QUAL: Quantile Alignment Improves Zero-Shot Time-Series Foundation Models

Junhyeok Kang; Sangjun Han; Jun Seo; Seunghan Lee; Jaehoon Lee; Dongwan Kang; Minjae Kim; Sungdong Yoo

cs.AIOct 30, 2026

QUAL: Quantile Alignment Improves Zero-Shot Time-Series Foundation Models

Authors: Junhyeok Kang, Sangjun Han, Jun Seo, Seunghan Lee, Jaehoon Lee, Dongwan Kang, Minjae Kim, Sungdong Yoo,

Organizations: LG AI Research

Abstract

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 ( $\downarrow$ )					CRPS ( $\downarrow$ )
Model	Origin.	Align.	$\Delta^{\text{Align}}_{\text{Imp}}$	LOO	$\Delta^{\text{LOO}}_{\text{Imp}}$	Origin.	Align.	$\Delta^{\text{Align}}_{\text{Imp}}$	LOO	$\Delta^{\text{LOO}}_{\text{Imp}}$
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.

\Delta^{\text{Align}}_{\text{Imp}}

and

\Delta^{\text{LOO}}_{\text{Imp}}

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 ( $\downarrow$ )	CRPS ( $\downarrow$ )
Quantile mean	$\times$	$\times$	0.6860	0.4677
Huber aggregation	$\times$	✓	0.6830	0.4657
Alignment $+$ mean	✓	$\times$	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

Time series forecasting predicts future values from ordered observations using statistical, neural, and probabilistic models to support decisions under uncertainty.

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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.

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