# Error Adjustment Based on Spatiotemporal Correlation Fusion for Traffic Forecasting

arXiv: https://arxiv.org/abs/2510.23656 · HTML: https://mlsanity.com/paper/2510.23656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 25 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Residual Attention Network for Image Classification](https://mlsanity.com/paper/1704.06904/) (2017)
- [GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphs](https://mlsanity.com/paper/1803.07294/) (2018)
- [Learning Traffic as Images: A Deep Convolutional Neural Network for Large-Scale Transportation Network Speed Prediction](https://mlsanity.com/paper/1701.04245/) (2017)
- [Pay Attention to Evolution: Time Series Forecasting with Deep Graph-Evolution Learning](https://mlsanity.com/paper/2008.12833/) (2020)
- [Deep Learning for Road Traffic Forecasting: Does it Make a Difference?](https://mlsanity.com/paper/2012.02260/) (2020)
- [Adjusting for Autocorrelated Errors in Neural Networks for Time Series](https://mlsanity.com/paper/2101.12578/) (2021)
- [Incrementally Improving Graph WaveNet Performance on Traffic Prediction](https://mlsanity.com/paper/1912.07390/) (2019)
- [Deep Time Series Forecasting with Shape and Temporal Criteria](https://mlsanity.com/paper/2104.04610/) (2021)
- [Adversarial Vulnerabilities in Large Language Models for Time Series Forecasting](https://mlsanity.com/paper/2412.08099/) (2024)
- [Dual Teaching: A Practical Semi-supervised Wrapper Method](https://mlsanity.com/paper/1611.03981/) (2016)

## Abstract (arXiv)

Deep neural networks (DNNs) play a significant role in an increasing body of research on traffic forecasting due to their effectively capturing spatiotemporal patterns embedded in traffic data. A general assumption of training the said forecasting models via mean squared error estimation is that the errors across time steps and spatial positions are uncorrelated. However, this assumption does not really hold because of the autocorrelation caused by both the temporality and spatiality of traffic data. This gap limits the performance of DNN-based forecasting models and is overlooked by current studies. To fill up this gap, this paper proposes Spatiotemporally Autocorrelated Error Adjustment (SAEA), a novel and general framework designed to systematically adjust autocorrelated prediction errors in traffic forecasting. Unlike existing approaches that assume prediction errors follow a random Gaussian noise distribution, SAEA models these errors as a spatiotemporal vector autoregressive (VAR) process to capture their intrinsic dependencies. First, it explicitly captures both spatial and temporal error correlations by a coefficient matrix, which is then embedded into a newly formulated cost function. Second, a structurally sparse regularization is introduced to incorporate prior spatial information, ensuring that the learned coefficient matrix aligns with the inherent road network structure. Finally, an inference process with test-time error adjustment is designed to dynamically refine predictions, mitigating the impact of autocorrelated errors in real-time forecasting. The effectiveness of the proposed approach is verified on different traffic datasets. Results across a wide range of traffic forecasting models show that our method enhances performance in almost all cases.