behavior of the daily sequence, we represent each yearly curve through a spectral feature capturing the strength of temporal oscillation at a fixed frequency.Classical changepoint methods often rely on parametric likelihoods or Gaussian approximations, which are hard to justify for skewed and heavy-tailed rainfall data. Furthermore, many procedures only return a point estimate. A confidence set for the change year is crucial in environmental applications to quantify temporal uncertainty and distinguish sharp transitions from weak evidence.This paper develops a distribution-free framework for detecting a synchronized structural change in yearly rainfall patterns across independently monitored locations. For each location-year pair, we compute a fixed-frequency nonparametric spectral density estimate. These features form a T × m data matrix. By exploiting the exchangeability of yearly spectral features before and after the true changepoint, alongside spatial independence, we construct finite-sample valid confidence sets for the unknown change year.
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BibTeX
@misc{jain2026distributionfree,
title = {{Distribution-Free Changepoint Inference for Rainfall Patterns}},
author = {Aaditya Jain and Abhishek Bhattacharjee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13594},
eprint = {2609.13594},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13594},
}
RIS
TY - UNPB
TI - Distribution-Free Changepoint Inference for Rainfall Patterns
AU - Aaditya Jain
AU - Abhishek Bhattacharjee
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13594
UR - https://arxiv.org/abs/2609.13594
AB - Long records of rainfall contain critical information about the temporal organization of precipitation within a year, including wet and dry spells. Detecting when this temporal pattern changes is central to climate-impact assessment and environmental monitoring.A common data structure features observations from m locations over T years. For location i and year t, the record is a vector of daily measurements X_i,t = (X_i,t,1, ..., X_i,t,D)^⊤, with D = 365. The goal is to identify an unknown year t_0 when the temporal rainfall pattern changes across the region. Because changes in the intra-annual pattern affect the frequency-domain behavior of the daily sequence, we represent each yearly curve through a spectral feature capturing the strength of temporal oscillation at a fixed frequency.Classical changepoint methods often rely on parametric likelihoods or Gaussian approximations, which are hard to justify for skewed and heavy-tailed rainfall data. Furthermore, many procedures only return a point estimate. A confidence set for the change year is crucial in environmental applications to quantify temporal uncertainty and distinguish sharp transitions from weak evidence.This paper develops a distribution-free framework for detecting a synchronized structural change in yearly rainfall patterns across independently monitored locations. For each location-year pair, we compute a fixed-frequency nonparametric spectral density estimate. These features form a T × m data matrix. By exploiting the exchangeability of yearly spectral features before and after the true changepoint, alongside spatial independence, we construct finite-sample valid confidence sets for the unknown change year.
ER -