Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to hold for time series due to their temporally correlated nature. In this work, we present a novel use of conformal prediction for time series forecasting that incorporates time series decomposition. This approach allows us to model different temporal components individually. By applying specific conformal algorithms to each component and then merging the obtained prediction intervals, we customize our methods to account for the different exchangeability regimes underlying each component. Our decomposition-based approach is thoroughly discussed and empirically evaluated on synthetic and real-world data. We find that the method provides promising results on well-structured time series, but can be limited by factors such as the decomposition step for more complex data.

翻译：保形预测为无分布不确定性量化提供了一个实用框架，在数据可交换性相对温和的假设下提供有限样本覆盖保证。然而，由于时间序列具有时间相关性，这些假设对时间序列不再成立。在本研究中，我们提出了一种结合时间序列分解的保形预测新方法，用于时间序列预测。该方法允许我们对不同时间分量进行独立建模。通过对每个分量应用特定的保形算法，然后合并获得的预测区间，我们定制了相应方法以考虑各分量所遵循的不同可交换性机制。我们基于分解的方法在合成数据和真实数据上进行了深入讨论和实证评估。研究发现，该方法在结构良好的时间序列上能提供有前景的结果，但对于更复杂的数据，可能受到分解步骤等因素的限制。