ProbFM: Probabilistic Time Series Foundation Model with Uncertainty Decomposition

Paper: arXiv 2601.10591

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10 (capped from 6.5: transaction costs not modelled; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (19)

1. Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting (2023) — link
2. Evidential Deep Learning to Quantify Classification Uncertainty (2018)
3. Deep Evidential Regression (2020)
4. DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks (2020)
5. Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting (2021)
6. TimeGPT-1 (2023) — link
7. Toto: Time Series Optimized Transformer for Observability (2024) — link
8. Unified Training of Universal Time Series Forecasting Transformers (2024) — link

0 of 19 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.