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鲁棒可靠机器学习系统的关键步骤。共形预测是一种无分布假设的不确定性量化算法，因其易于实现、具有统计覆盖保证以及适用于多种底层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。我们证明了CopulaCPTS具有有限样本的有效性保证。在多个合成和真实世界多变量时间序列数据集上，我们展示了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。