Not All Frequencies Are Created Equal: Towards a Dynamic Fusion of Frequencies in Time-Series Forecasting

Xingyu Zhang, Siyu Zhao, Zeen Song, Huijie Guo, Jianqi Zhang, Changwen Zheng, Wenwen Qiang

Abstract: 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. Experiment results and ablation studies demonstrate the effectiveness of FreDF.

Primary Subject Area: [Content] Media Interpretation

Secondary Subject Area: [Generation] Generative Multimedia

Relevance To Conference: This work makes several significant contributions to multimedia processing: 1) Time series forecasting is crucial in various multimedia processing applications such as video streaming, content recommendation systems, and multimedia data analysis. By addressing the challenge of long-term time series forecasting, this work directly contributes to improving the accuracy and reliability of predictions in multimedia applications; 2) By leveraging Fourier analysis, the work offers a valuable alternative for capturing reusable and periodic patterns in multimedia data. This not only enhances the forecasting accuracy but also makes the methods applicable to a wide range of multimedia processing tasks where periodic patterns are prevalent; 3) The proposed insight into the generalization ability of time series forecasting and the derivation of the generalization bound further advances our understanding of forecasting models, which is beneficial for developing more robust multimedia processing algorithms.

Submission Number: 3022