将量化回归融入卷积低秩模型，实现高精度时间序列预测区间估计
Convolutionally Low-Rank Models with Modified Quantile Regression for Interval Time Series Forecasting
- 用改进的分位数回归增强卷积低秩模型的不确定性建模能力
- 在超10万条真实时间序列上验证，预测区间覆盖率显著提升
- 适合需要可靠置信区间的工业预测场景，如能源与金融
预测模型中的不确定性量化对可靠决策至关重要，但仍是重大挑战。区间时间序列预测通过提供预测区间（PIs）来解决该问题，表明真实值落在预测范围内的概率。本文研究了一种名为基于学习的卷积核范数最小化（LbCNNM）的点预测方法，该方法利用训练数据导出的卷积低秩特性，直接生成多步前向预测。尽管理论完备且实证有效，但LbCNNM缺乏内在不确定性估计能力，这与许多先进预测方法一致。为解决此问题，我们改进了经典的分位数回归（QR），并将其整合进LbCNNM，提出一种新型区间预测方法——LbCNNM-MQR。此外，设计了区间校准技术以进一步提升预测区间的准确性。在超过10万条真实世界时间序列上的大量实验表明，LbCNNM-MQR性能优越。
原文摘要 · Abstract (English)
The quantification of uncertainty in prediction models is crucial for reliable decision-making, yet remains a significant challenge. Interval time series forecasting offers a principled solution to this problem by providing prediction intervals (PIs), which indicates the probability that the true value falls within the predicted range. We consider a recently established point forecasts (PFs) method termed Learning-Based Convolution Nuclear Norm Minimization (LbCNNM), which directly generates multi-step ahead forecasts by leveraging the convolutional low-rankness property derived from training data. While theoretically complete and empirically effective, LbCNNM lacks inherent uncertainty estimation capabilities, a limitation shared by many advanced forecasting methods. To resolve the issue, we modify the well-known Quantile Regression (QR) and integrate it into LbCNNM, resulting in a novel interval forecasting method termed LbCNNM with Modified Quantile Regression (LbCNNM-MQR). In addition, we devise interval calibration techniques to further improve the accuracy of PIs. Extensive experiments on over 100,000 real-world time series demonstrate the superior performance of LbCNNM-MQR.
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