Exploring time series analysis in frequency domain with complex-valued spectral attention and bidirectional variable mamba

Recently, deep learning has made significant strides in multivariate time series forecasting. While frequency-domain-based methods have shown promising results, existing models often struggle with frequency misalignment when handling diverse frequency combinations, leading to reduced forecasting accuracy. To address these issues, we propose the Spectral Attention Module (SAM), which integrates temporal and frequency-domain information to effectively capture both local and global dependencies in time series data. Within the frequency-domain module, we introduce an Extended Discrete Fourier Transform to overcome frequency misalignment challenges and design a Complex-Valued Spectral Attention Mechanism (CV-SAM) to identify and exploit complex relationships among different frequency combinations. To further capture inter-variable correlations, we propose the Bidirectional Variable Mamba. It uses linear layers to encode timestamps for each variable and employs the Mamba layer to extract inter-variable correlations, supported by a feedforward network to learn temporal dependencies. By combining the SAM and the BV-Mamba, we construct the SpectroMamba, which demonstrates superior performance over state-of-the-art methods in long-term time series forecasting across multiple real-world datasets.