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#artificial intelligence Preprint Open access

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 Tae Yoon Lim Hwanil Choi Soonyoung Lee Wonbin Ahn
Nov 2026
Artificial Intelligence

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.

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