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
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.