Compose the Horizon: Parameter-Shared Blockwise Forecasting under a Sequential-Compute Trade-off

Most long-horizon forecasters emit the complete future in one pass. We ask whether a compact operator can instead be reused to emit contiguous future blocks, trading stored parameters for sequential computation. Recursive Functional Decomposition (RFD) factorizes the horizon mapping into three parameter-shared block predictions. The blocks occupy disjoint future intervals and are concatenated, not added as trend, seasonal, or residual components, and each emitted block joins the rolling context that conditions the next application. In controlled three-seed experiments, removing forward feedback hurts all four evaluated datasets while stopping gradients through it changes little, so the useful signal is the evolving forecast state itself; reapplying the shared operator helps consistently, but by less than widening it. The model uses 0.08--0.46M parameters, yet its sequential channel-wise execution is slower and more memory-intensive than an iterative baseline at high channel count. In a frozen long-context evaluation against ten strong baseline families, RFD records lower test error in 23 of 24 cells; the comparison is cross-protocol, with RFD using 512/720-step context and the baselines using 96.