The Genesis of Uncertainty: Structural Analysis of Stochastic Chaos in Finance Markets

Abstract

The presented article is methodological in nature and is devoted to the analysis of observation series of financial asset quotation changes in capital markets. The most important feature of these processes is their instability, which manifests itself in high sensitivity to seemingly minor disturbing factors. This phenomenon is well-studied in the theory of nonlinear dynamical systems and is described by models of deterministic chaos. However, for the processes considered in the article, the dynamic instability of the immersion environment is exacerbated by stochastic uncertainty caused by random fluctuations in the pricing process. As a result, describing observation series of quotations of financial assets is difficult because it involves stochastic chaos. This article analyzes and classifies chaotic series of observations to help model and forecast related processes.

Fractal Patterns in Groundwater Radon Disturbances Prior to the Great 7.9 Mw Wenchuan Earthquake, China

“…The time evolution of fractal phenomena, as well as the roughness of the related time series, can be identified using the Hurst exponent [1,42,43]. Various research topics have been investigated with the use of Hurst exponent, such as hydrology [40,41], astrophysics and applications [44,45], processes of capital markets [46][47][48][49], noisy observations of traces in traffic [50][51][52], seizures prior to epilepsy [53][54][55], climatic dynamics [56], and precursory time series before impending earthquakes [1,7,8,57].…”