Efficiently Generating Correlated Sample Paths from Multi-step Time Series Foundation Models
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.
Cite
@article{arxiv.2510.02224,
title = {Efficiently Generating Correlated Sample Paths from Multi-step Time Series Foundation Models},
author = {Ethan Baron and Boris Oreshkin and Ruijun Ma and Hanyu Zhang and Kari Torkkola and Michael W. Mahoney and Andrew Gordon Wilson and Tatiana Konstantinova},
journal= {arXiv preprint arXiv:2510.02224},
year = {2025}
}