Robust Causal Discovery in Real-World Time Series with Power-Laws

Exploring causal relationships in stochastic time series is a challenging yet crucial task with a vast range of applications, including finance, economics, neuroscience, and climate science. Many algorithms for Causal Discovery (CD) have been proposed; however, they often exhibit a high sensitivity to noise, resulting in spurious causal inferences on real data. In this paper, we observe that the frequency spectra of many real-world time series follow a power-law distribution, notably due to an inherent self-organizing behavior. Leveraging this insight, we build a robust CD method based on the extraction of power‑law spectral features that amplify genuine causal signals. Our method consistently outperforms state-of-the-art alternatives on both synthetic benchmarks and real-world datasets with known causal structures, demonstrating its robustness and practical relevance.

Standard algorithms for discovering cause-and-effect relationships often mistake correlations for genuine causal links, especially when data is noisy or changes over time. In our paper, we observe that in many complex systems, from financial markets and economic networks to biology and physics, the observed data follow distinctive patterns that repeat across multiple timescales, a property called "scale-free" behavior. We show that this structural property can be leveraged to find causation more reliably, and we introduce PLaCy, a framework that operates in the frequency domain rather than directly on raw observations. PLaCy tracks how each signal's frequency pattern evolves over time and identifies whether shifts in one signal's pattern reliably precede shifts in another's, interpreting these shifts as evidence of causation. Across both controlled experiments and real-world datasets, PLaCy consistently outperforms existing methods, particularly in noisy, non-stationary settings where current approaches struggle most.