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

TL;DR

FTMixer tackles time-series forecasting by unifying time- and frequency-domain representations. It uses a real-valued $DCT$ to avoid complex arithmetic and introduces two modules: FCC for global frequency interactions and WFTC for local frequency-time patterns, complemented by depth-wise separable convolutions and a dual-domain loss. Across seven real-world datasets, FTMixer achieves state-of-the-art forecasting accuracy with improved computational efficiency, and ablation studies confirm the essential roles of FCC, WFTC, and the dual-domain supervision. This work demonstrates the practical impact of exploiting frequency-domain information alongside time-domain signals for robust, scalable time-series forecasting.

Abstract

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.

Figures (4)

• Figure 1: (a) Visualizations of the Fully Connected (FC) layer weights learned in the time and frequency domains on the ETTh1 dataset, with both the input and output length equal to 96, resulting in a $96\times96$ weight matrix ($y$-axis: the output, $x$-axis: the input). Note that we train the frequency domain FC layer by employing the Discrete Cosine Transform (DCT). From the FC layer weight visualizations, we can see that learning in the frequency domain identifies clearer diagonal dependencies and key patterns than in the time domain. (b) Predictions of the frequency domain FC layer and the time domain FC layer. The frequency domain output is smoother and emphasizes periodic information with smaller MSE=0.379, while the time domain output captures more local dependencies with larger MSE=0.383.
• Figure 2: The framework of FTMixer. FTMixer comprises two main modules: FCC and WFTC. An example $\mathbf{X}$ containing four channels is visualized here for easier understanding. The model predictor is a Linear layer.
• Figure 3: The visualization of predictions by FTMixer, PatchTST, and ModernTCN on the ETTh1 dataset shows that the proposed FTMixer achieves the best performance with an MSE of 0.356, compared to PatchTST's 0.382 and ModernTCN's 0.375.
• Figure 4: Visualization of Meta-Tuner forecasting on six dataset.