JacoWaveNet: Wavelet Residual Pyramid with Jacobi Polynomial Spectral Mapping for Heterogeneous Time Series Forecasting

Time series forecasting benefits from modeling long-range dependencies and cross-scale relations, yet existing approaches often suffer from feature entanglement across scales and insufficient modeling of negative temporal dependencies, limiting their ability to capture heterogeneous temporal interactions. We propose JacoWaveNet, a dual-subband wavelet residual pyramid framework that introduces structured multi-scale representations by separating approximation and detail components, reducing redundant low-frequency semantics and emphasizing scale-wise differential dynamics. Building on this decoupled representation space, we develop a Jacobi Mapping (JM) module based on Jacobi polynomial spectral modeling, which jointly captures global smooth trends and local negative dependencies via polynomial filtering, and progressively models nonlinear temporal relations through Jacobi polynomial message passing. Experiments on seven benchmarks demonstrate consistent improvements over strong baselines, especially for medium and long horizon forecasting.