QPath: Joint Anomaly Detection from Marginal Quantile Forecasts

Time-series foundation models increasingly use direct quantile forecasting to provide efficient uncertainty estimates without specifying a parametric predictive distribution. Yet marginal quantiles leave dependence across horizon steps unspecified: a path can be ordinary at individual steps while being jointly anomalous. QPath addresses this gap at the detection stage without changing the forecaster or constructing a joint predictive distribution. It combines the mean quantile loss across forecast quantiles with a temporal direction factor estimated from historical median residuals, followed by reference normalization and channel averaging. We evaluate QPath on synthetic anomaly patterns and the univariate and multivariate TSB-AD benchmarks using Chronos-2 and TimesFM 2.5. Across zero-shot and head-only fine-tuned settings, average relative improvements in whole-series VUS-PR over a quantile-loss-only baseline (quantile error) are 22.1% on TSB-AD-U and 4.3% on TSB-AD-M; the univariate absolute gains are 0.069–0.074. Multivariate gains remain inconclusive under source-cluster inference. Removing explicit cross terms eliminates the mean univariate gain in a matched diagonal control; replacing absolute error with quantile loss adds 0.003–0.010 on TSB-AD-U.