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

TL;DR

This paper introduces LbCNNM-MQR, a novel interval forecasting method combining convolutional low-rank models with modified quantile regression, achieving superior uncertainty quantification in real-world time series.

Contribution

It develops a new interval forecasting approach that integrates modified quantile regression into convolutional low-rank models, enhancing uncertainty estimation.

Findings

LbCNNM-MQR outperforms existing methods on over 100,000 real-world time series.

The method provides more accurate and reliable prediction intervals.

Interval calibration techniques further improve PI accuracy.

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.