Convolutionally Low-Rank Models with Modified Quantile Regression for Interval Time Series Forecasting

• URL: http://arxiv.org/abs/2604.15791v1
• Date: Fri, 17 Apr 2026 07:52:21 GMT
• Title: Convolutionally Low-Rank Models with Modified Quantile Regression for Interval Time Series Forecasting
• Abstract summary: Interval time series forecasting offers a principled solution to the problem of quantifying uncertainty.<n>We consider a recently established point forecasts (PFs) method termed Learning-Based Convolution Nuclear Norm Minimization (LbCNNM)<n>While theoretically complete and empirically effective, LbCNNM lacks inherent uncertainty estimation capabilities.<n>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)
• Score: 18.452655953569696
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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