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Signatures of Quantum-like Chaos in Dow Jones Index

A. Mary Selvam
Year: 2003 Pages: 6
Keywords: inverse power law spectra, Dow Jones index, chaos, fractals, nonlinear dynamics, 1/f noise, self-organized criticality

Dow Jones Index time series exhibit irregular or fractal fluctuations on all time scales from days, months to years. The apparently irregular (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 in space or time is generic to all dynamical systems in nature and is identified as self-organized criticality. Selfsimilarity implies long-range space-time correlations or non-local connections. It is important to quantify the total pattern of fractal fluctuations for predictability studies, e.g., weather and climate prediction, stock market trends, etc. The author has developed a general systems theory for universal quantification of the observed inverse power law spectra in dynamical systems. The model predictions are as follows.

  1. The power spectra of fractal fluctuations follow the universal and unique inverse power law form of the statistical normal distribution.
  2. The nonlocal connections or long-range correlations in space or time exhibited by the fractal fluctuations are signatures of quantum-like chaos in dynamical systems.
  3. The apparently irregular geometry of the fractal fluctuations forms the component parts of a unified whole precise geometrical pattern of the logarithmic spiral with quasiperiodic Penrose tiling pattern for the internal structure. Conventional power spectral analyses will resolve the logarithmic spiral pattern as an eddy continuum with progressive increase in eddy phase angle.
  4. 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.

The fractal fluctuations of the non-stationary Dow Jones Index time series therefore exhibit signature of quantum-like chaos on all time scales from days to years.