Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary time series, these methods encounter the $\textit{spectral entanglement}$ and the computational burden of complex-valued learning. The $\textit{spectral entanglement}$ refers to the overlap of trends, periodicities, and noise across the spectrum due to $\textit{spectral leakage}$ and the presence of non-stationarity. However, existing decompositions are not suited to resolving spectral entanglement. To address this, we propose the Frequency Decomposition Network (FreDN), which introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain. Furthermore, we propose a theoretically supported ReIm Block to reduce the complexity of complex-valued operations while maintaining performance. We also re-examine the frequency-domain loss function and provide new theoretical insights into its effectiveness. Extensive experiments on seven long-term forecasting benchmarks demonstrate that FreDN outperforms state-of-the-art methods by up to 10\%. Furthermore, compared with standard complex-valued architectures, our real-imaginary shared-parameter design reduces the parameter count and computational cost by at least 50\%.

翻译：时间序列预测在众多实际应用中至关重要。近年来，频域方法因其捕捉全局依赖的能力而受到越来越多的关注。然而，当应用于非平稳时间序列时，这些方法会遇到$\textit{谱纠缠}$问题以及复值学习的计算负担。$\textit{谱纠缠}$指的是由于$\textit{频谱泄漏}$和非平稳性的存在，趋势、周期性和噪声在整个频谱上发生重叠。然而，现有的分解方法并不适合解决谱纠缠问题。为此，我们提出了频率分解网络（FreDN），它引入了一个可学习的频率解缠模块，直接在频域中分离趋势分量和周期分量。此外，我们提出了一个具有理论支持的实虚部共享参数模块，以在保持性能的同时降低复值运算的复杂度。我们还重新审视了频域损失函数，并对其有效性提供了新的理论见解。在七个长期预测基准数据集上进行的大量实验表明，FreDN的性能优于现有最先进方法，提升幅度最高可达10%。此外，与标准的复值架构相比，我们的实虚部共享参数设计将参数量和计算成本降低了至少50%。