Spectral Regime Analysis of Economic Systems

The author presents a spectral framework for analyzing instability across economic systems, including macroeconomic indicators, financial markets, and policy regimes. Macroeconomic fluctuations exhibit nonlinear dynamics resembling spectral systems observed in turbulence and statistical physics. ^[1][2][3] This paper introduces Spectral Regime Analysis (SRA) and an Additive-Multiplicative (AM) regulator for measuring economic instability.

The instability frequency parameter,

λ= ∆X σ X

Captures deviation relative to volatility; Sorting λ values across macroeconomic indicators produces a 100-point instability spectrum whose normalized spacing shows structural similarities with eigenvalue spacing patterns studied in the Riemann Hypothesis. ^[16][17][18]

Using international macroeconomic data, the author constructs ten empirical tables covering growth, inflation, labor, debt, trade, monetary policy, markets, and financial risk. ^[6][8]

An AM regulator,

Ω λ = 1 1+ e (λ-1)

Damps instability and generates regulated economic observables.