New measure of multifractality and its application in finances

Abstract

We provide an alternative method for analysis of multifractal properties of time series. The new approach takes into account the behaviour of the whole multifractal profile of the generalized Hurst exponent $h(q)$ for all moment orders $q$, not limited only to the edge values of $h(q)$ describing in MFDFA scaling properties of smallest and largest fluctuations in signal. The meaning of this new measure is clarified and its properties are investigated for synthetic multifractal data and real signals taken from stock market. We show that the proposed new measure is free of problems one can meet in real nonstationary signals, while searching their multifractal signatures.