Do We Still Need Trend Decomposition? Patch-State and Delta-Dynamics Modeling for Time Series Forecasting

Time-series forecasting uses trends in historical observations to inform the extrapolation of future trajectories. Decomposition-based forecasting organizes this process around trend and seasonal components, separating sustained changes from recurrent fluctuations and learning their temporal dependencies separately. This component-wise modeling paradigm also extends to patch-based forecasting, where consecutive observations are encoded as local trajectory tokens. However, we find that raw patches already preserve the local tendencies and recurring patterns targeted by decomposition, revealing substantial overlap in their representational roles. Moreover, similar local tendencies and shapes do not uniquely determine the magnitude and evolution of successive changes, motivating explicit modeling of transition dynamics alongside trajectory structure. We therefore introduce a state–dynamics forecasting paradigm and instantiate it as the Patch-State and Delta-Dynamics Network (PaDNet). Delta-Dynamics explicitly represents the direction and magnitude of adjacent changes and compares increments across steps to characterize their evolution. In parallel, Patch-State regularizes trajectory encoding to capture the overall temporal tendency and structure of local trajectories. Together, these representations condition forecasting on both local trajectory states and their transition dynamics. Extensive experiments on time-series datasets demonstrate the effectiveness of PaDNet, achieving average reductions of up to 7.3% in MSE and 5.1% in MAE over the best-performing state-of-the-art baseline.