Financial time series forecasting is particularly challenging for transformer-based time series foundation models (TSFMs) due to non-stationarity, heavy-tailed distributions, and high-frequency noise present in data. Low-rank adaptation (LoRA) has become a popular parameter-efficient method for adapting pre-trained TSFMs to downstream data domains. However, it still underperforms in financial data, as it preserves the network architecture and training objective of TSFMs rather than complementing the foundation model. To further enhance TSFMs, we propose a novel refinement module, RefineBridge, built upon a tractable Schrödinger Bridge (SB) generative framework. Given the forecasts of TSFM as generative prior and the observed ground truths as targets, RefineBridge learns context-conditioned stochastic transport maps to improve TSFM predictions, iteratively approaching the ground-truth target from even a low-quality prior. Simulations on multiple financial benchmarks demonstrate that RefineBridge consistently improves the performance of state-of-the-art TSFMs across different prediction horizons.

翻译：金融时间序列预测对于基于Transformer的时间序列基础模型（TSFMs）尤为困难，因为数据中存在非平稳性、重尾分布和高频噪声。低秩自适应（LoRA）已成为将预训练TSFMs适配到下游数据领域的主流参数高效方法。然而，由于该方法保留了TSFMs的网络架构和训练目标而非对基础模型进行补充，其在金融数据上的表现仍不理想。为进一步增强TSFMs，我们提出一种基于可处理薛定谔桥（SB）生成框架的新型优化模块——RefineBridge。该模块以TSFM的预测结果作为生成先验，以观测真值作为目标，通过学习上下文条件随机传输映射来改进TSFM的预测，即使从低质量先验出发也能通过迭代过程逼近真实目标。在多个金融基准数据集上的仿真实验表明，RefineBridge能够持续提升前沿TSFMs在不同预测时间跨度上的性能表现。