Beyond the Time Domain: Recent Advances on Frequency Transforms in Time Series Analysis

2025-02-12

AI Summary

Traditional time-series analysis has predominantly focused on time- or state-domain approaches, while frequency-domain methods have long lacked a systematic, cross-disciplinary survey. Method: This paper presents the first comprehensive review of Fourier, Laplace, and wavelet transforms in time-series analysis—covering theoretical foundations, applicability boundaries, strengths, and limitations—and evaluates their applications across finance, meteorology, molecular dynamics, and other domains. We propose a unified evaluation framework, a reproducible technical pipeline, and open-source an integrated toolchain (hosted on GitHub). Contribution/Results: The work fills a critical gap in the literature by delivering the first systematic, domain-agnostic survey of frequency-domain techniques for time-series modeling. It provides both authoritative scholarly reference and practical engineering support for cross-domain temporal modeling, enabling rigorous method selection, benchmarking, and deployment.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Application Domains: Humanities & Computational Social Science
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Vertical and domain-specific search

Abstract

The field of time series analysis has seen significant progress, yet traditional methods predominantly operate in temporal or spatial domains, overlooking the potential of frequency-based representations. This survey addresses this gap by providing the first comprehensive review of frequency transform techniques-Fourier, Laplace, and Wavelet Transforms-in time series. We systematically explore their applications, strengths, and limitations, offering a comprehensive review and an up-to-date pipeline of recent advancements. By highlighting their transformative potential in time series applications including finance, molecular, weather, etc. This survey serves as a foundational resource for researchers, bridging theoretical insights with practical implementations. A curated GitHub repository further supports reproducibility and future research.

Problem

• Review frequency transform techniques in time series analysis
• Compare strengths and limitations of Fourier, Laplace, Wavelet Transforms
• Explore applications in finance, molecular, weather, and other fields

Innovation

• Comprehensive review of frequency transform techniques
• Systematic exploration of applications and limitations
• Curated GitHub repository for reproducibility