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

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  • Sergey A. Kamenshchikov

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.

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  • Sergey A. Kamenshchikov, 2014. "Transport catastrophe analysis as an alternative to a fractal description: theory and application to financial crisis time series," Papers 1405.6990, arXiv.org, revised Sep 2014.
    • Handle: RePEc:arx:papers:1405.6990
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    1. Dubovikov, M.M & Starchenko, N.V & Dubovikov, M.S, 2004. "Dimension of the minimal cover and fractal analysis of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 591-608.
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    Cited by:

    1. Ju Zhang & Qingwu Hu & Shaohua Wang & Mingyao Ai, 2017. "Variation Trend Analysis of Runoff and Sediment Time Series Based on the R / S Analysis of Simulated Loess Tilled Slopes in the Loess Plateau, China," Sustainability, MDPI, vol. 10(1), pages 1-17, December.
    2. Sergey Kamenshchikov, 2015. "Bifurcation patterns of market regime transition," Papers 1507.03141, arXiv.org, revised Jan 2016.

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