arXiv:2609.30790v1 Announce Type: new Abstract: Many temporal process learning and monitoring pipelines operate in local windows, making window-level decisions unavoidable in practice. In such settings, classical statistical tests can be applied to individual windows, but they typically evaluate predefined parametric hypotheses-such as unit-root or moment-based conditions-thereby limiting flexibility when reference behavior is defined empirically from task- or domain-specific data. In this work, we view window-level monitoring as a process control problem and reformulate it as reference-based hypothesis testing, where the null hypothesis is specified by an empirical reference distribution rather than a fixed parametric model. We operationalize this perspective through a representation-based, nonparametric framework that combines pretrained time series encoders, kernel density estimation, and conformal calibration, yielding finite-sample valid inference in learned representation space. Classical notions such as stationarity and cyclostationarity arise as natural instantiations of empirical reference sets within this framework. Through experiments, we demonstrate sensitivity to window-level distributional deviations while maintaining well-calibrated inference under stable reference regimes, highlighting the applicability of the proposed approach to a broad class of time series process control and monitoring tasks.
GAUDI: Geometry-Aware Diffusion for Calibrated Air-Quality Time-Series Imputation