DCD: Decomposition-based Causal Discovery from Autocorrelated and Non-Stationary Temporal Data
Decomposition-based causal discovery (DCD) separates trend, seasonal, residual components, improving causal inference in non-stationary time series by 20-30% over baselines.
Key Findings
Methodology
This paper introduces a framework combining spectral decomposition and causal inference. It decomposes multivariate time series into trend, seasonal, and residual parts using STL. Trend components are tested with ADF/KPSS for long-term dependencies, seasonal parts via HSIC for cyclicity, and residuals through constraint-based causal discovery. These component graphs are integrated into a unified multi-scale causal graph, ensuring theoretical guarantees under spectral separability and bounded leakage. The approach effectively isolates different causal effects, reducing spurious links common in raw data analysis.
Key Results
- On synthetic datasets, DCD achieved a TPR of 0.79 and FDR of 0.38, outperforming PCMCI+ and DYNOTEARS, especially under high autocorrelation and non-stationarity. In real climate and electricity data, DCD accurately recovered ground-truth causal structures with SHD reduced by over 20% compared to baselines.
- Across sample sizes (500-1500) and variable counts (4-10), DCD maintained TPR around 0.77-0.80, with minimal FDR increase (~0.04). It effectively detected long-lag dependencies, outperforming existing methods in robustness and precision.
- Ablation studies confirmed that multi-scale integration significantly boosts accuracy, with spectral separation being crucial. Single-scale or naive decomposition methods showed inferior performance, validating the theoretical insights.
Significance
This work advances causal inference in non-stationary, autocorrelated time series, a long-standing challenge in fields like climate science, finance, and healthcare. By leveraging spectral separation and multi-scale analysis, it reduces false positives caused by trends and seasonalities, enabling more reliable causal structure recovery. The framework enhances interpretability and robustness, facilitating better decision-making and scientific understanding of complex dynamic systems.
Technical Contribution
Technically, the paper introduces a novel spectral separation condition for causal identifiability, combined with STL-based decomposition and frequency-domain dependence tests. It provides formal guarantees under linear Gaussian models, deriving bounds on structural errors related to spectral leakage. The multi-scale graph fusion mechanism is a key engineering contribution, enabling scalable and interpretable causal analysis across different temporal resolutions.
Novelty
This is the first systematic integration of spectral decomposition with causal discovery, establishing spectral separability as a core condition for identifiability in non-stationary data. Unlike prior works relying solely on temporal or statistical independence, this approach explicitly isolates causal effects at different frequency bands, significantly reducing confounding from trends and seasonality. The theoretical guarantees and practical algorithms set a new standard for multi-scale causal inference.
Limitations
- The method assumes spectral support separation, which may be violated in highly overlapping trend and seasonal components, reducing accuracy.
- Extensions to nonlinear or non-Gaussian systems are non-trivial; current guarantees rely on linear Gaussian assumptions.
- Computational complexity increases with data dimensionality and length, limiting real-time applications in very large systems.
Future Work
Future directions include relaxing spectral assumptions, extending to nonlinear models, and integrating deep learning for adaptive decomposition. Improving computational efficiency and scalability will be prioritized, alongside exploring dynamic spectral boundaries to handle evolving systems. These enhancements aim to broaden applicability and robustness in real-world complex systems.
AI Executive Summary
Understanding causal relationships in multivariate time series is vital across many scientific and industrial fields, yet traditional methods struggle when data exhibit non-stationarity, long-term trends, and seasonal patterns. These issues often lead to spurious causal links, obscuring true mechanisms. Existing approaches like Granger causality or constraint-based algorithms typically operate directly on raw observations, making them vulnerable to confounding effects caused by non-stationary components.
This paper proposes a novel framework called Decomposition-based Causal Discovery (DCD), which addresses these challenges by explicitly separating each time series into trend, seasonal, and residual components using STL (Seasonal-Trend decomposition via LOESS). The trend component is tested with stationarity tests (ADF/KPSS) to identify long-term dependencies, the seasonal component is examined with HSIC to detect cyclic influences, and the residuals are analyzed with a constraint-based causal discovery method to uncover short-term interactions. The resulting component-specific graphs are then integrated into a comprehensive multi-scale causal structure.
The core innovation lies in leveraging spectral separation—assuming that different components occupy distinct frequency bands—to guarantee the identifiability of causal links. Theoretical analysis demonstrates that under linear Gaussian assumptions, the method can bound the error introduced by spectral leakage, ensuring reliable causal inference even in complex non-stationary settings.
Empirical results on synthetic data show that DCD outperforms state-of-the-art baselines such as PCMCI+ and DYNOTEARS, achieving higher true positive rates and lower false discoveries, especially under conditions of strong autocorrelation and non-stationarity. Real-world climate and electricity datasets further validate its effectiveness, recovering ground-truth causal structures with notable accuracy.
This work significantly advances causal analysis in dynamic systems, providing a scalable, interpretable, and theoretically grounded approach. It opens avenues for more robust causal inference in fields where non-stationarity and spectral confounding are prevalent, such as climate modeling, financial analysis, and biomedical research. Future efforts will focus on extending the framework to nonlinear models, improving computational efficiency, and adapting to evolving spectral properties, ultimately broadening its impact across scientific disciplines.
Deep Dive
Abstract
Multivariate time series in domains such as finance, climate science, and healthcare often exhibit long-term trends, seasonal patterns, and short-term fluctuations, complicating causal inference under non-stationarity and autocorrelation. Existing causal discovery methods typically operate on raw observations, making them vulnerable to spurious edges and misattributed temporal dependencies. We introduce a decomposition-based causal discovery framework that separates each time series into trend, seasonal, and residual components and performs component-specific causal analysis. Trend components are assessed using stationarity tests, seasonal components using kernel-based dependence measures, and residual components using constraint-based causal discovery. The resulting component-level graphs are integrated into a unified multi-scale causal structure. This approach isolates long- and short-range causal effects, reduces spurious associations, and improves interpretability. Across extensive synthetic benchmarks and real-world climate data, our framework more accurately recovers ground-truth causal structure than state-of-the-art baselines, particularly under strong non-stationarity and temporal autocorrelation.