InRelCast: In-Context Relation Learning for Time Series Forecasting with Exogenous Variables

Exogenous variables such as weather and schedules are essential for forecasting a target series, and their values over the forecast horizon are often known or predicted in advance. Prevailing methods learn the forecast end to end from the look-back window and the future exogenous variables by fusing their representations or modeling temporal and channel correlations. However, these two inputs play different roles. The future exogenous variables specify the conditions ahead, whereas how the target responds to them depends on the current state of the series, so the forecast has to judge the current relation between the exogenous conditions and the target. The evidence for this judgment lies in the look-back window, where each transition from one period to the next pairs its conditions with the response that followed. Thus, these observed transitions act as answered examples and the future transitions, whose responses are unknown, act as new cases, which is precisely the setting of in-context learning. Nevertheless, prevailing methods encode both inputs together and leave this pairing and its use to implicit learning. Therefore, we propose InRelCast, an In-context Relation learning framework for foreCasting with exogenous variables, which infers the relation of each future transition in context from the observed transitions. Specifically, each observed transition serves as a demonstration and each future transition as a query, whose inferred relation generates low-rank parameter increments of a shared residual forecaster that corrects a baseline forecast from the target history. Since future responses are unobserved, training uses later observed transitions as pseudo-queries, whose hidden responses supervise the relations inferred for them. Experiments on multiple real-world datasets show that InRelCast outperforms state-of-the-art baselines, both in-domain and in zero-shot transfer to unseen series. The code is available at https://anonymous.4open.science/r/InRelCast.