Time series forecasting is crucial for various applications, such as weather, traffic, electricity, and energy predictions. Currently, common time series forecasting methods are based on Transformers. However, existing approaches primarily model limited time series or fixed scales, making it more challenging to capture diverse features cross different ranges. Additionally, traditional methods like STL for complex seasonality-trend decomposition require pre-specified seasonal periods and typically handle only single, fixed seasonality. We propose the Hybrid Decomposition Dual-Stream Adaptive Transformer (DSAT-HD), which integrates three key innovations to address the limitations of existing methods: 1) A hybrid decomposition mechanism combining EMA and Fourier decomposition with RevIN normalization, dynamically balancing seasonal and trend components through noise Top-k gating; 2) A multi-scale adaptive pathway leveraging a sparse allocator to route features to four parallel Transformer layers, followed by feature merging via a sparse combiner, enhanced by hybrid attention combining local CNNs and global interactions; 3) A dual-stream residual learning framework where CNN and MLP branches separately process seasonal and trend components, coordinated by a balanced loss function minimizing expert collaboration variance. Extensive experiments on nine datasets demonstrate that DSAT-HD outperforms existing methods overall and achieves state-of-the-art performance on some datasets. Notably, it also exhibits stronger generalization capabilities across various transfer scenarios.