cs.LGAug 25, 2026

Causal Analysis for Time Series Foundation Models

Authors: Mathis Jander, Wouter van Heeswijk, Martijn Mes

Organizations: Faculty of Behavioral, Management and Social Sciences, University of Twente, Enschede, Netherlands · European Central Bank, Frankfurt am Main, Germany

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

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.

Figures & tables

Figure 1: The causal analysis framework. Parameter intervention on θi\theta_{i} serves as controlled dose and parameter statistics on y\mathbf{y} and M(y)M(\mathbf{y}) serve as observed responses.
ExperimentGeneratorIntervention Sweepδ\delta
1Random Walkμ∈{−0.05,−0.025,…,0.05}\mu\in\{-0.05,-0.025,\dots,0.05\}μ^\hat{\mu}
2AR(1)β∈{−0.5,0.0,…,0.98}\beta\in\{-0.5,0.0,\dots,0.98\}β^\hat{\beta}
3Harmonic Oscillatorλ∈{5,10,25,50,75,100}\lambda\in\{5,10,25,50,75,100\}λ^\hat{\lambda}
4Regime Switchτ∈{5,10,25,50,75,100}\tau\in\{5,10,25,50,75,100\}τ^\hat{\tau}
5Energy-releaseκ∈{5,10,25,50,75,100}\kappa\in\{5,10,25,50,75,100\}κ^\hat{\kappa}
6fBMH∈{0.15,0.3,…,0.85}H\in\{0.15,0.3,\dots,0.85\}H^\hat{H}
Table 1: Summary of experiments with generators, intervention sweeps and parameter statistics.
Figure 2: Trajectories across intervention sweep for a single noise realization in Experiment 1. Both time series foundation models seem to preserve the drift while removing noise. Towards the end of the trajectory, TimesFM-2.5 seems to pull values towards zero.
Figure 3: Distributions of parameter statistics for trajectory and model outputs across noise realizations in Experiment 1 ( n=50n=50 ). TimesFM-2.5 displays lower magnitudes for drift than the trajectory.
Figure 4: Comparison of model parameter statistic δ(M(y))\delta(M(\mathbf{y})) against trajectory parameter statistic δ(y)\delta(\mathbf{y}) for Experiment 1 ( n=6×50=300n=6\times 50=300 per model). Both models center around the idea line, while TimesFM-2.5 shows bias towards zero.
Figure 5: Trajectories across intervention sweep for a single noise realization in Experiment 2. Trajectories collapse close to flat lines for both time series foundation models.
Figure 6: Distributions of parameter statistics for trajectory and model outputs across noise realizations in Experiment 2 ( n=50n=50 ). Both time series foundation models overestimate β\beta for lower values, except for do⁡(β ⁣= ⁣−0.5)\operatorname{do}(\beta\!=\!-0.5) , where Chronos-2 seems to estimate β\beta better than TimesFM-2.5
Figure 7: Comparison of model parameter statistic δ(M(y))\delta(M(\mathbf{y})) against trajectory parameter statistic δ(y)\delta(\mathbf{y}) for Experiment 2 ( n=6×50=300n=6\times 50=300 per model). Both time series foundation models seem to produce outputs with a higher β^\hat{\beta} than in the input trajectory for 0<β<0.850<\beta<0.85 .
Figure 8: Trajectories across intervention sweep for a single noise realization in Experiment 3. Both time series foundation models seem to preserve wavelength across interventions.
Figure 9: Distributions of parameter statistics for trajectory and model outputs across noise realizations in Experiment 3 ( n=50n=50 ). Both models’ distributions align with the trajectory distribution and display no variance.
Figure 10: Comparison of model parameter statistic δ(M(y))\delta(M(\mathbf{y})) against trajectory parameter statistic δ(y)\delta(\mathbf{y}) for Experiment 3 ( n=6×50=300n=6\times 50=300 per model). Both models show ideal alignment with no visible deviations.
Figure 11: Trajectories across intervention sweep for a single noise realization in Experiment 4. Chronos-2 and TimesFM-2.5 fail to preserve regimes for interventions where τ≥50\tau\geq 50 and τ≥25\tau\geq 25 , respectively.
Figure 12: Distributions of parameter statistics for trajectory and model outputs across noise realizations in Experiment 4 ( n=50n=50 ). TimesFM-2.5 exhibits stronger variance and deviation from trajectory parameter statistic than Chronos-2 for higher values of τ\tau . Further TimesFM-2.5 seems to overestimate τ\tau while Chronos-2 seems to underestimate it with increasing values of τ\tau .
Figure 13: Comparison of model parameter statistic δ(M(y))\delta(M(\mathbf{y})) against trajectory parameter statistic δ(y)\delta(\mathbf{y}) for Experiment 4 ( n=6×50=300n=6\times 50=300 per model). TimesFM-2.5 seems to produce outputs with higher τ^\hat{\tau} than the trajectories for τ≥50\tau\geq 50 , while Chronos-2 produces outputs with lower τ^\hat{\tau} for τ≥50\tau\geq 50 .
Figure 14: Trajectories across intervention sweep for a single noise realization in Experiment 5. Chronos-2 preserves the threshold pattern across the full range of interventions while TimesFM-2.5 seems to start smoothing at κ≥25\kappa\geq 25 and loses pattern completely for κ≥50\kappa\geq 50 .
Figure 15: Distributions of parameter statistics for trajectory and model outputs across noise realizations in Experiment 5 ( n=50n=50 ). Chronos-2 is better at preserving the threshold pattern across the range of interventions than TimesFM-2.5 .
Figure 16: Comparison of model parameter statistic δ(M(y))\delta(M(\mathbf{y})) against trajectory parameter statistic δ(y)\delta(\mathbf{y}) for Experiment 5 ( n=6×50=300n=6\times 50=300 per model). Chronos-2 displays better aligment than TimesFM-2.5 .
Figure 17: Trajectories across intervention sweep for a single noise realization in Experiment 6. Both models struggle with preserving the jaggedness for interventions where H<0.5H<0.5 and both smooth out the input trajectory y\mathbf{y} across interventions.
Figure 18: Distributions of parameter statistics for trajectory and model outputs across noise realizations in Experiment 6 ( n=50n=50 ). Distributions of both models overestimate HH relative to the trajectory distribution, while Chronos-2 does so less than TimesFM-2.5 .
Figure 19: Comparison of model parameter statistic δ(M(y))\delta(M(\mathbf{y})) against trajectory parameter statistic δ(y)\delta(\mathbf{y}) for Experiment 6 ( n=6×50=300n=6\times 50=300 per model). Both models are biased towards overestimating H^\hat{H} .
PatternChronos-2 BehaviorTimesFM-2.5 BehaviorRecommendation
Random WalkPreserves drift magnitude ( μ^\hat{\mu} closer to trajectory)Underestimates drift magnitude (bias toward zero)Chronos-2
AR(1)Output collapses to lineOutput collapses to lineAvoid
Harmonic OscillatorPreserves λ^\hat{\lambda} ; cuts amplitude for some wavelengthsPreserves λ^\hat{\lambda} ; cuts amplitude for some wavelengthsTie
Regime SwitchPreserves regimes and dwell time up to τ=50\tau=50Deviates earlier; leaves ideal line at τ=25\tau=25Chronos-2
Energy-releasePreserves pattern across range; underestimates at κ=100\kappa=100Smoothes at 25<κ<5025<\kappa<50 ; strong underestimation at κ=100\kappa=100Chronos-2
fBmOverestimates H^\hat{H} ; strong smoothing for H<0.5H<0.5Overestimates H^\hat{H} ; strong smoothing for H<0.5H<0.5Avoid
Table 2: Comparison of model behaviors, failure modes, and model selection recommendations across patterns.
Figure 22

Explore similar work

CardsList
Oct 1, 2026cs.LG

Foundations without Fundamentals: Zero-Shot Blind Spots in Time Series FMs

Despite the success of Time Series Foundation Models (TSFMs) on broad benchmarks, their ability to internalize basic temporal logic, especially in settings supported by exogenous covariates, remains under-examined. We introduce SimpleTimeBench, a diagnostic univariate and multivariate "unit test" suite for primitives such as monotonic trends, periodic signals and leading indicator covariates, scenarios where near-perfect forecasts should be trivial. Surprisingly, prominent multivariate TSFMs (Chronos-2, Moirai and Toto) frequently produce suboptimal zero-shot forecasts for these inputs. While fine-tuning Chronos-2 improves its behaviour on specific tasks, we show that this adaptation degrades performance on other fundamental patterns rather than enhancing its generalizable foundational capabilities. This reveals a gap between pre-training scale and basic temporal reasoning, suggesting that current TSFMs could potentially lack the inductive biases needed to capture simple predictable functions. We further demonstrate that these failures are not merely synthetic curiosities: they persist in real-world sensor forecasting, where TSFMs consistently underutilize leading indicators available in observed covariates. This inability to capture simple relationships limits the practical utility and reliability of current multivariate models.

Nafiseh Ghoroghchian, Haipeng Zhang, Shuyi Han +2

Layer6 AI

Multivariate Time Series ForecastingZero-Shot Time Series ForecastingTime Series ReasoningTime Series ForecastingForecasting BenchmarksTime-Series Foundation Models
AskPDF
Sep 28, 2026cs.AI

Dynamical Parameters: An Interpretability Framework for Time-Series Foundation Models

This work studies a central gap in interpreting time-series foundation models (TSFMs): a dynamical property may be accessible in a hidden state even when the forecast fails to respond correctly as that property changes. We formalize these properties as Dynamical Parameters, including trend slope, oscillation frequency, and autoregressive dependence. We compare their representation accessibility, measured by recovery from hidden states, with their forecast response, measured by agreement with the expected forecast change. Across nine frozen TSFMs and thirteen laws, 42 of 63 model-parameter cells achieve accessibility above 0.95, whereas their median reference-aligned response relative to the conditional reference is only 0.46. To explain this gap, causal geometry compares the hidden-state change required to produce the reference response with the change induced by the parameter intervention. Directly modifying the hidden state recovers the reference response, but the parameter intervention often moves the state in a different direction. These results show that accessible parameter information need not be expressed in forecasts when input changes miss the required hidden-state direction.

Kang Yang, Gaofeng Dong, Liying Han +1

Department of Electrical and Computer Engineering University of California, Los Angeles

Explainable Time Series ForecastingRepresentation ProbingTime Series Representation LearningTime-Series Foundation Models
AskPDF
Jul 6, 2026cs.LG

When Do Foundation Models Pay Off? A Break-Even Analysis of Pretrained Time Series Forecasters

Deploying a time series foundation model requires GPU infrastructure, engineering overhead, and carries no guarantee of improvement over XGBoost. We provide the first systematic break-even analysis answering when this investment pays off. Across 30 benchmark datasets, we compare zero-shot and LoRA fine-tuned foundation models (Chronos, Moirai, Lag-Llama) against classical baselines (Naive, ETS, ARIMA, XGBoost) at six training set sizes from 2% to 100% of available data. Foundation models outperform classical methods at every evaluated training fraction on 15 of 30 datasets -- GPU deployment is unconditionally justified on these regardless of data volume. On 6 datasets, classical methods surpass zero-shot foundation models with as little as 2% of training data (21-2,768 samples); on the remaining 9, break-even ranges from 24 to 8,361 samples. One robust deployment rule requires no model training: if n_train < 700 and seasonality is non-negligible, use FM zero-shot and skip fine-tuning -- this resolves 10 of 30 deployment decisions immediately. Contrary to common practice, LoRA fine-tuning can actively degrade performance on short series. We operationalise these findings as a two-step decision framework -- compute dataset length and seasonality strength, run a brief 5-10% pilot only if needed -- enabling practitioners to make the FM-versus-classical decision before committing to full infrastructure. Four dataset features motivate mechanistic hypotheses for the remaining cases, though reliable automated prediction at this benchmark scale remains an open problem. Code, benchmark, and decision tools are available at https://github.com/nicolaisi/fm-breakeven.

Nicholas Tan Jerome, Frank Simon

Karlsruhe Institute of Technology (KIT) Eggenstein-Leopoldshafen, Germany

Zero-Shot Time Series ForecastingTime Series ForecastingForecasting BenchmarksTime-Series Foundation Models
AskPDF