A Survey of Deep Time Series Forecasting with Spectral Analysis

Time series forecasting is a core technology in critical domains such as energy dispatch and traffic management, yet its performance is hindered by challenges including long-term dependencies, multi-scale structures, and data non-stationarity. In recent years, integrating spectral analysis with deep learning has emerged as a significant trend for improving forecasting accuracy and efficiency. This paper systematically reviews progress in this field by introducing a challenge-oriented classification framework encompassing four dimensions: long-term dependency modeling, multi-scale feature extraction, lightweight design, and multi-task general-purpose modeling. Within this framework, we conduct a comparative analysis of representative methods, including Autoformer, FEDformer, and TimesNet, among others. These methods enhance modeling capacity for complex temporal patterns through mechanisms such as spectral sparsification, adaptive frequency filtering, and temporal multi-periodic transformations. We evaluate methods on eight mainstream benchmark datasets across multiple forecast horizons (96–720 steps). Results demonstrate that spectral sparsification and memory filtering mitigate error accumulation in long-term forecasting; multi-scale decomposition structures balance short-term fluctuations and long-term trends; and lightweight linear models achieve superior parameter efficiency on high-dimensional stationary data. By synthesizing technical pathways and scenario-based comparisons, this study offers practical guidance for model selection in engineering applications. Finally, we outline future research directions, including time-varying period detection and joint time-frequency representation, to enhance the robustness of forecasting models in non-stationary environments and facilitate their real-world deployment.