Time-series foundation models (TSFMs) provide zero-shot forecasts for unseen series, but their accuracy varies across datasets. Combining several models can reduce this variability, yet zero-shot deployment provides no target labels for selecting or weighting them. We find that a model pool is useful not only as a final ensemble, but also as a probability reference for transforming each member forecast. Aligning quantiles through this pool-relative reference improves every member forecast in aggregate. Motivated by this finding, we propose QUAL (Quantile alignment), a simple label-free framework for improving and combining diverse TSFMs. QUAL first produces aligned member forecasts, then applies Huber aggregation and rearrangement to obtain a robust combined forecast without training or model modification. On GIFT-Eval, quantile alignment reduces average member MASE and CRPS by 7.4% and 9.8%. The full framework remains robust when weak forecasters enter a candidate pool whose quality cannot be verified in advance. Code is available at https://github.com/junhyeokkang/QUAL.
Figures & tables
Figure 1: Parameter efficiency and subset win rate on GIFT-Eval. MASE and CRPS panels plot each pool against total parameter count; markers are single TSFMs, red lines are Pareto frontiers. Win rate is the fraction of subsets that beat the best individual model on both metrics.
MASE ( ↓ )
CRPS ( ↓ )
Model
Origin.
Align.
ΔImpAlign
LOO
ΔImpLOO
Origin.
Align.
ΔImpAlign
LOO
ΔImpLOO
TiRex-2 [ 23 ]
0.6969
0.6810
2.3%
0.6818
2.2%
0.4789
0.4704
1.8%
0.4716
1.5%
PatchTST-FM [ 29 ]
0.7069
0.6835
3.3%
0.6850
3.1%
0.4829
0.4732
2.0%
0.4741
1.8%
Timer-S1 [ 22 ]
0.6935
0.6783
2.2%
0.6811
1.8%
0.4856
0.4748
2.2%
0.4764
1.9%
FlowState [ 13 ]
0.7015
0.6824
2.7%
0.6836
2.6%
0.4866
0.4738
2.6%
0.4747
2.4%
TiRex [ 4 ]
0.7158
0.6838
4.5%
0.6840
4.4%
0.4885
0.4743
2.9%
0.4748
2.8%
Table 1: Per-member GIFT-Eval accuracy before ( Origin. ) and after ( Align. ) quantile alignment; LOO (leave-one-out) removes the evaluated model from the pooled reference. ΔImpAlign and ΔImpLOO are the percent improvements of Align. and LOO over Origin. Every member improves on both metrics.
Figure 2: CRPS degradation when weak forecasters enter the pool.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Method
Quantile alignment
Huber robust aggregation
MASE ( ↓ )
CRPS ( ↓ )
Quantile mean
×
×
0.6860
0.4677
Huber aggregation
×
✓
0.6830
0.4657
Alignment + mean
✓
×
0.6795
0.4646
QUAL (Ours)
✓
✓
0.6793
0.4646
Appendix
Table 2: Component ablation of QUAL on the strong pool. Each row toggles quantile alignment and Huber robust aggregation on or off while sharing the same TSFM forecasts; scores are averaged over the 97 GIFT-Eval configurations.
Figure 3: Alignment examples on a selected ETT1 window. Shading denotes the 10 – 90% prediction intervals; solid lines are the reported medians.
equal weights
fitted weights
quantile average
0.4672
0.4642
linear opinion pool
0.4634
0.4604
Appendix
Table 3: CRPS for equal or fitted weights crossed with quantile averaging or the linear opinion pool on the 97 GIFT-Eval configurations, using the six-TSFM pool.
Figure 4: Transfer of measured skill across the 97 GIFT-Eval configurations, computed on a six-TSFM diagnostic subset. (a) Rank correlation between backtest and forecast losses; (b) forecast-period rank of the backtest winner. The dashed baseline marks random selection.
Figure 5: Zero-shot accuracy by pool size across all 247 subsets of the strong pool, combined by QUAL. Boxes span subset quartiles; lines mark the median over the 97 GIFT-Eval configurations.
Time series forecasting predicts future values from ordered observations using statistical, neural, and probabilistic models to support decisions under uncertainty.
Time Series Foundation Models (TSFMs) currently provide state-of-the-art results in forecasting tasks. They are available out-of-the-box and rely on in-context learning to make their predictions, which makes the quality of their performance highly sensitive to the user-selected lookback, covariates, horizon and training data distributions. In practise, the quality of the forecasts are variable but complementary, which highlights the need for a principled ensembling approach, rather than selecting the best context. This paper introduces Latent Inference-Time Guidance for TSFMs, which adaptively combines a pool of TSFM forecasts through a time-dependent latent space with independent components. The framework comes equipped with identifiability and reconstruction guarantees, whilst maintaining the off-the-shelf aspect of foundation models. We provide experiments on datasets at various frequencies and from multiple domains: these show that the approach is competitive with traditional ensembling approaches.
Foundation models have transformed natural language processing and computer vision, and a rapidly growing literature on time-series foundation models (TSFMs) seeks to replicate this success in forecasting. While recent open-source models demonstrate the promise of TSFMs, the field lacks a comprehensive and community-accepted model evaluation framework. We see at least four major issues impeding progress on the development of such a framework. First, existing evaluation frameworks comprise benchmark forecasting tasks derived from often outdated datasets (e.g., M3), many of which lack clear metadata and overlap with the corpora used to pre-train TSFMs. Second, these frameworks evaluate models along a narrowly defined set of benchmark forecasting tasks, such as forecast horizon length or domain, but overlook core statistical properties such as non-stationarity and seasonality. Third, domain-specific models (e.g., XGBoost) are often compared unfairly, as existing frameworks do not enforce a systematic and consistent hyperparameter tuning convention for all models. Fourth, visualization tools for interpreting comparative performance are lacking. To address these issues, we introduce TempusBench, an open-source evaluation framework for TSFMs. TempusBench consists of 1) new datasets which are not included in existing TSFM pretraining corpora, 2) a set of novel benchmark tasks that go beyond existing ones, 3) a model evaluation pipeline with a standardized hyperparameter tuning protocol, and 4) a tensorboard-based visualization interface. We provide access to our code on GitHub: https://github.com/Smlcrm/TempusBench and maintain a live leaderboard at https://smlcrm.com/tempusbench.
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.