  Long-term time series forecasting is a long-standing challenge in various
applications. A central issue in time series forecasting is that methods should
expressively capture long-term dependency. Furthermore, time series forecasting
methods should be flexible when applied to different scenarios. Although
Fourier analysis offers an alternative to effectively capture reusable and
periodic patterns to achieve long-term forecasting in different scenarios,
existing methods often assume high-frequency components represent noise and
should be discarded in time series forecasting. However, we conduct a series of
motivation experiments and discover that the role of certain frequencies varies
depending on the scenarios. In some scenarios, removing high-frequency
components from the original time series can improve the forecasting
performance, while in others scenarios, removing them is harmful to forecasting
performance. Therefore, it is necessary to treat the frequencies differently
according to specific scenarios. To achieve this, we first reformulate the time
series forecasting problem as learning a transfer function of each frequency in
the Fourier domain. Further, we design Frequency Dynamic Fusion (FreDF), which
individually predicts each Fourier component, and dynamically fuses the output
of different frequencies. Moreover, we provide a novel insight into the
generalization ability of time series forecasting and propose the
generalization bound of time series forecasting. Then we prove FreDF has a
lower bound, indicating that FreDF has better generalization ability. Extensive
experiments conducted on multiple benchmark datasets and ablation studies
demonstrate the effectiveness of FreDF.
