Accurate uncertainty measurement is a key step to building robust and reliable machine learning systems. Conformal prediction is a distribution-free uncertainty quantification algorithm popular for its ease of implementation, statistical coverage guarantees, and versatility for underlying forecasters. However, existing conformal prediction algorithms for time series are limited to single-step prediction without considering the temporal dependency. In this paper, we propose a Copula Conformal Prediction algorithm for multivariate, multi-step Time Series forecasting, CopulaCPTS. We prove that CopulaCPTS has finite sample validity guarantee. On several synthetic and real-world multivariate time series datasets, we show that CopulaCPTS produces more calibrated and sharp confidence intervals for multi-step prediction tasks than existing techniques.

翻译：准确的不确定性度量是构建稳健可靠机器学习系统的关键步骤。共形预测作为一种无需分布假设的不确定性量化算法，因其易于实现、具备统计覆盖保证且适用于多种基础预测模型而广受欢迎。然而，现有针对时间序列的共形预测算法仅限于单步预测，未考虑时间依赖性。本文提出一种面向多变量多步时间序列预测的 Copula 共形预测算法 CopulaCPTS，并证明了 CopulaCPTS 具有有限样本有效性保证。在多个合成及真实世界的多变量时间序列数据集上，实验表明 CopulaCPTS 相较于现有技术能够为多步预测任务生成更校准且更尖锐的置信区间。