Teger: Spatiotemporal Covariance for Probabilistic Traffic Forecasting

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.