DySCo: Dynamic Semantic Compression for Effective Long-term Time Series Forecasting

Time Series Forecasting (TSF) faces persistent challenges in modeling intricate temporal dependencies across different scales. Despite recent advances leveraging different decomposition operations and novel architectures based on CNN, MLP or Transformer, existing methods still struggle with static decomposition strategies, fragmented dependency modeling, and inflexible fusion mechanisms, limiting their ability to model intricate temporal dependencies. To explicitly solve the mentioned three problems respectively, we propose a novel Dynamic Multi-Scale Coordination Framework (DMSC) with Multi-Scale Patch Decomposition block (EMPD), Triad Interaction Block (TIB) and Adaptive Scale Routing MoE block (ASR-MoE). Specifically, EMPD is designed as a built-in component to dynamically segment sequences into hierarchical patches with exponentially scaled granularities, eliminating predefined scale constraints through input-adaptive patch adjustment. TIB then jointly models intra-patch, inter-patch, and cross-variable dependencies within each layer's decomposed representations. EMPD and TIB are jointly integrated into layers forming a multi-layer progressive cascade architecture, where coarse-grained representations from earlier layers adaptively guide fine-grained feature extraction in subsequent layers via gated pathways. And ASR-MoE dynamically fuses multi-scale predictions by leveraging specialized global and local experts with temporal-aware weighting. Comprehensive experiments on thirteen real-world benchmarks demonstrate that DMSC consistently maintains state-of-the-art (SOTA) performance and superior computational efficiency for TSF tasks. Code is available at https://github.com/1327679995/DMSC.

Long-term time series forecasting finds extensive applications in domains such as power demand, traffic flow, meteorological observation, and renewable energy dispatch. Forecasting dynamically varying long-term time series poses inherent challenges, including statistical nonstationarity, local high-frequency disturbances, and coupled cross-period dependencies, which make it difficult for lightweight models to balance parameter efficiency and forecasting performance. To address this issue, this study presents TA-SparseMG, a lightweight cross-period forecasting model built on SparseTSF's sparse cross-period modeling framework. It incorporates three key modules: a trend-aware reversible instance normalization module, a scale-adaptive gated denoising module, and a multiscale gated-attention MLP forecasting module. The trend-aware normalization module captures input-window statistics and calibrates forecast-window distributions, effectively mitigating distribution shift. The scale-adaptive gated denoising module performs feature smoothing and residual suppression before period rearrangement, thereby reducing interference from high-frequency perturbations. The multiscale gated attention prediction module strengthens the prediction head's adaptive representational capacity via conditional gating and feature modulation. Extensive experiments across multiple LTSF benchmarks demonstrate that the proposed TA-SparseMG consistently achieves superior, stable performance. Ablation studies confirm that each module independently improves distribution adaptation, input robustness, and cross-period feature mapping capability.

Long-term time series forecasting has made significant progress by leveraging multi-scale information to capture hierarchical temporal patterns and model long-range dependencies. However, temporal downsampling in existing multi-scale methods inevitably smooths detailed temporal fluctuations, and this information loss is further aggravated by their emphasis on dominant trends across scales, resulting in insufficiently expressive representations. To address this, we propose a Multi-Scale Wavelet Mixing (MWMixer) model, which incorporates a Bidirectional Frequency-Bands Mixing strategy to recover lost temporal details across scales, enabling complementary cross-scale information interactions. Then, a Dynamic Scale-Adaptive Fusion module learns time-varying weights for each scale to fuse multi-scale forecasts into the final prediction, enhancing the flexibility of multi-scale aggregation. In addition, a cross-scale consistency loss aligns each coarse-scale prediction with the interval-averaged fine-scale outputs, while a multi-scale supervision loss enforces prediction accuracy at each scale, promoting consistent learning across scales. Extensive experiments on seven real-world datasets demonstrate that MWMixer achieves competitive performance in long-term forecasting.