Cutting through the noise: Explaining residuals in multivariate time series with motif analysis

Modeling real-world system dynamics is challenging due to non-periodic patterns, such as stimuli-dependent physiological responses in health, event-driven traffic in mobility, and news-triggered interactions in societal systems. In the absence of contextual data, state-of-the-art methods—including advanced deep learning architectures—struggle to model these irregular behaviors. Furthermore, their predictive focus often limits their utility for descriptive analysis, hampering knowledge acquisition. This work addresses these challenges by proposing a methodology to decompose multivariate time series residuals into statistically significant, meaningful events, effectively filtering noise. We extend the motif discovery task to identify irregular patterns satisfying key properties: non-triviality, statistical significance, multi-dimensionality, and actionability. Our approach introduces principles to mitigate biases, evaluate statistical significance, place robust hyperparameterization, explore relationships in multivariate residuals, and incorporate domain knowledge through specialized masks. Real-world case studies validate the proposed methodology, uncovering explainable patterns relevant to human activity recognition, energy consumption, and urban planning, accounting for up to 50% of irregular components and revealing hidden system behaviors. • Novel methodology to decompose residuals in multivariate time series into statistically significant patterns. • Extended motif discovery with non-triviality and statistical significance guarantees to reveal relevant non-periodic events. • Real-world case studies on activity recognition, energy optimization, and urban planning show that specific patterns explain up to 50% of the’noise’. • Integration of user preferences and domain knowledge for enhanced explainability. • Open-access tool enables user-friendly pattern exploration in irregular components.