论文标题
时间序列的共形预测
Conformal prediction for time series
论文作者
论文摘要
我们开发了一个通用框架，用于构建时间序列的无分配预测间隔。从理论上讲，我们在估计的预测间隔的条件和边际覆盖范围上建立了明确的界限，在其他假设下，该间隔渐近地收敛到零。我们获得了Oracle和估计预测间隔之间集差的大小的相似界限。从方法论上讲，我们引入了一种称为\ texttt {enbpi}的计算有效算法，该算法围绕着集合预测变量，该算法与保形预测（CP）密切相关，但不需要数据交换性。 \ texttt {enbpi}避免了数据分解，并且可以通过避免重新训练并因此可扩展到依次产生预测间隔，从而在计算上有效。我们进行了广泛的仿真和真实数据分析，以证明其与现有方法相比的有效性。我们还讨论了其他各种应用程序上\ texttt {enbpi}的扩展。
We develop a general framework for constructing distribution-free prediction intervals for time series. Theoretically, we establish explicit bounds on conditional and marginal coverage gaps of estimated prediction intervals, which asymptotically converge to zero under additional assumptions. We obtain similar bounds on the size of set differences between oracle and estimated prediction intervals. Methodologically, we introduce a computationally efficient algorithm called \texttt{EnbPI} that wraps around ensemble predictors, which is closely related to conformal prediction (CP) but does not require data exchangeability. \texttt{EnbPI} avoids data-splitting and is computationally efficient by avoiding retraining and thus scalable to sequentially producing prediction intervals. We perform extensive simulation and real-data analyses to demonstrate its effectiveness compared with existing methods. We also discuss the extension of \texttt{EnbPI} on various other applications.
