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Rule-Based Detection of Structural Outliers in Non-Stationary Time Series
1Institute of Information Technology, Lodz University of Technology, Al. Politechniki 8, 93-590 Lodz, Poland.
Entropy (Basel, Switzerland)
|July 28, 2026
Summary
This study introduces a rule-based method to detect structural outliers in non-stationary time series by analyzing relational patterns. The approach identifies atypical behavior through rule violations, offering a simpler alternative to traditional statistical outlier detection.
Area of Science:
- Time Series Analysis
- Data Mining
- Financial Econometrics
Background:
- Traditional outlier detection focuses on extreme values, insufficient for non-stationary systems.
- Atypical behavior in complex systems often involves disruptions in relationships, not just numerical extremeness.
Purpose of the Study:
- Propose a novel rule-based framework for identifying structural outliers in non-stationary time series.
- Develop an interpretable method that avoids complex probabilistic modeling.
Main Methods:
- Represent normal system behavior using deterministic IF-THEN rules defining stable relational patterns.
- Estimate a structural inconsistency score based on the fraction of violated rule consequences.
- Identify atypical observations lacking support from high-frequency contexts.
Main Results:
- Demonstrated the framework's effectiveness on daily EUR/USD exchange rate data (2010-2022).
- Identified structurally atypical events using technical indicators (EMA, RSI) and log-returns.
- Showcased detection of outliers missed by traditional statistical methods.
Conclusions:
- The rule-based framework offers a practical approach for detecting structural outliers in non-stationary time series.
- Relational analysis provides valuable insights for monitoring complex systems beyond numerical extremeness.
- The deterministic and interpretable nature simplifies implementation and understanding.
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