We study the problem of uncertainty quantification for time series prediction, with the goal of providing easy-to-use algorithms with formal guarantees. The algorithms we present build upon ideas from conformal prediction and control theory, are able to prospectively model conformal scores in an online setting, and adapt to the presence of systematic errors due to seasonality, trends, and general distribution shifts. Our theory both simplifies and strengthens existing analyses in online conformal prediction. Experiments on 4-week-ahead forecasting of statewide COVID-19 death counts in the U.S. show an improvement in coverage over the ensemble forecaster used in official CDC communications. We also run experiments on predicting electricity demand, market returns, and temperature using autoregressive, Theta, Prophet, and Transformer models. We provide an extendable codebase for testing our methods and for the integration of new algorithms, data sets, and forecasting rules.

翻译：我们研究时间序列预测中的不确定性量化问题，旨在提供具有形式化保证、易于使用的算法。我们提出的算法融合了保形预测与控制理论的思想，能够在线环境中前瞻性地建模保形分数，并自适应处理由季节性、趋势及一般分布偏移导致的系统性误差。我们的理论工作既简化又强化了现有在线保形预测分析。在美国全州COVID-19死亡人数四周前瞻预测实验中，该方法在覆盖范围上优于美国疾控中心官方通讯中使用的集成预测器。我们还使用自回归模型、Theta模型、Prophet模型及Transformer模型进行了电力需求、市场回报与温度预测实验。我们提供了一个可扩展的代码库，用于测试所提方法及集成新算法、数据集与预测规则。