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

Authors: Boya Zhang, Shuaijie Yin, Huiwen Zhu, Xing He Date: 2026-03-10 Paper ID: openalex:2603.09661

Summary

This paper introduces FreqCycle, a novel framework for time series forecasting that addresses the under-modeling of mid to high-frequency components dominant in existing deep learning approaches. The framework integrates two key modules: FECF for learning shared low-frequency periodic patterns and SFPL for boosting the energy proportion of mid-to-high frequencies via adaptive filtering. To handle complex, coupled multi-periodicity and long lookback windows, the authors extend the method to MFreqCycle, which leverages cross-scale interactions to decouple nested periodic features. Experimental results across seven benchmarks show that FreqCycle and MFreqCycle achieve superior accuracy while maintaining competitive inference speed.

Key Contributions

• Proposal of FreqCycle, a novel framework that combines a Filter-Enhanced Cycle Forecasting (FECF) module for low-frequency pattern extraction and a Segmented Frequency-domain Pattern Learning (SFPL) module for mid-to-high frequency enhancement.
• Introduction of MFreqCycle, a hierarchical extension of FreqCycle designed to decouple nested periodic features and handle long lookback windows by modeling coupled multi-periodicity.
• Demonstration of state-of-the-art accuracy across seven diverse time series benchmarks while achieving faster inference speeds compared to existing models.
• Addressing the common limitation in deep learning models of overlooking mid to high-frequency components, which are crucial for comprehensive time series analysis.

Limitations

The abstract does not explicitly detail limitations, but the hierarchical extension (MFreqCycle) suggests complexity in managing increasingly deep nested periodicities.

Open Questions & Future Work

• annual-cycle-modeling-in-mfreqcycle

Key Concepts

• Filter-Enhanced Cycle Forecasting: A module designed to extract low-frequency features by explicitly learning shared periodic patterns in the time domain for time series forecasting.
• Segmented Frequency-domain Pattern Learning: A module that enhances the proportion of mid to high-frequency energy in time series data using learnable filters and adaptive weighting.

Datasets

• ETTh1
• Traffic
• Weather

Limitations

The abstract does not explicitly detail limitations, but the hierarchical extension (MFreqCycle) suggests complexity in managing increasingly deep nested periodicities.

Links

• Abstract
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