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

TL;DR

FreqCycle is a novel multi-scale time-frequency analysis framework that improves time series forecasting by effectively capturing low, mid, and high frequency features, addressing coupled multi-periodic patterns, and achieving state-of-the-art accuracy.

Contribution

It introduces FreqCycle, a new framework with modules for extracting diverse frequency features and extends to MFreqCycle for handling nested periodicities in time series.

Findings

Achieves state-of-the-art forecasting accuracy on seven benchmarks.

Maintains faster inference speeds compared to existing methods.

Effectively captures multi-scale frequency features and coupled periodicities.

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.