Time Series Foundation Models (TSFMs) have emerged as a promising approach for zero-shot financial forecasting, demonstrating strong transferability and data efficiency gains. However, their adoption in financial applications is hindered by fundamental limitations in uncertainty quantification: current approaches either rely on restrictive distributional assumptions, conflate different sources of uncertainty, or lack principled calibration mechanisms. While recent TSFMs employ sophisticated techniques such as mixture models, Student's t-distributions, or conformal prediction, they fail to address the core challenge of providing theoretically-grounded uncertainty decomposition. For the very first time, we present a novel transformer-based probabilistic framework, ProbFM (probabilistic foundation model), that leverages Deep Evidential Regression (DER) to provide principled uncertainty quantification with explicit epistemic-aleatoric decomposition. Unlike existing approaches that pre-specify distributional forms or require sampling-based inference, ProbFM learns optimal uncertainty representations through higher-order evidence learning while maintaining single-pass computational efficiency. To rigorously evaluate the core DER uncertainty quantification approach independent of architectural complexity, we conduct an extensive controlled comparison study using a consistent LSTM architecture across five probabilistic methods: DER, Gaussian NLL, Student's-t NLL, Quantile Loss, and Conformal Prediction. Evaluation on cryptocurrency return forecasting demonstrates that DER maintains competitive forecasting accuracy while providing explicit epistemic-aleatoric uncertainty decomposition. This work establishes both an extensible framework for principled uncertainty quantification in foundation models and empirical evidence for DER's effectiveness in financial applications.

翻译：时间序列基础模型已成为零样本金融预测的一种有前景的方法，展现出强大的可迁移性和数据效率优势。然而，其在金融应用中的采用受到不确定性量化方面根本性局限的阻碍：现有方法要么依赖于限制性的分布假设，要么混淆了不同来源的不确定性，或者缺乏原则性的校准机制。尽管近期的时间序列基础模型采用了混合模型、学生t分布或保形预测等复杂技术，但它们未能解决提供理论依据的不确定性分解这一核心挑战。我们首次提出了一种新颖的基于Transformer的概率框架——ProbFM（概率基础模型），该框架利用深度证据回归来提供具有显式认知-偶然不确定性分解的原则性不确定性量化。与预先指定分布形式或需要基于采样推理的现有方法不同，ProbFM通过高阶证据学习来学习最优的不确定性表示，同时保持单次计算效率。为了独立于架构复杂性而严格评估核心的深度证据回归不确定性量化方法，我们使用一致的LSTM架构对五种概率方法进行了广泛的受控比较研究：深度证据回归、高斯负对数似然、学生t分布负对数似然、分位数损失和保形预测。在加密货币收益率预测上的评估表明，深度证据回归在保持竞争力的预测准确性的同时，提供了显式的认知-偶然不确定性分解。这项工作既为基础模型中的原则性不确定性量化建立了一个可扩展的框架，也为深度证据回归在金融应用中的有效性提供了实证证据。