Multifractal properties of the Ukraine stock market

Abstract

Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. We used two possible procedures of analyzing multifractal properties of a time series. The first one uses the continuous wavelet transform and extracts scaling exponents from the wavelet transform amplitudes over all scales. The second method is the multifractal version of the detrended fluctuation analysis method (MF- DFA). The multifractality of a time series we analysed by means of the difference of values singularity stregth αmax and αmin as a suitable way to characterise multifractality. Singularity spectrum calculated from daily re- turns using a sliding 1000 day time window in discrete steps of 1. . . 10 days. We discovered that changes in the multifractal spectrum display distinctive pattern around significant “drawdowns”. Finally, we discuss applications to the construction of crushes precursors at the financial markets.