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

Ethan Baron, Boris N. Oreshkin, Ruijun Ma, Hanyu Zhang, Kari Torkkola, Michael W. Mahoney, Andrew Gordon Wilson, Tatiana Konstantinova

Keywords: time series, foundation models, copula, sample paths

TL;DR: We present an efficient copula-based technique to generate high-quality 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.

Submission Number: 11