Complex waveforms appearing in natural phenomena can often be analyzed by representing them as the sum of individual, superimposed frequencies and their harmonics, a common technique in Fourier analysis. The graphical representation of this is known as a power spectrum, where each peak in the spectrum corresponds to a specific frequency in the original signal. A complex signal, perhaps indistinguishable by visual inspection from white noise, can easily be revealed as a series of peaks and valleys where the position on the x-axis signifies the frequency, and the height along the y direction is the relative strength of the signal at that frequency. Power spectra are extensively used in many disciplines, including electrical engineering, image processing, and, as this monograph shows, human behavior.

Here is an interesting application of this technique, demonstrating how underlying many so-called random phenomena, as well as activities we like to think of as strictly under human control, arise directly out of the statistical properties of quantum space-time. The universe appears to be neither random NOR deterministic. It isn’t something “in between” either. It appears to be something else altogether.

It might be tempting to attempt to harness these principles in order to make a killing on the stock market, but I suspect the Uncertainty Principle will forbid this. The introduction of hedge funds designed to damp out the effect of random variation in the market led inevitably to financial instability when indiscriminately and inappropriately applied. Stochastic processes do not respond predictably to deliberate human intervention.

Spectral Analysis of Dow Jones Index and Comparison with
Model Predicted Cycles During 1900-2005
by A. M. Selvam

http://arxiv.org/ftp/physics/papers/0603/0603065.pdf

Abstract
The day-to day fluctuations of Dow Jones Index exhibit fractal fluctuations,
namely, a zigzag pattern of successive increases followed by decreases on all
space-time scales. Self-similar fractal fluctuations are generic to dynamical
systems in nature and imply long-range space-time correlations. The
apparently unpredictable (chaotic) fluctuations of dynamical systems exhibit
underlying order with the power spectra exhibiting inverse power law form,
now identified as self-organized criticality. The physics of self-organized
criticality is not yet identified. A general systems theory developed by the
author shows that self-similar fractal fluctuations are signatures of quantumlike
chaos in dynamical systems of all size scales ranging from the subatomic
dynamics of quantum systems to macro-scale fluid flows. The model predicts
the universal inverse power-law form of the statistical normal distribution for
the power spectra of fractal space-time fluctuations of dynamical systems. In
this paper it is shown that the power spectrum of 100 years of normalized
month to month fluctuations of Dow Jones index exhibits the universal
inverse power law form of the statistical normal distribution consistent with
model prediction. It is shown that prediction of times of occurrence of
maxima and minima during the two years subsequent to the data period used
for the study is possible using the dominant peak periodicities obtained from
the continuous periodogram spectral analysis of historic data.