This paper presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), is suitable for nonstationary and heteroscedastic time series data, and can be applied on top of any forecasting model, including deep learning architectures that are trained on long data sequences. EnCQR exploits a bootstrap ensemble estimator, which enables the use of conformal predictors for time series by removing the requirement of data exchangeability. The ensemble learners are implemented as generic machine learning algorithms performing quantile regression, which allow the length of the PIs to adapt to local variability in the data. In the experiments, we predict time series characterized by a different amount of heteroscedasticity. The results demonstrate that EnCQR outperforms models based only on quantile regression or conformal prediction, and it provides sharper, more informative, and valid PIs.

翻译：本文展示了一种新型的概率预测方法,叫做“整体相容四分位回归 ” ( EnCQR ) 。 EnCQR 构建了无分布性且基本有效的预测间隔(PIs), 适合非静止和异性时间序列数据, 并且可以在任何预测模型之上应用, 包括经过长数据序列培训的深学习结构。 EnCQR 开发了一个靴子陷阱共位估计器, 通过取消数据互换性的要求, 使得能够对时间序列使用符合的预测器。 共性学习者作为通用机器学习算法, 进行量回归, 使 PIs 的长度能够适应数据的本地变异性。 在实验中, 我们预测的时间序列具有不同程度的超异性。 结果表明, EnCQR 的外形模型仅以四分位回归或符合性预测为基础, 并且提供更精确、更翔实和有效的 PIs。