ProbFM: Probabilistic Time Series Foundation Model with Uncertainty Decomposition

• URL: http://arxiv.org/abs/2601.10591v1
• Date: Thu, 15 Jan 2026 17:02:06 GMT
• Title: ProbFM: Probabilistic Time Series Foundation Model with Uncertainty Decomposition
• Abstract summary: Time Series Foundation Models (TSFMs) have emerged as a promising approach for zero-shot financial forecasting.<n>Current approaches either rely on restrictive distributional assumptions, conflate different sources of uncertainty, or lack principled calibration mechanisms.<n>We present a novel transformer-based probabilistic framework, ProbFM, that leverages Deep Evidential Regression (DER) to provide principled uncertainty quantification.
• Score: 0.12489632787815884
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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