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

2025-10-02

AI Summary

Existing multistep time series foundation models output only independent marginal distributions per timestep, failing to capture genuine temporal dependency structures required for realistic joint sample paths. To address this, we propose the first copula-based single-forward-sampling framework that integrates pretrained models’ marginal forecasts with flexible copula modeling, enabling efficient generation of highly correlated, high-fidelity full-length sample paths via inverse transform sampling. Our approach circumvents the high computational cost and error accumulation inherent in autoregressive sampling, accelerating inference by several orders of magnitude. Empirically, it significantly improves path quality and prediction robustness across multiple benchmark tasks. Notably, it achieves zero-shot, one-shot generation of high-quality joint distribution samples from off-the-shelf time series foundation models—without any fine-tuning—marking the first such capability in the literature.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Reasoning under Uncertainty: Relational Probabilistic Models
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Generating correlated sample paths from time series models
• Overcoming expensive autoregressive sampling limitations
• Producing accurate joint predictive distributions efficiently

Innovation

• Copula-based approach generates correlated sample paths
• One forward pass replaces expensive autoregressive sampling
• Mitigates snowballing error for improved path quality