Rule-Based Detection of Structural Outliers in Non-Stationary Time Series

Outlier detection in time series is traditionally formulated as the identification of rare or extreme observations with respect to global statistical properties. While effective for stationary processes, this perspective becomes insufficient in complex and non-stationary systems, where atypical behavior may manifest as disruptions of stable relationships rather than numerical extremeness. This paper proposes a rule-based framework for detecting structural outliers in non-stationary time series. Regular system behavior is represented by an interpretable set of deterministic IF-THEN rules describing stable relational patterns between features. Each rule defines a logical context and an admissible range of a diagnostic quantity, estimated nonparametrically from historical observations satisfying the rule condition. For a given observation, the set of active rules is identified and a structural inconsistency score is computed as the fraction of violated rule consequences. Additionally, observations lacking support from high-frequency contexts are treated as candidates for structural atypicality. The method is deterministic and avoids the need for explicit probabilistic modeling or iterative parameter learning, which simplifies interpretation and implementation. The framework is illustrated on daily EUR/USD data (2010-2022) using technical indicators (EMA, RSI) and absolute log-returns as the diagnostic measure. Results provide evidence that structurally atypical events can be identified even when global statistical thresholds remain unviolated, suggesting the practical relevance of relational analysis for non-stationary time series monitoring contexts.