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ProbFM: Probabilistic Time Series Foundation Model with Uncertainty Decomposition

Arundeep Chinta, Lucas Vinh Tran, Jay Katukuri

TL;DR

Evaluation on cryptocurrency return forecasting demonstrates that DER maintains competitive forecasting accuracy while providing explicit epistemic-aleatoric uncertainty decomposition, establishing both an extensible framework for principled uncertainty quantification in foundation models and empirical evidence for DER's effectiveness in financial applications.

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.

ProbFM: Probabilistic Time Series Foundation Model with Uncertainty Decomposition

TL;DR

Evaluation on cryptocurrency return forecasting demonstrates that DER maintains competitive forecasting accuracy while providing explicit epistemic-aleatoric uncertainty decomposition, establishing both an extensible framework for principled uncertainty quantification in foundation models and empirical evidence for DER's effectiveness in financial applications.

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.
Paper Structure (46 sections, 23 equations, 3 figures, 34 tables)

This paper contains 46 sections, 23 equations, 3 figures, 34 tables.

Table of Contents

  1. Introduction
  2. Methodology: ProbFM Architecture and Training
  3. Problem Formulation and Theoretical Foundation
  4. ProbFM Architecture Design
  5. Input Encoding and Patch-Based Processing
  6. Transformer Architecture
  7. Deep Evidential Regression Head
  8. Enhanced Loss Function via Coverage Integration
  9. Evidential Loss Function.
  10. Coverage Loss Component.
  11. Combined Training Objective.
  12. Training Procedure and Optimization
  13. Single-Stage Training Protocol
  14. Optimization Strategy
  15. Inference and Uncertainty Quantification
  16. ...and 31 more sections

Figures (3)

  • Figure 1: 1-day log return distribution across assets in the cryptocurrency dataset. Left panel shows the training set distribution, right panel shows the test set distribution .
  • Figure 2: Distribution of actual versus predicted 1-day returns across all cryptocurrency assets using Evidential Regression. (Best viewed in color).
  • Figure 3: Overview of the ProbFM architecture pipeline, illustrating the end-to-end methodology from input processing to single-pass inference (Best viewed in color).