Who Contributes to Whom? Cross-Entity Attribution in Panel Time Series Forecasting

A forecast indicates what may happen, but understanding the factors that shape the prediction can provide additional evidence for interpreting and assessing it. In panel time series, multiple entities may contain predictive information about one another. Identifying these entity-level contributions can therefore reveal which entities are relevant to a target forecast and help domain experts investigate cross-entity relationships. However, most existing panel forecasting models focus primarily on prediction and do not directly quantify how individual entities contribute to each target forecast. To our knowledge, XPanelNet is the first panel time-series forecasting architecture to integrate entity-level predictive attribution directly into the forecasting process. XPanelNet decomposes each entity's history into trend, seasonal, cyclic, and residual components to construct a base forecast, and then augments it with signed cross-entity contributions computed through a latent vector-autoregressive (VAR) coupling over a low-dimensional shared representation to obtain the final prediction. This additive formulation makes entity-level attribution an intrinsic part of the forecasting process rather than a post hoc interpretation derived from attention or similarity weights. Across nine real-world panel datasets spanning finance, energy, climate, hydrology, transportation, and public safety, XPanelNet achieves the best result of any model, including 10 deep forecasting baselines (TimeKAN, TimeMixer, iTransformer, CrossGNN, PatchTST, TimesNet, DLinear, SCINet, Non-stationary Transformer, and Autoformer), on 7 of 9 evaluated datasets by MAE and 4 of 9 by MSE, while simultaneously providing entity-level predictive attributions.