Causal-Audit: A Framework for Risk Assessment of Assumption Violations in Time-Series Causal Discovery

Marco Ruiz; Miguel Arana-Catania; David R. Ardila; Rodrigo Ventura

cs.LGApr 2, 2026

Causal-Audit: A Framework for Risk Assessment of Assumption Violations in Time-Series Causal Discovery

Authors: Marco Ruiz, Miguel Arana-Catania, David R. Ardila, Rodrigo Ventura

Organizations: Institute for Systems and Robotics, Instituto Superior Técnico, 1049-001 Lisbon, Portugal · Digital Scholarship at Oxford, University of Oxford, Oxford, OX1 3BG, United Kingdom · Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

Abstract

Time-series causal discovery methods rely on assumptions such as stationarity, regular sampling, and bounded temporal dependence. When these assumptions are violated, structure learning can produce confident but misleading causal graphs without warning. We introduce Causal-Audit, a framework that formalizes assumption validation as calibrated risk assessment. The framework computes effect-size diagnostics across five assumption families (stationarity, irregularity, persistence, nonlinearity, and confounding proxies), aggregates them into four calibrated risk scores with uncertainty intervals, and applies an abstention-aware decision policy that recommends methods (e.g., PCMCI+, VAR-based Granger causality) only when evidence supports reliable inference. The semi-automatic diagnostic stage can also be used independently for structured assumption auditing in individual studies. Evaluation on a synthetic atlas of 500 data-generating processes (DGPs) spanning 10 violation families demonstrates well-calibrated risk scores (AUROC > 0.95), a 62% false positive reduction among recommended datasets, and 78% abstention on severe-violation cases. On 21 external evaluations from TimeGraph (18 categories) and CausalTime (3 domains), recommend-or-abstain decisions are consistent with benchmark specifications in all cases. An open-source implementation of our framework is available.

Figures & tables

Family	Assumption	Consequence if Violated	Error
@BTrule []Stationarity	No trends or regime changes	Spurious links from trends	FP
Irregularity	No gaps or missing values	Selection bias, incorrect lags	Bias
Persistence	Low autocorrelation	Inflated significance	FP
Nonlinearity	Linear relationships	Missed nonlinear effects	FN
Confounding proxies	Stable model coefficients	Spurious links from instability	FP

Table 1: Assumption families and consequences of violations. Causal-Audit computes diagnostics for all five families and aggregates four (all except nonlinearity) into calibrated risk scores.

Figure 4: Detailed flowcharts for each pipeline stage. (a) Stage I: Diagnostic Auditing computes five diagnostic families from input

\mathbf{X}

, producing the diagnostic vector

\mathbf{d}=[d_{1},\ldots,d_{5}]

. (b) Stage II: Risk Estimation transforms diagnostics into calibrated risk scores via logistic aggregation, isotonic calibration, and bootstrap uncertainty quantification. (c) Stage III: Decision Policy evaluates thresholds to output Recommend

m^{*}

or Abstain .

VIF Range	Linear (VAR/Granger)	PCMCI+ (ParCorr)	Transfer Entropy
@BTrule [] $<10$	Reliable	Reliable	Reliable
$10$ to $100$	Caution	With regularization	Reliable
$100$ to $10^{4}$	Unreliable	Pseudo-inverse needed	Caution
$>10^{4}$	Unreliable	Consider alternatives	Caution

Table 2: Expected method-specific VIF tolerance, derived from the statistical properties of each estimator class. The VIF

<10

threshold follows the widely adopted rule of thumb [ 70 ] , though recent work suggests context-dependent interpretation [ 71 ] . Higher VIF ranges reflect the known sensitivity of OLS-based and partial-correlation-based estimators to collinear inputs; information-theoretic estimators avoid numerical instability from collinearity but suffer from degraded conditional distribution estimates in finite samples.

Risk Dimension	Model	Key Features
@BTrule [] $R_{\mathrm{nonstat}}$	$\sigma(-2.0+1.0\cdot x_{\mathrm{break\_mag}}+2.0\cdot x_{\mathrm{drift}}$	Break magnitude and drift
	$+0.5\cdot x_{\mathrm{adf}}+0.5\cdot x_{\mathrm{kpss}})$	slope dominate
@BTrule [] $R_{\mathrm{irreg}}$	$\sigma(-1.5+2.5\cdot x_{\mathrm{gap\_cv}}+2.0\cdot x_{\mathrm{missing}}$	Gap regularity is primary
	$+1.5\cdot x_{\mathrm{seasonal\_miss}})$	contributor
@BTrule [] $R_{\mathrm{persist}}$	$\sigma(-1.5+(-3.0)\cdot x_{T_{\mathrm{eff}}/T}$	Negative weight: lower
	$+2.0\cdot x_{\tau_{\mathrm{int}}})$	$T_{\mathrm{eff}}/T\rightarrow$ higher risk

Table 3: Risk-specific logistic regression models. Weights are initialized from domain knowledge and refined via hierarchical Bayesian calibration.

Parameter	Value
@BTrule []Calibration / validation split	396(79%) / 100 (21%)
Stratification	By violation family
Isotonic binning	10 quantile bins
Stability assessment	5-fold and 10-fold stratified CV

Table 4: Calibration configuration.

Method	$R_{\mathrm{comp}}$	$R_{\mathrm{nonstat}}$	$R_{\mathrm{irreg}}$	$R_{\mathrm{confound}}$	$R_{\mathrm{persist}}$
@BTrule []Granger (VAR)	$\leq 0.30$	Hard $\leq 0.60$	Hard $\leq 0.50$	Hard $\leq 0.60$	Soft $\leq 0.75$
PCMCI+	$\leq 0.70$	Hard $\leq 0.80$	Soft $\leq 0.60$	Soft $\leq 0.80$	Soft $\leq 0.85$
LPCMCI †	$\leq 0.80$	Hard $\leq 0.80$	Soft $\leq 0.70$	Soft $\leq 0.90$	Soft $\leq 0.85$
Transfer Entropy †	$\leq 0.90$	Soft $\leq 0.85$	Soft $\leq 0.80$	Soft $\leq 0.95$	Soft $\leq 0.90$

Table 5: Method-assumption constraint mapping. Per-dimension thresholds reflect the relative robustness of each method to each violation type, informed by documented method properties (see text); composite thresholds are validated to ensure expected failure rates below 20% on the calibration corpus.

Table 6: Synthetic DGP Atlas: 10 violation families with severity gradations. Each family contains 50 datasets whose violation-controlling parameters span the severity levels listed in the rightmost column. Families F1–F9 use

N\in\{5,6,7,8\}

variables and

T\in\{500,750,1000\}

observations; F10 uses wider ranges (

N\in\{3\text{--}12\}

T\in\{200\text{--}2000\}

) to stress-test boundary conditions. Families F2–F5 correspond directly to the four calibrated risk dimensions. The remaining families target additional assumptions or combine multiple violations.

Time-Series Causal Discovery

Time-series causal discovery seeks to infer which variables influence others over time and when those effects occur.

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ISR-Lisbon, Instituto Superior Técnico, Av. Rovisco Pais 1, Lisbon, 1049-001, Portugal · Digital Scholarship at Oxford, University of Oxford, Oxford, OX1 3BG, United Kingdom · Jet Propulsion Lab., Caltech, Pasadena, CA 91109, California, USA

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TCD-Arena: Assessing Robustness of Time Series Causal Discovery Methods Against Assumption Violations

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Computer Vision Group Jena Friedrich Schiller University Jena Jena, Thuringia, 07743, DE

Time-Series Causal Discovery Causal Discovery

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Causal Discovery (CD) is a powerful framework for scientific inquiry. Yet, its practical adoption is hindered by a reliance on strong, often unverifiable assumptions and a lack of robust performance assessment. To address these limitations and advance empirical CD evaluation, we present TCD-Arena, a modularized, highly customizable, and extendable testing kit to assess the robustness of time series CD algorithms against stepwise more severe assumption violations. For demonstration, we conduct an extensive empirical study comprising around 30 million individual CD attempts and reveal nuanced robustness profiles for 33 distinct assumption violations. Further, we investigate CD ensembles and find that they have the potential to improve general robustness, which has implications for real-world applications. With this, we strive to ultimately facilitate the development of CD methods that are reliable for a diverse range of synthetic and potentially real-world data conditions.

Abstract

Time-Series Causal Discovery

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