  Time series data can be represented in both the time and frequency domains,
with the time domain emphasizing local dependencies and the frequency domain
highlighting global dependencies. To harness the strengths of both domains in
capturing local and global dependencies, we propose the Frequency and Time
Domain Mixer (FTMixer). To exploit the global characteristics of the frequency
domain, we introduce the Frequency Channel Convolution (FCC) module, designed
to capture global inter-series dependencies. Inspired by the windowing concept
in frequency domain transformations, we present the Windowing Frequency
Convolution (WFC) module to capture local dependencies. The WFC module first
applies frequency transformation within each window, followed by convolution
across windows. Furthermore, to better capture these local dependencies, we
employ channel-independent scheme to mix the time domain and frequency domain
patches. 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.
