Decoding Cryptocurrency Cycles: A Systematic Literature Review of Spectral Analysis, Econophysical Signal Processing, and Complexity Frameworks

The cryptocurrency market constitutes a complex, non-linear financial ecosystem where traditional econometric frameworks frequently struggle to capture abrupt regime shifts and heavy-tailed crash dynamics. To address this gap, this study synthesizes the application of econophysical signal processing and complexity science in decoding digital asset cycles. Guided by the PRISMA 2020 protocol and a five-domain Risk of Bias (RoB) quality appraisal, this Systematic Literature Review evaluates 30 core empirical and methodological studies (within a 51-source bibliography), establishing a taxonomic classification of time-frequency analysis, adaptive signal decomposition, fractal dynamics, and hybrid machine learning architectures with explicit mathematical formulations and performance benchmarks. The findings indicate that wavelet transforms and Empirical Mode Decomposition (EMD) isolate non-stationary, multi-scale cyclical behaviors more effectively compared to classical Fourier methods. Furthermore, the temporal evolution of informational complexity metrics—such as Lempel-Ziv Complexity, Bandt-Pompe Permutation Entropy, and Approximate Entropy—reveals pre-crash compression of pattern diversity as a consistent empirical precursor to liquidity evaporation. Additionally, integrating adaptive signal decomposition with hybrid deep learning and α-stable Lévy distributions generally improves forecasting accuracy over standalone linear benchmarks, though regularized parsimonious models (e.g., LASSO and ARIMAX) remain competitive under high noise. Ultimately, non-linear signal engineering provides actionable early warning systems for quantitative asset pricing, latency-aware algorithmic trading, and macroprudential regulatory oversight.