Although Transformer-based methods have significantly improved state-of-the-art results for long-term series forecasting, they are not only computationally expensive but more importantly, are unable to capture the global view of time series (e.g. overall trend). To address these problems, we propose to combine Transformer with the seasonal-trend decomposition method, in which the decomposition method captures the global profile of time series while Transformers capture more detailed structures. To further enhance the performance of Transformer for long-term prediction, we exploit the fact that most time series tend to have a sparse representation in well-known basis such as Fourier transform, and develop a frequency enhanced Transformer. Besides being more effective, the proposed method, termed as Frequency Enhanced Decomposed Transformer ({\bf FEDformer}), is more efficient than standard Transformer with a linear complexity to the sequence length. Our empirical studies with six benchmark datasets show that compared with state-of-the-art methods, FEDformer can reduce prediction error by $14.8\%$ and $22.6\%$ for multivariate and univariate time series, respectively. the code will be released soon.

翻译：虽然以变异器为基础的方法大大改善了长期系列预测的最新最新结果,但不仅计算成本昂贵,更重要的是,它们无法捕捉时间序列的全球视角(如总体趋势)。为了解决这些问题,我们提议将变异器与季节-趋势分解法相结合,在这种方法中,分解法可以捕捉时间序列的全球概况,而变异器则捕捉更为详细的结构。为了进一步提高变异器的长期预测性能,我们利用以下事实,即大多数时间序列在众所周知的基础,如Fourier变异器中往往代表很少,而且开发一个频率增强变异器。除了更加有效外,拟议的方法,即“频率增强变异器”(bf FEDexext})比标准变异器效率更高,且直线复杂到序列长度。我们用六个基准数据集进行的经验研究表明,与最新方法相比,FEDFEDfrew可以分别将多变异器和未变换式时间序列的预测误差减少14.8美元和22.6美元。