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

2026-03-10

AI Summary

This work addresses the limitations of existing deep learning approaches in time series forecasting, which predominantly focus on low-frequency patterns while neglecting mid- and high-frequency components and struggle to effectively model coupled multi-periodicity with long look-back windows. To this end, we propose FreqCycle, a novel framework that employs a time-domain filtering-enhanced periodic prediction module to capture low-frequency features and introduces a segmented frequency-domain pattern learning module to reinforce mid- and high-frequency energy. Furthermore, we develop MFreqCycle, which adopts a hierarchical architecture to decouple nested periodicities across multiple scales. Our method is the first to systematically model mid- and high-frequency time–frequency characteristics, incorporating learnable filters and adaptive weighting mechanisms. It achieves state-of-the-art accuracy across seven benchmark domains while maintaining efficient inference, striking an optimal balance between performance and computational efficiency.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Computer Vision: Multi-modal Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• time series forecasting
• time-frequency analysis
• multi-periodicity
• high-frequency features
• long lookback window

Innovation

• time-frequency analysis
• multi-scale modeling
• frequency-domain learning
• coupled periodicity
• deep time series forecasting