Pink Noise in Economic Time Series from Synchronization and Amplitude Demodulation

Pink noise, characterized by a power spectral density $S(\omega)\propto\omega^{\beta}$ with $\beta\simeq -1$, appears in economic indices as well as in many natural systems. We summarize a unified mesoscopic interpretation in which pink spectra arise from repeated synchronization, amplitude modulation, and demodulation. In economic time series, we identify two kinds of pink-noise behavior: one that appears in the raw data (property A), and another that appears only after detrending and demodulation (property B). A stochastic Kuramoto model provides a minimal dynamical model of repeated synchronization and desynchronization among many economic circulations. It produces approximate $1/f$ spectra over a broad coupling--system-size domain and gives variance--mean scaling, Taylor's law. The same amplitude-modulation/demodulation mechanism also gives a compact explanation of pink spectra in music, earthquakes, variable stars, solar flares, and black-hole accretion systems. Pink noise is therefore interpreted not merely as a statistical regularity, but as a diagnostic of slowly modulated collective coherence in complex flow systems.