ReFocus: Reinforcing Mid-Frequency and Key-Frequency Modeling for Multivariate Time Series Forecasting
Guoqi Yu, Yaoming Li, Juncheng Wang, Xiaoyu Guo, Angelica I. Aviles-Rivero, Tong Yang, Shujun Wang
TL;DR
This work tackles two core challenges in multivariate time series forecasting: the Mid-Frequency Spectrum Gap and the underutilization of shared Key-Frequency across channels. It introduces AMEO to amplify mid-frequency energy, EKPB to efficiently capture cross-channel Key-Frequency, and KET to strengthen training by mixing spectral information across channels. Empirical results on eight real-world datasets (including eight ETTh/ETTm variants, Traffic, Weather, Solar_Energy, and Electricity) show consistent $MSE$ reductions, notably 4-6% over the previous SOTA iTransformer on Traffic, ECL, and Solar. The approach leverages FFT-based spectral processing and a convolutional-residual design, with code and training scripts available on GitHub to facilitate reproducibility and practical adoption.
Abstract
Recent advancements have progressively incorporated frequency-based techniques into deep learning models, leading to notable improvements in accuracy and efficiency for time series analysis tasks. However, the Mid-Frequency Spectrum Gap in the real-world time series, where the energy is concentrated at the low-frequency region while the middle-frequency band is negligible, hinders the ability of existing deep learning models to extract the crucial frequency information. Additionally, the shared Key-Frequency in multivariate time series, where different time series share indistinguishable frequency patterns, is rarely exploited by existing literature. This work introduces a novel module, Adaptive Mid-Frequency Energy Optimizer, based on convolution and residual learning, to emphasize the significance of mid-frequency bands. We also propose an Energy-based Key-Frequency Picking Block to capture shared Key-Frequency, which achieves superior inter-series modeling performance with fewer parameters. A novel Key-Frequency Enhanced Training strategy is employed to further enhance Key-Frequency modeling, where spectral information from other channels is randomly introduced into each channel. Our approach advanced multivariate time series forecasting on the challenging Traffic, ECL, and Solar benchmarks, reducing MSE by 4%, 6%, and 5% compared to the previous SOTA iTransformer. Code is available at this GitHub Repository: https://github.com/Levi-Ackman/ReFocus.