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 $X_{i,t} = (X_{i,t,1}, ..., X_{i,t,D})^\top$, 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 $T \times m$ 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.