Spectrum-DualNet: Spectrum-Guided Routing of Time-Frequency Dual-Network via Adaptive Decomposition for Time Series Forecasting

Multivariate time series often contain temporal patterns evolving at different characteristic timescales, resulting in entangled long-term trends and short-term oscillations. Disentangling these heterogeneous dynamics using spectrum information can facilitate more effective forecasting by enabling specialized modeling of different temporal scales. However, widely used trend-seasonal decomposition methods typically rely on predefined decomposition structures and are not designed to adaptively identify multiple spectrum modes with distinct central frequencies across different datasets; existing decomposition-based forecasting methods often apply the same modeling mechanism to different resulting components, without explicitly accounting for their distinct spectrum characteristics. Yet, how to separate band-limited modes according to their spectra and assign them to spectrum-specialized branches remains underexplored in general multivariate time series forecasting. To address this, we propose Spectrum-DualNet, a dual-branch forecasting network that adaptively separates multivariate signals from various datasets into band-limited modes with distinct characteristic spectra using Multivariate Variational Mode Decomposition (MVMD). The lowest-frequency mode is routed to a trend branch in the time domain to capture long-term dependencies, while the remaining high-frequency modes are routed to a fluctuation branch that models non-stationary dynamics in the frequency domain. The two branches are fused through a gating network in which a multi-layer perceptron computes mixing coefficients that weight the trend and fluctuation components. The decomposition residual is re-injected through a second gate to restore information lost during decomposition. A prediction head maps the fused representation to the forecast. Extensive experiments on real-world multivariate time series datasets demonstrate that Spectrum-DualNet achieves superior forecasting performance.