DecompPatchTST: A Hybrid Framework Fusing Learnable Polynomials and Patch Transformers for Time-Series Forecasting

In real-world data, the structural symmetry of time series across temporal scales is often disrupted by the entanglement of trend, seasonal, and high-frequency components. This poses significant challenges to reliable time-series forecasting (TSF) in applications like power dispatch and meteorological analysis. Transformer-based methods typically model mixed signals without explicit inductive bias, while current decomposition-based approaches often rely on linear approximations for trend evolution, leading to unstable extrapolation in long-term forecasting. To overcome these challenges, this paper proposes the Decomposition Patch Time Series Transformer (DecompPatchTST), a hybrid forecasting framework integrating decomposition, trend extrapolation, and patch-based representation. A moving-average operator first decomposes the sequence into trend and residual parts. The trend is extrapolated via a learnable polynomial basis, which adaptively models complex nonlinear trends to ensure smooth long-range dynamics, whereas the residual is divided into temporal patches and modeled by a shared transformer encoder to capture seasonal and high-frequency variations. The final forecast aggregates both components through an additive structure. Experiments on ETT datasets show that DecompPatchTST is more stable with relatively smoother error growth from 96 to 720 forecasting steps. Its practical performance is further demonstrated on real-world Australian electricity data.