# Teger: Spatiotemporal Covariance for Probabilistic Traffic Forecasting

arXiv: https://arxiv.org/abs/2605.18068 · HTML: https://mlsanity.com/paper/2605.18068/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 11 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting with Correlated Errors](https://mlsanity.com/paper/2402.01000/) (2024)

## Abstract (arXiv)

Traffic conditions drift -- demand patterns, incident dynamics, and sensor behavior shift over a deployment's lifetime -- so a joint uncertainty estimate fit once at training time and left static will miscalibrate as conditions change. We present TEGER, a residual covariance model that keeps a forecaster's joint predictive uncertainty current at test time through closed-form updates, not retraining. A fixed sensor graph supplies a low-dimensional spatial precision factor encoding which sensors' errors move together; at inference, Gaussian conditioning corrects The next forecast's mean and covariance from only the most recently observed residuals, and an exponential moving-average volatility term rescales marginal uncertainty to track local drift while preserving the learned correlation structure. Neither update touches the forecasting backbone's weights, so the same mechanism attaches to a frozen time-series foundation model: no gradient passes through it, turning a static point forecast into one with continually refreshed, correlated uncertainty at negligible added cost. In four traffic datasets, the fixed-graph covariance improves 60-minute CRPSsum over a temporal-only baseline in different configurations of the backbone and datasets. Applied post hoc to a frozen time-series foundation model, Chronos, the same test-time correction reduces CRPSsum from 0.1798 to 0.1736 without foundation-model fine-tuning. These results support closed-form test-time residual correction, rather than a covariance fixed once at training time.