ATFNet: Adaptive Time-Frequency Ensembled Network for Long-term Time Series Forecasting

TL;DR

ATFNet tackles long-term time series forecasting by marrying time-domain local dependencies with frequency-domain global dependencies in a dual-block architecture. It introduces Extended DFT to align input spectra with the complete series, a Complex-valued Spectrum Attention mechanism to capture interactions in the frequency domain, and Dominant Harmonic Series Energy Weighting to adaptively fuse the two branches based on periodicity. Theoretical results bound the energy concentration in dominant harmonics and empirical results on eight real-world datasets show state-of-the-art performance, especially for long horizons, with ablations confirming the contributions of each component. This adaptive time-frequency framework provides a principled, efficient path to leverage both local and global patterns in diverse time series, with potential applicability to non-periodic data and broader spectral analyses.

Abstract

The intricate nature of time series data analysis benefits greatly from the distinct advantages offered by time and frequency domain representations. While the time domain is superior in representing local dependencies, particularly in non-periodic series, the frequency domain excels in capturing global dependencies, making it ideal for series with evident periodic patterns. To capitalize on both of these strengths, we propose ATFNet, an innovative framework that combines a time domain module and a frequency domain module to concurrently capture local and global dependencies in time series data. Specifically, we introduce Dominant Harmonic Series Energy Weighting, a novel mechanism for dynamically adjusting the weights between the two modules based on the periodicity of the input time series. In the frequency domain module, we enhance the traditional Discrete Fourier Transform (DFT) with our Extended DFT, designed to address the challenge of discrete frequency misalignment. Additionally, our Complex-valued Spectrum Attention mechanism offers a novel approach to discern the intricate relationships between different frequency combinations. Extensive experiments across multiple real-world datasets demonstrate that our ATFNet framework outperforms current state-of-the-art methods in long-term time series forecasting.

Figures (10)

• Figure 1: Real-world time series with distinct periodic pattern.
• Figure 2: Model architecture of ATFNet. ATFNet is mainly composed of three sub-parts: 1) T-Block to capture local dependency from time domain; 2) F-Block to capture global dependency from frequency domain. The Extended DFT is used to generate frequency-aligned spectrum of input series. 3) The Dominant Harmonic Series Energy Weighting to allocate appropriate weights for F-Block and T-Block according to the periodic property of input series.
• Figure 3: By employing Extended DFT, it becomes possible to obtain the spectrum of the input series with a discrete frequency group that aligns with the DFT spectrum of the complete series.
• Figure 4: Top: Periodic time series, sampled from Traffic dataset. It can be observed that there exists an obvious harmonic group. Bottom: Non-periodic time series, sampled from Weather dataset. There are no obvious harmonic group in non-periodic series.
• Figure 5: Examples of weights allocation for distinct time series from 4 different datasets.

Theorems & Definitions (4)

• Theorem 1
• Theorem 2
• proof
• proof