Transport catastrophe analysis as an alternative to a fractal description: theory and application to financial crisis time series

TL;DR

This paper introduces a transport catastrophe analysis method as an alternative to fractal descriptions for financial time series, successfully identifying critical market transitions during the 2007-2009 financial crisis.

Contribution

It extends the Hurst factor with phase diffusion analysis and combines diffusive and Reynolds parameters to detect market bifurcations and systemic failures.

Findings

Identified pre-catastrophic stabilization as a bifurcation indicator.

Detected extreme parameter values during October 2008 financial crisis.

Distinguished short-memory and long-memory market shifts.

Abstract

The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for fractal 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. Basic conclusions of a diffusive analysis have been compared to the Lyapunov stability model. 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 short-memory and long memory shifts of a market evolution. It was stated that a systematic large scale failure of a financial system has begun in October 2008 and started fading in February 2009.