The aim of this paper is to propose an adaptation of the well known adaptive conformal inference (ACI) algorithm to achieve finite-sample coverage guarantees in multi-step ahead time-series forecasting in the online setting. ACI dynamically adjusts significance levels, and comes with finite-sample guarantees on coverage, even for non-exchangeable data. Our multi-step ahead ACI procedure inherits these guarantees at each prediction step, as well as for the overall error rate. The multi-step ahead ACI algorithm can be used with different target error and learning rates at different prediction steps, which is illustrated in our numerical examples, where we employ a version of the confromalised ridge regression algorithm, adapted to multi-input multi-output forecasting. The examples serve to show how the method works in practice, illustrating the effect of variable target error and learning rates for different prediction steps, which suggests that a balance may be struck between efficiency (interval width) and coverage.t

翻译：本文旨在对著名的自适应保形推断算法进行改进，以实现在线环境下多步提前时间序列预测的有限样本覆盖保证。自适应保形推断动态调整显著性水平，即使对于非可交换数据也能提供有限样本覆盖保证。我们提出的多步提前自适应保形推断方法在每个预测步骤以及整体错误率方面均继承了这些理论保证。该算法可在不同预测步骤采用不同的目标错误率和学习率，这一点在我们的数值实验中得到展示——我们采用了适用于多输入多输出预测的保形化岭回归算法变体。实验结果表明该方法在实际应用中的运行机制，揭示了不同预测步骤采用可变目标错误率和学习率的效果，说明可以在预测效率（区间宽度）与覆盖概率之间寻求平衡。