FTMixer: Frequency and Time Domain Representations Fusion for Time Series Forecasting

Time series data can be represented in both the time and frequency domains, with the time domainemphasizing local dependencies and the frequency domain highlighting global dependencies. To harness the strengths of both domains in capturing local and global dependencies, we propose a novel Frequency and Time Domain Mixer (FTMixer) method. To exploit the global characteristics of the frequency domain, we introduce a novel Frequency Channel Convolution (FCC) module, designed to capture global inter-series dependencies. Inspired by the windowing concept in frequency domain transformations, we further propose a novel Windowed Frequency-Time Convolution (WFTC) module, which captures local dependencies by leveraging both frequency domain representations obtained from windowed transformations and time domain representations. Notably, FTMixer employs the Discrete Cosine Transformation (DCT) with real numbers instead of the complex-number-based Discrete Fourier Transformation (DFT), enabling direct utilization of modern deep learning operators in the frequency domain. Extensive experimental results across seven real-world long-term time series datasets demonstrate the superiority of FTMixer, in terms of both forecasting performance and computational efficiency.