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：准确的置信区间测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、统计覆盖保证以及对底层预测器的通用性而广受欢迎。然而，现有针对时间序列的共形预测算法仅限于单步预测，且未考虑时间依赖性。本文提出一种用于多变量、多步时间序列预测的 Copula 共形预测算法 CopulaCPTS。我们证明 CopulaCPTS 具有有限样本有效性保证。在多个合成及真实世界多变量时间序列数据集上，我们表明 CopulaCPTS 在多步预测任务中能生成比现有技术更校准且更尖锐的置信区间。