Efficiently Generating Correlated Sample Paths from Multi-step Time Series Foundation Models

2025/10/02 by Ethan Baron, Baron, Ethan, Boris N. Oreshkin +13
Computer Science · #Time Series Analysis and Forecasting #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2510.02224

Abstract

Many time series applications require access to multi-step forecast trajectories in the form of sample paths. Recently, time series foundation models have leveraged multi-step lookahead predictions to improve the quality and efficiency of multi-step forecasts. However, these models only predict independent marginal distributions for each time step, rather than a full joint predictive distribution. To generate forecast sample paths with realistic correlation structures, one typically resorts to autoregressive sampling, which can be extremely expensive. In this paper, we present a copula-based approach to efficiently generate accurate, correlated sample paths from existing multi-step time series foundation models in one forward pass. Our copula-based approach generates correlated sample paths orders of magnitude faster than autoregressive sampling, and it yields improved sample path quality by mitigating the snowballing error phenomenon.

Citations

• TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning
• From Tables to Time: Extending TabPFN-v2 to Time Series Forecasting
• Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systems
• The pitfalls of next-token prediction
• A decoder-only foundation model for time-series forecasting
• TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series
• TACTiS: Transformer-Attentional Copulas for Time Series
• Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting
• From Predictions to Decisions: The Importance of Joint Predictive Distributions
• On Simulation and Trajectory Prediction with Gaussian Process Dynamics
• Multivariate Forecasting Evaluation: On Sensitive and Strictly Proper Scoring Rules
• Deep Generative Quantile-Copula Models for Probabilistic Forecasting
• An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling
• On the Properties of Neural Machine Translation: Encoder-Decoder Approaches

Related

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• TFMAdapter: Lightweight Instance-Level Adaptation of Foundation Models for Forecasting with Covariates
• Online conformal inference for multi-step time series forecasting