Time Series Forecasting May Be as Simple as Controlling Polynomials

Time series forecasting is commonly formulated as a representation-and-decoding problem, where historical observations are encoded into latent representations and future sequences are subsequently generated from them. In this paradigm, history is primarily treated as a source of information to be encoded and extracted. Modern architectures have made historical representation increasingly adaptive, selective, and expressive. Yet history is still primarily processed to obtain a representation from which the future is subsequently predicted. We ask whether history can play a more direct role: instead of merely being represented, can history actively govern how the future is formed? Based on this perspective, we learn a bank of polynomial predictive functions directly over the future horizon. A lightweight controller converts history into horizon-wise control signals that dynamically modulate their contributions. Complex future dynamics are then synthesized through the history-conditioned coordination of these simple functions. We refer to this model as PolyCtrl, reflecting its history-driven control of polynomial predictive functions. Extensive experiments on eight real-world datasets across multiple forecasting horizons demonstrate that this simple formulation achieves highly competitive forecasting performance. Further analysis reveals a consistent capacity-saturation phenomenon. Once the polynomial order and the size of the predictive-function bank provide sufficient representational capacity, further increasing either of them yields only marginal improvements. Accurate forecasts also rarely depend on only a few dominant functions. Instead, they typically emerge from the coordinated contributions of multiple simple polynomial predictive functions. These findings suggest that the future-generation mechanism required for strong time series forecasting may be considerably simpler than commonly assumed. With a sufficiently rich collection of simple predictive functions and history-driven dynamic control, complex future dynamics can already be effectively modeled.