ProbFM: Probabilistic Time Series Foundation Model with Uncertainty Decomposition

ArXiv ID: 2601.10591 “View on arXiv”

Authors: Arundeep Chinta, Lucas Vinh Tran, Jay Katukuri

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.

Keywords: Time Series Foundation Models (TSFMs), Deep Evidential Regression (DER), Probabilistic Forecasting, Epistemic-Aleatoric Uncertainty, Zero-Shot Forecasting, Cryptocurrency

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper introduces advanced Bayesian concepts (Deep Evidential Regression, NIG priors) and derives uncertainty decompositions, yet backs it with a rigorous controlled comparison study, uncertainty-aware trading backtests, and specific performance metrics on cryptocurrency data.

  flowchart TD
    A["Research Goal<br/>Zero-Shot TSFM with<br/>Principled Uncertainty Quantification"] --> B["Methodology<br/>Deep Evidential Regression DER"]
    B --> C["Data<br/>Cryptocurrency Time Series"]
    C --> D["Training<br/>LSTM with DER Evidence Learning"]
    D --> E{"Evaluation"}
    E --> F["Comparison Methods<br/>Gaussian NLL, Student-t NLL, Q-Loss, CP"]
    E --> G["DER Results"]
    G --> H["Outcome: Epistemic-Aleatoric<br/>Uncertainty Decomposition"]