Causal Analysis for Time Series Foundation Models

Mathis Jander; Wouter van Heeswijk; Martijn Mes

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Causal Analysis for Time Series Foundation Models

Mathis Jander, Wouter van Heeswijk, Martijn Mes

arXiv:2608.24303v1Aug 25, 2026cs.LG

TL;DR

Time series foundation models expose many applications to shared biases and failure modes, while existing validation provides limited causal evidence before deployment. This paper formalizes an in-vitro causal analysis framework and finds stable pattern preservation alongside persistence bias and pattern-specific failures in Chronos-2 and TimesFM-2.5.

Problem
Foundation models can propagate shared biases and failure modes across many applications, while validation largely benchmarks uncontrolled real-world data rather than isolated causal mechanisms.
Method
The paper formalizes causal analysis using synthetic generators, interventions, and dose-response analysis across six time-series generators and five interventions.
Results
Chronos-2 and TimesFM-2.5 preserve some trend and harmonic patterns but overestimate persistence, fail on regime switches, and show energy-release failures for TimesFM-2.5.
Takeaways & Limitations
More diverse training data may help address identified biases and failure modes, while experimental findings support application-specific model selection.
Takeaways & Limitations
The findings are limited to comparisons with benchmark evidence that cannot establish whether experimental patterns transfer to real-world datasets.

Abstract

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Transitioning from bespoke time series models towards time series foundation models changes the relationship of model and application from one-to-one to one-to-many. This shift introduces concentration risk as many, potentially high-risk, forecasting applications are exposed to the same biases and failure modes of a single time series foundation model. At the same time, this centralization allows for economies of scale in model development and validation. In this study we investigate how biases and failure modes of time series foundation models can be identified before deployment. We propose a causal analysis framework to investigate the ability of a time series foundation model to preserve time series patterns. To achieve this, we intervene on parameterized synthetic time series generators and measure the corresponding change in model output under ceteris paribus conditions. We apply our causal analysis framework to Chronos-2 and TimesFM-2.5 and test them across six distinct time series patterns. We find safe configurations for trend and harmonic oscillation patterns. The results also indicate a bias in both models towards overestimating persistence, sudden failures for both models against the regime switch pattern and failure for TimesFM-2.5 against the energy-release pattern. Our review of the original works for both models indicates that the findings might be explained by the data used for pretraining. We conclude our study with suggestions for further model development, recommendations for application-specific model selection, and a discussion of limitations and further research directions.

1 Introduction

Time series forecasting supports critical decisions, but increasingly large models are becoming less interpretable. The shift from bespoke models to foundation models offers economies of scale while reducing deployment insight into biases and failure modes and introducing systemic risk.

Forecasts inform decision-making in critical domains including finance, energy, and policy, while larger datasets and parameter counts make time series models less interpretable.
Traditionally, each forecasting application used a bespoke model trained on an application-specific dataset, with development and deployment handled within one team or organization.
Foundation models create economies of scale in training and application but reduce deploying organizations’ insight into model development, biases, and failure modes.
Using one foundation model across many downstream applications introduces systemic risk.

2 Literature Review

The literature review situates causal analysis of time series foundation models within high-risk technology evaluation and adjacent machine-learning research. It identifies a methodological gap: existing causal time-series studies infer relationships between variables rather than evaluate models using interventions on time-series data.

Review scope: The review compares time series foundation-model research with risk-management practices from other engineering disciplines before examining Chronos-2, TimesFM-2.5, causal analysis, and adjacent research.Its scope begins with the original model studies, broadens to causal analysis of time series foundation models, and then considers related research streams.
Methodological gap: No identified literature applies causal analysis to study time series foundation models.Prior work on Granger causality and Pearlian structural causal models seeks causal relationships between variables, not model evaluation with time-series interventions.
Adjacent research: Adjacent explainable-AI research quantifies relationships between machine-learning inputs and outputs using techniques including SHAP, LIME, and Partial Dependence Plots.These prominent techniques were developed for tabular data, according to the reviewed passage.
Engineering precedents: High-risk technology evaluation in other engineering disciplines uses staged testing, beginning with in vitro causal analysis under ceteris paribus conditions and progressing to more realistic in vivo testing.The staged process trades realism for identifying causal mechanisms initially, then supports mapping dose-response relationships under more realistic conditions.

3 Methodology

The study uses a causal framework that intervenes on generator parameters while holding realization noise and other parameters constant, then compares parameter statistics of observed and forecast trajectories. It evaluates Chronos-2 and TimesFM-2.5 across six synthetic time-series generators under fixed experimental settings.

Causal analysis framework: The framework models the causal chain θ → y → M(y), where a parameterized generator produces a trajectory and the foundation model returns an output trajectory.A parameter statistic δ compresses trajectories into scalar estimates of generator properties.
Causal analysis framework: Parameter interventions set θ_i to α while keeping all other parameters and the noise sequence ϵ constant, isolating causal changes in δ(y) and δ(M(y)).The resulting mappings establish dose-response relationships between interventions and observed responses.
Experimental configuration: The empirical study applies the framework to Chronos-2 and TimesFM-2.5 across six generators, using T = 200, H = 200, and n = 50 independent noise realizations.The generators represent random walk with drift, AR(1), harmonic oscillation, regime switch, energy release, and fractional Brownian motion patterns.
Experimental configuration: The experiments intervene on drift, autoregressive coefficient, wavelength, dwell time, energy threshold, and Hurst exponent to test preservation of trend, persistence, periodicity, structural breaks, trigger events, and long-range dependence.Sweeps include µ ∈ {−0.05, −0.025, −0.005, 0.005, 0.025, 0.05}, β ∈ {−0.5, 0.0, 0.3, 0.6, 0.85, 0.98}, λ ∈ {5, 10, 25, 50, 75, 100}, τ ∈ {5, 10, 25, 50, 75, 100}, and κ ∈ {5, 10, 25, 50, 75, 100}.

4 Results

The causal analysis identifies stable preservation of drift and harmonic oscillation, alongside systematic persistence bias and failures on regime-switch, energy-release, and jaggedness patterns. Chronos-2 generally preserves threshold patterns better than TimesFM-2.5, while both models exhibit pattern-specific distortions.

Persistence bias: Both models overestimate persistence, producing higher ˆβ than the input trajectory for 0 < β < 0.85.For do(β = −0.5), Chronos-2 estimates β better than TimesFM-2.5.
Regime-switch failure: Chronos-2 and TimesFM-2.5 fail to preserve regimes for interventions where τ ≥50 and τ ≥25, respectively.At higher τ, TimesFM-2.5 shows stronger variance and deviation, overestimates τ, while Chronos-2 underestimates it.
Energy-release failure: Chronos-2 preserves the energy-release threshold pattern across interventions, whereas TimesFM-2.5 starts smoothing at κ ≥25 and loses the pattern completely for κ ≥50.Chronos-2 also shows better alignment and threshold-pattern preservation than TimesFM-2.5 across n = 50 noise realizations and n = 6×50 = 300 per model comparisons.
Jaggedness failure: Both models smooth the input trajectory and struggle to preserve jaggedness when H < 0.5, with both models biased toward overestimating ˆH.Chronos-2 overestimates H less than TimesFM-2.5.
Stable configurations: Both models preserve drift and harmonic oscillation characteristics within the tested configurations, although TimesFM-2.5 biases drift toward zero.In Experiment 1, both models preserve drift while removing noise; TimesFM-2.5 shows lower drift magnitudes and pulls late values toward zero.

5 Discussion

The discussion relates the causal findings to benchmark and case-study evidence, examines whether training data may explain observed behaviors, and derives implications for model development and application-specific selection. It emphasizes that more diverse training data may help target identified biases and failure modes.

Benchmark evidence: Benchmark aggregate metrics limit direct comparisons between the causal findings and reported performance on individual time series.The study reports Average Win Rate and Skill Score per model for each benchmark, without individual-series performance.
Benchmark evidence: Chronos-2 strongly smooths jagged patterns in Rossmann univariate sales forecasting, aligning with findings from Experiments 1, 2, and 6.This evidence comes from a case study rather than benchmark-level individual-series results.
Benchmark evidence: TimesFM-2.5 shows no clear domination on Darts and mixed dataset rankings on both Darts and Monash, including datasets presumed to contain trend or cyclical patterns.TimesFM-2.5 dominates on Monash overall, but rankings remain mixed across datasets.
Training-data interpretation: TimesFM-2.5 training data includes four of nineteen datasets categorized as trend, many datasets with periodic patterns, and synthetic piece-wise linear, ARMA, and seasonal data.Illustrative examples also heavily emphasize cyclical time series, which may help explain the observed findings.
Implications: For future development, the findings and review indicate that more diverse training data may help target the identified failure modes and biases.The discussion groups implications into future model development and model selection for applications.

6 Conclusion

The study presents a causal analysis framework for time series foundation models, identifying dose-response relationships and potential persistence-overestimation bias. It also outlines future research spanning broader experiments, domain-specific evaluation, model-behavior analysis, mitigation, and real-world validation.

Contributions: The study formalizes a causal analysis framework for time series foundation models and examines Chronos-2 and TimesFM-2.5 across six generators and five interventions.The authors describe this as the first study to formalize such a framework.
Contributions: Both models show potential bias toward overestimating persistence in Experiments 2 and 6.This finding is reported as one of the study’s identified model biases.
Future research: Future work could test more generators and time series foundation models, including domain-specific experiments for climate, finance, and sales.These extensions are proposed to analyze model suitability across domains.
Future research: The causal framework could be adapted to study how model components affect inference behavior and structure–behavior relationships.This direction aims to understand how different components influence model behavior during inference.
Future research: Future efforts should mitigate identified biases and failure modes and validate the findings in vivo using real-world datasets.The authors suggest that structured in vitro analysis could improve capabilities and inform application and regulation.