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DCD: Decomposition-based Causal Discovery from Autocorrelated and Non-Stationary Temporal Data

Muhammad Hasan Ferdous, Md Osman Gani

TL;DR

The paper tackles causal discovery in non-stationary, autocorrelated multivariate time series by decomposing each series into trend, seasonal, and residual components and performing component-specific causal analysis before integrating results into a unified multi-scale graph. It formalizes identifiability guarantees under a set of assumptions, including spectral separability and a bounded leakage term within a Linear Gaussian SEM, and provides empirical validation on synthetic and real-world climate data showing improved recovery and interpretability over baselines. The decomposition-based framework isolates long-term and short-term causal effects, reducing spurious edges and yielding domain-consistent insights across finance, climate science, and healthcare. This approach enhances the reliability and interpretability of causal inferences in complex temporal systems and offers a pathway to bridging time series forecasting with causal discovery.

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.

DCD: Decomposition-based Causal Discovery from Autocorrelated and Non-Stationary Temporal Data

TL;DR

The paper tackles causal discovery in non-stationary, autocorrelated multivariate time series by decomposing each series into trend, seasonal, and residual components and performing component-specific causal analysis before integrating results into a unified multi-scale graph. It formalizes identifiability guarantees under a set of assumptions, including spectral separability and a bounded leakage term within a Linear Gaussian SEM, and provides empirical validation on synthetic and real-world climate data showing improved recovery and interpretability over baselines. The decomposition-based framework isolates long-term and short-term causal effects, reducing spurious edges and yielding domain-consistent insights across finance, climate science, and healthcare. This approach enhances the reliability and interpretability of causal inferences in complex temporal systems and offers a pathway to bridging time series forecasting with causal discovery.

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.
Paper Structure (36 sections, 5 theorems, 19 equations, 6 figures, 5 tables, 4 algorithms)

This paper contains 36 sections, 5 theorems, 19 equations, 6 figures, 5 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Theoretical Framework and Methodology
  4. Theoretical Guarantees and Identifiability
  5. Formal Problem Setup
  6. Assumptions
  7. Identifiability Analysis
  8. Empirical Verification of Seasonal Projection
  9. Data-Generating Process.
  10. Validation Results.
  11. The DCD Framework
  12. Decomposition (Satisfying Assumptions A2 & A3)
  13. Component-Specific Causal Analysis
  14. Integration of Multi-Scale Causal Graphs
  15. Results and Discussion
  16. ...and 21 more sections

Key Result

Lemma 1

Consider a causal pathway $S_X(t) \to Y(t)$ where $S_X$ is a seasonal driver. Under Assumption A3, the decomposition of $Y(t)$ projects this influence onto $S_Y(t)$, orthogonal to the residual subspace $R_Y(t)$ up to order $\varepsilon$.

Figures (6)

  • Figure 1: Overview of the proposed Decomposition-based Causal Discovery (DCD) framework. The multivariate time series dataset is decomposed into trend, seasonal, and residual components using STL decomposition. Each component undergoes a specific causal analysis—ADF/KPSS tests identify variables with long-term dependencies, HSIC tests identify variables with cyclical dependencies, and constraint-based search derives short-term causal relationships. The resulting causal graphs are then integrated into a comprehensive causal structure capturing multi-scale causal dependencies.
  • Figure 2: Empirical verification of Lemma \ref{['lem:projection']}. (a) The true seasonal component $S_X$ drives $S_Y$. (b) The true residual $R_X$ drives $R_Y$. (c) STL decomposition successfully separates the estimated seasonal $\widehat{S}_Y$ and residual $\widehat{R}_Y$ components. (d) Scatter plot confirming that the seasonal driver $S_X$ is orthogonal to the estimated residual $\widehat{R}_Y$ ($\rho \approx 0.0008$), confirming that seasonal leakage is negligible.
  • Figure 3: Performance evaluation of different causal discovery methods on synthetic datasets. The plots show True Positive Rate (TPR, higher is better), False Discovery Rate (FDR, lower is better), and Structural Hamming Distance (SHD, lower is better). Our method (DCD) demonstrates consistently superior performance across all metrics.
  • Figure 4: Impact of Sample Size on Causal Discovery Performance. The results indicate that our proposed method (DCD) achieves consistently high TPR, lower FDR, and lower SHD compared to baseline methods across different sample sizes. This demonstrates the robustness of our approach in varying data availability conditions.
  • Figure 5: Impact of dataset characteristics on causal discovery performance. The first row evaluates the effect of temporal lag, and the second row assesses the impact of the number of variables. Our approach remains robust across different experimental conditions.
  • ...and 1 more figures

Theorems & Definitions (10)

  • Lemma 1: Projection of Seasonal Influence
  • proof
  • Lemma 2: Weak Dependence of Residuals
  • proof
  • Corollary 1: Seasonal-to-Residual Removal
  • proof
  • Corollary 2: Trend--Seasonal Leakage Bound
  • proof
  • Theorem 1: Identifiability under Linear Gaussianity
  • proof