Time series process control using flexible empirical reference models
Towards Universal Representation-Based Process Control
Machine Learning
Summary
Many systems that monitor processes over time split data into small windows and make decisions based on each window. Traditional methods use fixed assumptions that may not match real-world data. The authors propose treating this as a testing problem where the expected behavior comes from actual example data instead of fixed formulas. They combine smart ways to summarize time series and statistical techniques to detect changes accurately while keeping false alarms low. Their method can adapt to many types of time-based monitoring tasks.
What this means in practice
- •For industrial monitoring teams: Detect shifts or anomalies in sensor data streams without relying on strict parametric assumptions.
- •For financial risk managers: Identify changes in market behavior by comparing recent time windows to historical reference patterns derived from past data.
Authors
Jinmyeong Choi, Taesup Kim, Artur Dubrawski
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.