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

2026-04-17

AI Summary

This work addresses the common limitation of state-of-the-art time series point forecasting methods—their inability to provide reliable uncertainty estimates. We propose a novel approach that, for the first time, integrates enhanced quantile regression with low-rank convolutional modeling (LbCNNM), enabling the generation of high-quality prediction intervals while preserving strong multi-step point forecasting performance. The method further incorporates a dedicated interval calibration mechanism to effectively balance coverage and sharpness. Evaluated on over 100,000 real-world time series, our approach significantly outperforms existing techniques, achieving simultaneous high coverage and sharpness in uncertainty quantification.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• interval time series forecasting
• uncertainty quantification
• prediction intervals
• convolutional low-rankness
• quantile regression

Innovation

• Convolutional Low-Rankness
• Modified Quantile Regression
• Interval Time Series Forecasting
• Prediction Intervals
• LbCNNM-MQR