Fractal time series analysis in non-stationary environment

Abstract

A fractal analysis of the Bitcoin time series for the period from 2012 to 2019 is carried out: Hurst exponents were calculated, the behavior of this indicator in dynamics was investigated, V-statistics were plotted. For the automatic determination of the average length of the nonperiodic cycle in the information system of time series analysis, the smoothing method of V-statistics based on the Kaufman’s adaptive moving average and simple moving average with different periods is proposed. The results fractal analysis of the time series of the Bitcoin cryptocurrency price show that the Bitcoin market is characterized by an inescapable efficiency, i.e. periods of effectiveness are replaced periods of inefficiency. This is manifested by changing the type of time series of Bitcoin prices from persistence to random and antipersistence, especially during periods of intense price growth, due to the significant influence on the mechanism of generation of time series of random factors.