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.

翻译：许多时间序列应用需要以样本路径的形式获取多步预测轨迹。近期，时间序列基础模型通过利用多步前瞻预测来提升多步预测的质量与效率。然而，这些模型仅能预测各时间步的独立边缘分布，而非完整的联合预测分布。为生成具有现实相关结构的预测样本路径，通常需采用自回归采样方法，其计算成本可能极为高昂。本文提出一种基于copula的方法，能够通过单次前向传播，从现有的多步时间序列基础模型中高效生成精确且具有相关性的样本路径。该基于copula的方法生成相关样本路径的速度比自回归采样快数个数量级，并通过缓解误差累积现象提升了样本路径的质量。