Signatures of Quantum-like Chaos in Dow Jones Index and Turbulent Fluid Flows

Abstract

Dow Jones Index time series exhibit irregular or fractal fluctuations on all time scales from days, months to years. The nonlinear fluctuations are selfsimilar as exhibited in inverse power law form for power spectra of temporal fluctuations. Inverse power law form for power spectra of fractal fluctuations is generic to all dynamical systems in nature and is identified as self-organized criticality.The author has developed a general systems theory for universal quantification of the observed self-organized criticality in dynamical systems. The model predicts that the power spectra of fractal fluctuations follow the universal and unique inverse power law form of the statistical normal distribution and is identified as a signature of quantum-like chaos. Continuous periodogram power spectral analyses of normalised daily, monthly and annual Dow Jones Index for the past 100-years show that the power spectra follow the universal inverse power law form of the statistical normal distribution in agreement with model prediction. Dow Jones Index therefore exhibits self-organized criticality which is a signature of quantum-like chaos on all time scales from days to years. All the data sets exhibit periodicities close to model predicted values. The apparently noisy, irregular fractal fluctuations of the Dow Jones Index contribute to the formation of robust selfsimilar geometrical structures which indicate the surprising resilience of market economy over a period of 100 years.