ProbFM: Probabilistic Time Series Foundation Model with Uncertainty Decomposition

TL;DR

This paper introduces ProbFM, a transformer-based probabilistic time series model that uses Deep Evidential Regression for explicit uncertainty decomposition, improving financial forecasting with principled uncertainty quantification.

Contribution

It presents the first application of DER in a transformer-based TSFM, enabling explicit epistemic-aleatoric uncertainty decomposition with efficient single-pass inference.

Findings

DER achieves competitive forecasting accuracy.

DER provides clear epistemic-aleatoric uncertainty separation.

ProbFM demonstrates effective uncertainty quantification in cryptocurrency forecasting.

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.