Transport Catastrophe Analysis as an Alternative to a Monofractal Description: Theory and Application to Financial Crisis Time Series. (11th September 2014)

• Record Type: Journal Article
• Authors: Kamenshchikov, Sergey A.
• Other Names: Marwan Norbert Academic Editor.
• Is Part Of: Journal of chaos. Volume 2014(2014)
• Publication Date: 2014-09-11
• Subjects: Quantum chaos -- Periodicals; Chaotic behavior in systems -- Periodicals; Chaotic behavior in systems; Quantum chaos; Electronic journals; Periodicals; 515.39
• DOI: 10.1155/2014/346743
• Languages: English
• ISSNs: 2356-7228

Abstract

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.