Table of Contents
Journal of Chaos
Volume 2014 (2014), Article ID 346743, 8 pages
http://dx.doi.org/10.1155/2014/346743
Research Article

Transport Catastrophe Analysis as an Alternative to a Monofractal Description: Theory and Application to Financial Crisis Time Series

1Faculty of Physics, Moscow State University of M. V. Lomonosov, Leninskie Gory, Moscow 119991, Russia
2Analytics Division, IFC Markets Corp., 145-157 St. John Street, London EC1V 4PY, UK

Received 25 May 2014; Revised 3 August 2014; Accepted 18 August 2014; Published 14 September 2014

Academic Editor: Norbert Marwan

Copyright © 2014 Sergey A. Kamenshchikov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 precatastrophic 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 introduced as an indicator of phase transition. A combination of diffusive and Reynolds analyses has been applied for a description of a time series of Dow Jones Industrial weekly prices for the world financial crisis of 2007–2009. Diffusive and Reynolds parameters showed 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.