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 · #Autoregressive integrated moving average #Autoregressive model #Neural Networks and Applications #Path (computing) #STAR model #Sample (material) #Series (stratigraphy) #Time Series Analysis and Forecasting #Time series

paper · pdf · doi:10.48550/arxiv.2510.02224

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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
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• 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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• Online conformal inference for multi-step time series forecasting