Time Series Analysis in Frequency Domain: A Survey of Open Challenges, Opportunities and Benchmarks

Frequency-domain analysis has emerged as a powerful paradigm for time series analysis, offering unique advantages over traditional time-domain approaches while introducing new theoretical and practical challenges. This survey provides a comprehensive examination of spectral methods from classical Fourier analysis to modern neural operators, systematically summarizing three open challenges in current research: (1) causal structure preservation during spectral transformations, (2) uncertainty quantification in learned frequency representations, and (3) topology-aware analysis for non-Euclidean data structures. Through rigorous reviewing of over 100 studies, we develop a unified taxonomy that bridges conventional spectral techniques with cutting-edge machine learning approaches, while establishing standardized benchmarks for performance evaluation. Our work identifies key knowledge gaps in the field, particularly in geometric deep learning and quantum-enhanced spectral analysis. The survey offers practitioners a systematic framework for method selection and implementation, while charting promising directions for future research in this rapidly evolving domain.