FreDN: Spectral Disentanglement for Time Series Forecasting via Learnable Frequency Decomposition

TL;DR

FreDN introduces a learnable frequency disentangler and a real-imaginary shared-parameter design to improve spectral decomposition and forecasting accuracy in non-stationary time series, reducing complexity and outperforming state-of-the-art methods.

Contribution

The paper proposes FreDN with a learnable Frequency Disentangler and ReIm Block, advancing spectral decomposition for non-stationary time series forecasting.

Findings

Outperforms state-of-the-art methods by up to 10% in long-term forecasting.

Reduces parameter count and computational cost by at least 50%.

Provides theoretical insights into frequency-domain loss effectiveness.

Abstract

Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary time series, these methods encounter the $\textit{spectral entanglement}$ and the computational burden of complex-valued learning. The $\textit{spectral entanglement}$ refers to the overlap of trends, periodicities, and noise across the spectrum due to $\textit{spectral leakage}$ and the presence of non-stationarity. However, existing decompositions are not suited to resolving spectral entanglement. To address this, we propose the Frequency Decomposition Network (FreDN), which introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain. Furthermore, we propose a theoretically supported ReIm Block to reduce the complexity of complex-valued operations while maintaining performance. We also re-examine the frequency-domain loss function and provide new theoretical insights into its effectiveness. Extensive experiments on seven long-term forecasting benchmarks demonstrate that FreDN outperforms state-of-the-art methods by up to 10\%. Furthermore, compared with standard complex-valued architectures, our real-imaginary shared-parameter design reduces the parameter count and computational cost by at least 50\%.