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WFTNet: Exploiting Global and Local Periodicity in Long-term Time Series Forecasting

Peiyuan Liu, Beiliang Wu, Naiqi Li, Tao Dai, Fengmao Lei, Jigang Bao, Yong Jiang, Shu-Tao Xia

TL;DR

WFTNet tackles long-term time series forecasting by jointly modeling global and local periodic structures. It integrates Fourier (global) and continuous wavelet transforms (local) within WFTBlocks, using a Time-Frequency Inception Block and a Periodicity-Weighted Coefficient (PWC) to adaptively balance the two views. The approach yields state-of-the-art results across diverse datasets and horizons, with ablations showing the value of PWC in adjusting to dataset periodicity. This work advances practical forecasting by providing a unified, frequency-aware framework that adapts to varying temporal patterns and non-stationarities, with code available for replication.

Abstract

Recent CNN and Transformer-based models tried to utilize frequency and periodicity information for long-term time series forecasting. However, most existing work is based on Fourier transform, which cannot capture fine-grained and local frequency structure. In this paper, we propose a Wavelet-Fourier Transform Network (WFTNet) for long-term time series forecasting. WFTNet utilizes both Fourier and wavelet transforms to extract comprehensive temporal-frequency information from the signal, where Fourier transform captures the global periodic patterns and wavelet transform captures the local ones. Furthermore, we introduce a Periodicity-Weighted Coefficient (PWC) to adaptively balance the importance of global and local frequency patterns. Extensive experiments on various time series datasets show that WFTNet consistently outperforms other state-of-the-art baseline. Code is available at https://github.com/Hank0626/WFTNet.

WFTNet: Exploiting Global and Local Periodicity in Long-term Time Series Forecasting

TL;DR

WFTNet tackles long-term time series forecasting by jointly modeling global and local periodic structures. It integrates Fourier (global) and continuous wavelet transforms (local) within WFTBlocks, using a Time-Frequency Inception Block and a Periodicity-Weighted Coefficient (PWC) to adaptively balance the two views. The approach yields state-of-the-art results across diverse datasets and horizons, with ablations showing the value of PWC in adjusting to dataset periodicity. This work advances practical forecasting by providing a unified, frequency-aware framework that adapts to varying temporal patterns and non-stationarities, with code available for replication.

Abstract

Recent CNN and Transformer-based models tried to utilize frequency and periodicity information for long-term time series forecasting. However, most existing work is based on Fourier transform, which cannot capture fine-grained and local frequency structure. In this paper, we propose a Wavelet-Fourier Transform Network (WFTNet) for long-term time series forecasting. WFTNet utilizes both Fourier and wavelet transforms to extract comprehensive temporal-frequency information from the signal, where Fourier transform captures the global periodic patterns and wavelet transform captures the local ones. Furthermore, we introduce a Periodicity-Weighted Coefficient (PWC) to adaptively balance the importance of global and local frequency patterns. Extensive experiments on various time series datasets show that WFTNet consistently outperforms other state-of-the-art baseline. Code is available at https://github.com/Hank0626/WFTNet.
Paper Structure (15 sections, 4 equations, 2 figures, 2 tables)

This paper contains 15 sections, 4 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Discrete Fourier Transform
  4. Continuous Wavelet Transform
  5. Related Work
  6. Method
  7. Problem Statement
  8. Framework
  9. WFTBlock
  10. Periodicity-Weighted Coefficient
  11. Experiments
  12. Datasets
  13. Main Results
  14. Significance of PWC
  15. Conclusion

Figures (2)

  • Figure 1: Overall architecture of WFTNet (left) and details of WFTBlock (right). The encoder and decoder manage input normalization, embedding, and output projection. WFTBlocks transform the 1D time series into 2D representations using FFT for global periodic patterns and CWT for local features.
  • Figure 2: Visualization of the normalized mean channel values for the ECL and ETTh2 datasets. The plot reveals stronger periodicity in ECL compared to ETTh2.