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 adaptively re-estimate the conditional quantile of non-conformity scores (e.g., prediction residuals), upon exploiting the temporal dependence among them. More precisely, 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：我们提出了一种针对序列数据（例如时间序列）的新型无分布共形预测算法，称为序列预测共形推断（\texttt{SPCI}）。我们特别考虑了时间序列数据不可交换的性质，因此许多现有的共形预测算法并不适用。其主要思想是在利用非一致性分数（例如预测残差）之间的时间依赖性的基础上，自适应地重新估计这些分数的条件分位数。更精确地说，我们将共形预测区间问题转化为：在给定用户指定的点预测算法的情况下，预测未来残差的分位数。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的条件覆盖。通过模拟和真实数据实验，我们证明，在期望的经验覆盖率下，与现有其他方法相比，\texttt{SPCI}的区间宽度显著减小。