We present a new distribution-free conformal prediction algorithm for sequential data (e.g., time series), called the \textit{sequential predictive conformal inference} (\texttt{SPCI}). We specifically account for the nature that time series data are non-exchangeable, and thus many existing conformal prediction algorithms are not applicable. The main idea is to exploit the temporal dependence of non-conformity scores (e.g., prediction residuals); thus, the past residuals contain information about future ones. Then we cast the problem of conformal prediction interval as predicting the quantile of a future residual, given a user-specified point prediction algorithm. Theoretically, we establish asymptotic valid conditional coverage upon extending consistency analyses in quantile regression. Using simulation and real-data experiments, we demonstrate a significant reduction in interval width of \texttt{SPCI} compared to other existing methods under the desired empirical coverage.

翻译：我们提出了一种适用于序列数据（例如时间序列）的新型无分布共形预测算法，即序列预测共形推断（SPCI）。我们特别考虑了时间序列数据不可交换的特性，因此许多现有共形预测算法无法适用。其主要思想是利用非一致性得分（例如预测残差）的时间依赖性，从而过去的残差包含未来残差的信息。然后，我们将共形预测区间的问题转化为在给定用户指定的点预测算法下预测未来残差分位数的问题。理论上，通过扩展分位数回归中的一致性分析，我们建立了渐近有效条件覆盖。通过模拟和真实数据实验，我们证明在期望的经验覆盖下，与其他现有方法相比，SPCI 的区间宽度显著减小。