Beyond Uniform Updates: Drift Pattern Aware Online Time Series Forecasting Under Delayed Feedback

Abstract

Online time series forecasting relies on continual updates to cope with concept drift. In multi-step forecasting, however, the ground truth for an H-step prediction arrives only after H steps, so a delayed residual entangles persistent drifts with transient shocks and seasonal fluctuations. Existing methods typically apply a uniform update rule to all delayed errors, which can overreact to noise and under-adapt to real drift. We view delayed residuals as compressed observations of latent drift over the horizon, and propose PADRE, a drift evidence driven framework that converts each delayed feedback event into a context-sensitive adaptation decision. PADRE builds a Tri-View drift representation from (i) the current input context, (ii) recent delayed-residual trajectories, and (iii) retrieved typical types of drift, and quantifies their agreement via a geometric consistency measure. To exploit recurring drift structure, PADRE mines an offline Pattern Bank of regime-conditioned residual prototypes and retrieves a soft pattern prompt online. A lightweight prompt guided policy outputs a continuous update gate that scales the backbone’s gradient step, enabling decisive updates under coherent evidence and conservative updates otherwise. Experiments on five real-world benchmarks and three backbones demonstrate consistent gains under delayed feedback, reducing MSE by 6%–15% relative to recent baselines and improving update stability across horizons.