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 in 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.

翻译：探索随机时间序列中的因果关系是一项具有挑战性但至关重要的任务，广泛应用于金融、经济学、神经科学和气候科学等领域。目前已提出多种因果发现（Causal Discovery, CD）算法，但这些算法通常对噪声高度敏感，导致在真实数据中产生虚假的因果推断。本文观察到，许多现实时间序列的频谱遵循幂律分布，这主要源于其内在的自组织行为。基于这一发现，我们构建了一种鲁棒因果发现方法，该方法通过提取幂律频谱特征来放大真实因果信号。在合成基准测试和已知因果结构的真实数据集上，我们的方法始终优于现有最优方法，证明了其鲁棒性和实际应用价值。