The Hurst Exponent Application in the Fractal Analysis of the Russian Stock Market

Abstract

The main purpose of this report is to investigate dynamics and behaviour of the financial time series for the Russian market using the fractality conception which was initially introduced by Mandelbrot [1]. The fractals have already been proved themselves as a model which describes experimental data better than previously used conventional theories in such fields of science like radiolocation, natural resources investigations, distant sounding, navigation, meteorology, information processing from unmanned aerial vehicles (UAV) and synthetic aperture radars (SAR), medicine and biology [2, 3]. At the same time, there is no fractal unified theory of the financial data behaviour. There are just few separate works devoted this topic; however, some worthy efforts were already done in this area for the last years [4–6]. It was shown that price changes rather obeyed to the Levi flight rules than to the Gaussian distribution and also we could watch the evolution from the effective market hypothesis to the fractal market hypothesis which can better explain the market crashes, especially during crises. Here, we applied the fractal approach to the Russian young market (about 20 years of history, 2 significant crises) and calculated Hurst exponents for some stocks and indexes to prove the fractality.