Fractal volatility of price series

The problem of constructing an interval valuation of the volatility (root-mean-square deviation) of price time series is studied in this paper. Dependencies are given allowing determining the real, substantially different from the corresponding indicators under the normal law of their distribution, the volatility range based on the base time interval. The proposed methodology makes it possible to take into account the risks of investing in the real conditions of the functioning of the stock market. The study of the simplest algorithm for estimating the fractal dimensions of time series based on the calculation of the Hurst index is carried out. The method is based on a one-point approximation of the magnitude of the normalized span at the planning step by a linear function. The estimation of the spectrum of fractal dimensions based on the Hurst index is made, the analysis of which makes it possible to carry out a complex justification of the choice of a tool for investing. The practical approbation of the proposed methodology was carried out by examining the shares of issuers belonging to different echelons in terms of liquidity. The developed methods and algorithms are simple, unified and easily implemented, for example, in the MS Excel environment.