Effect Of Filters On Multivariate Multifractal Detrended Fluctuation Analysis

We investigate how various linear and nonlinear filters affect the scaling properties of long-range power-law multivariate synthetic series quantified by multivariate multifractal detrended fluctuation analysis (MV-MFDFA). We consider four types of transforms which are often encountered in physical and physiological processes: linear, nonlinear polynomial, logarithmic and power-law filters. The effect of filters is analyzed by numerical simulation of synthetic series generated by ARFIMA process and binomial multifractal model. The representation of auto-correlation properties of synthetic series before and after the transforms is illustrated by 3D Hurst surface, and the difference of effect is quantified by the proposed generalized mean distance. We find that the linear filters do not change the scaling properties of both synthetic series, while the effect of nonlinear polynomial is correlated with the power of the polynomial filter. For logarithmic and exponential filter, the scaling behavior is not affected for some values of the parameters.