Authors: Sergey A. Kamenshchikov
The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for monofractal Brownian processes: nondifferentiability, Brownian nature of process and a linear memory measure. We have extended a sense of a Hurst factor by consideration of a phase diffusion power law. It was shown that pre-catastrophic stabilization as an indicator of bifurcation leads to a new minimum of momentary phase diffusion, while bifurcation causes an increase of the momentary transport. An efficiency of a diffusive analysis has been experimentally compared to the Reynolds stability model application. An extended Reynolds parameter has been introduces as an indicator of phase transition. A combination of diffusive and Reynolds analysis has been applied for a description of a time series of Dow Jones Industrial weekly prices for a world financial crisis of 2007-2009. Diffusive and Reynolds parameters shown an extreme values in October 2008 when a mortgage crisis was fixed. A combined R/D description allowed distinguishing of market evolution short-memory and long memory shifts. It was stated that a systematic large scale failure of a financial system has begun in October 2008 and started fading in February 2009.
Comments: 12 Pages. Journal of Chaos, Volume 2014, Article ID 346743. Author: ru.linkedin.com/pub/sergey-kamenshchikov/60/8b1/21a/
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