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Madhurendra Mishra, Armaan Aryan, Arsh Gogia, Adarsh Ganesan · 2026-06-22
The paper takes a specific mathematical macroeconomic model (a fractional-order system with 'memory' built into interest rate, investment, and price dynamics) and shows its long-run behavior produces a 'frequency comb' — a set of evenly spaced, structured spectral lines borrowed from physics. This comb only appears within certain ranges of parameters like savings, investment cost, and demand elasticity, and tips into chaos when the memory exponents get high enough.
Why it matters: It suggests that a memory-bearing economic model can generate orderly, deterministic cyclical patterns rather than pure randomness, which is conceptually interesting for anyone thinking about long-run economic cycles. In practice this is highly theoretical and does not translate into a tradable signal or forecast.
⚠ This is an abstract theoretical result from a specific mathematical model with no empirical data, backtest, or trading application.
Frequency combs are discrete, equally spaced, phase-coherent spectral lines that emerge from nonlinear mode coupling in physical systems. We show that the incommensurate fractional-order financial model of Huang, Li, Ma, and Chen, whose Caputo derivatives encode macroeconomic long-range memory, generates an analogous structure in its steady-state spectrum. The comb appears only over specific values and ranges of the saving amount $a$, the investment cost $b$, and the demand elasticity $c$, outside which the spectral lines lose their equal spacing. It persists across extended parameter regimes and stays invariant to perturbations in the initial interest rate $x_0$ and investment demand $y_0$, while distinct spectral regimes appear at different initial price levels $z_0$. The comb is generated only when the fractional-order exponents $q_1$, $q_2$, and $q_3$ associated with interest rate, investment demand, and price index are above the critical threshold values. At even higher values of these exponents, the frequency comb transitions into chaos. These findings show that the long-run cyclic structure of a memory-bearing financial economy organises into a discrete, deterministic spectral fingerprint rather than a stochastic continuum.
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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.