## 1 Introduction  
Long-term time series prediction refers to the prediction of sequence changes over a longer period of time based on historical data, like predicting 24 points or more, which is indicated in Informer [1], Autoformer [2], and Fedformer [3]. It has widespread applications in fields such as electricity forecasting [1, 2], traffic flow prediction [4, 5, 6], inventory control [7], and healthcare management [8, 9]. For example, in the energy sector, long-term forecasting is used to optimize the operation and management of the power grid, improving energy efficiency and reliability. However, high nonlinearity, long-term temporal dependency, and entangled multi-scale temporal components (e.g., trend and seasonality) make long-term forecasting a very challenging task. First, learning multi-scale temporal dependency is nontrivial. Guided by the idea of time series decomposition, long sequences can be decoupled into more expressive seasonal and trend components. In traditional transformer-based methods [10], such as Informer [1], Reformer [11], and Preformer [12], attention values are often calculated based on the position-aware data points from the original time series. Due to the high noise and complexity in long-term forecasting tasks, these methods often produce suboptimal results. The latest methods for constructing seasonal-trend attention are still limited to single-perspective frequency domain learning [3] and fixed-length subsequence learning [2]. We believe that multi-view seasonal attention learning and variable-length sub-trend attention learning can flexibly capture more potential information in long sequences, thereby improving the predictive and generalization capabilities of the model. Second, on the basis of time series decomposition, effective learning of seasonal-trend representations becomes more important [13]. Existing methods that combine time series decomposition with the transformer architecture [10], such as Autotiformer [2] and FEDformer [3], have demonstrated strong predictive capabilities on datasets with strong seasonality and weak noise disturbances. Although these methods combine progressive decomposition, they still cannot effectively distinguish between seasonal and trend representations. At the same time, they often focus more on learning seasonal components and neglect long-term trend fluctuations, which greatly increases the limitations of these methods. Therefore, we believe that effective and targeted seasonal-trend representation learning can maximize the model's long-sequence prediction capabilities. To address all of the above challenges, a transformer model based on seasonal-trend decomposition is proposed, called DESTformer. Firstly, DESTformer effectively decouples and denoises complex sequences through frequency domain transform. Next, for the seasonal component, a multi-view attention mechanism (MVI-Attention) is proposed to replace the traditional self-attention mechanism for capturing complex periodic changes. MVI-Attention simultaneously calculates self-attention from three perspectives, i.e., frequency, amplitude, and phase, and then completes the conversion to the time domain through discrete Fourier inverse transformation. For the trend component, a multi-scale attention mechanism (MSC-Attention) is proposed to replace the traditional self-attention mechanism for capturing sub-trends under different receptive fields. MSC-Attention extracts sub-trends through one-dimensional convolution with multi-scale receptive fields and completes the attention aggregation of sub-trends by calculating the correlation coefficient between sequences. Finally, under the action of fast Fourier transform and sampling, DESTformer reduces the computational cost of the transformer from quadratic complexity to linear complexity.