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FreqCycle: A Multi-Scale Time-Frequency Analysis Method for Time Series Forecasting

Boya Zhang, Shuaijie Yin, Huiwen Zhu, Xing He

TL;DR

To address coupled multi-periodicity as well as long lookback window challenges, FreqCycle is extended hierarchically into MFreqCycle, which decouples nested periodic features through cross-scale interactions, striking an optimal balance between performance and efficiency.

Abstract

Mining time-frequency features is critical for time series forecasting. Existing research has predominantly focused on modeling low-frequency patterns, where most time series energy is concentrated. The overlooking of mid to high frequency continues to limit further performance gains in deep learning models. We propose FreqCycle, a novel framework integrating: (i) a Filter-Enhanced Cycle Forecasting (FECF) module to extract low-frequency features by explicitly learning shared periodic patterns in the time domain, and (ii) a Segmented Frequency-domain Pattern Learning (SFPL) module to enhance mid to high frequency energy proportion via learnable filters and adaptive weighting. Furthermore, time series data often exhibit coupled multi-periodicity, such as intertwined weekly and daily cycles. To address coupled multi-periodicity as well as long lookback window challenges, we extend FreqCycle hierarchically into MFreqCycle, which decouples nested periodic features through cross-scale interactions. Extensive experiments on seven diverse domain benchmarks demonstrate that FreqCycle achieves state-of-the-art accuracy while maintaining faster inference speeds, striking an optimal balance between performance and efficiency.

FreqCycle: A Multi-Scale Time-Frequency Analysis Method for Time Series Forecasting

TL;DR

To address coupled multi-periodicity as well as long lookback window challenges, FreqCycle is extended hierarchically into MFreqCycle, which decouples nested periodic features through cross-scale interactions, striking an optimal balance between performance and efficiency.

Abstract

Mining time-frequency features is critical for time series forecasting. Existing research has predominantly focused on modeling low-frequency patterns, where most time series energy is concentrated. The overlooking of mid to high frequency continues to limit further performance gains in deep learning models. We propose FreqCycle, a novel framework integrating: (i) a Filter-Enhanced Cycle Forecasting (FECF) module to extract low-frequency features by explicitly learning shared periodic patterns in the time domain, and (ii) a Segmented Frequency-domain Pattern Learning (SFPL) module to enhance mid to high frequency energy proportion via learnable filters and adaptive weighting. Furthermore, time series data often exhibit coupled multi-periodicity, such as intertwined weekly and daily cycles. To address coupled multi-periodicity as well as long lookback window challenges, we extend FreqCycle hierarchically into MFreqCycle, which decouples nested periodic features through cross-scale interactions. Extensive experiments on seven diverse domain benchmarks demonstrate that FreqCycle achieves state-of-the-art accuracy while maintaining faster inference speeds, striking an optimal balance between performance and efficiency.
Paper Structure (47 sections, 13 equations, 17 figures, 12 tables)

This paper contains 47 sections, 13 equations, 17 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. MLP-based Time Series Model
  4. Time Series Modeling with Frequency Learning
  5. Methodology
  6. Preliminaries
  7. Filter-Enhanced Cycle Forecasting
  8. Segmented Frequency-domain Pattern Learning
  9. MFreqCycle
  10. Experiments
  11. Experimental Setup
  12. Datasets
  13. Technical Implementation Details
  14. Baselines
  15. Evaluation Metrics
  16. ...and 32 more sections

Figures (17)

  • Figure 1: Shared periodic patterns present in the ETTm2 dataset.
  • Figure 2: Frequency spectrum of Traffic dataset before and after SFPL enhancement
  • Figure 3: The architecture of FreqCycle. (a) The overall architecture of FreqCycle. (b) FECF block is employed to explicitly learns shared periodic patterns in the time domain; (c) SFPL extracts critical frequency information in the spectral domain via learnable filters and adaptive weighting.(d) MFreqCycle explicitly decouples and models nested periodic features through cross-scale interactions.
  • Figure 4: Model efficiency comparison in terms of MSE, Peak memory consumption and Training speed. Using an input length $L=96$ and prediction horizon $H=96$ on the Electricity dataset.
  • Figure 5: Frequency spectrum of Electricity dataset before and after SFPL enhancement. The other datasets' results are available in Appendix E.
  • ...and 12 more figures