Pink Noise in Economic Time Series from Synchronization and Amplitude Demodulation

TL;DR

This paper explores the origins of pink noise in economic and natural systems, proposing a unified interpretation involving synchronization and amplitude modulation, supported by a stochastic Kuramoto model.

Contribution

It introduces a mesoscopic interpretation of pink noise through synchronization and demodulation, and demonstrates the model's applicability across diverse complex systems.

Findings

Pink noise arises from synchronization and amplitude modulation mechanisms.

The stochastic Kuramoto model reproduces 1/f spectra and Taylor's law.

Pink spectra are linked to collective coherence in complex systems.

Abstract

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.