Financial Frequency Combs

Battle Count: 69

This is a theoretical econophysics paper focused on the spectral properties of a stylized nonlinear financial model. It does not propose trading strategies, forecasting algorithms, or risk management tools directly applicable to quantitative trading. The findings about deterministic spectral fingerprints in memory-bearing financial systems could theoretically inform regime detection or cycle identification, but the paper provides no empirical validation, no trading signals, and no actionable framework for market participants. The relevance is primarily academic and conceptual rather than practical.

Implementation requires: (1) coding the Adams-Bashforth-Moulton predictor-corrector scheme for incommensurate Caputo fractional ODEs, which involves computing power-law convolution kernels; (2) performing FFT-based spectral analysis with appropriate windowing and transient removal; (3) conducting multi-dimensional parameter sweeps (1000 points per parameter across 6+ parameters); (4) generating spectrogram visualizations. The fractional-order integration is the most technically demanding component. No existing off-the-fly libraries directly handle incommensurate multi-order Caputo systems, though tools like FDE12 or custom implementations exist. The overall workflow is well-defined but requires careful numerical implementation.

The paper provides detailed numerical parameters (step size h=0.01, time window [0,2000], transient discard [0,1500], parameter ranges, initial conditions, and fractional order values). The Adams-Bashforth-Moulton scheme is well-documented. However, no code repository or supplementary data is provided. Reproduction requires implementing fractional-order ODE solvers and FFT analysis, which is feasible but non-trivial. The 1000-point sweeps across multiple parameters are computationally intensive but well-specified.