EFFECT OF LINEAR AND NONLINEAR FILTERS ON MULTIFRACTAL DETRENDED CROSS-CORRELATION ANALYSIS

When probing the dynamical properties of complex systems, such as physical and physiological systems, the output signal may be not the expected one. It is often a linear or nonlinear filter (or a transformation) of the right one represented the properties we want to investigate. Besides, for a multiple-component system, it is necessary to consider the relations between different influence factors. Here, we investigate what effect kinds of linear and nonlinear filters have on the cross-correlation properties of monofractal series and binomial multifractal series relatively. We use the multifractal detrended cross-correlation analysis (MFDCCA) that has been known well for its accurate quantization of cross-correlations between two time series. We study the effect of five filters: (i) linear (yi = axi + b); (ii) polynomial ; (iii) logarithmic (yi = log(xi + δ)); (iv) exponential (yi = exp(axi + b)); and (v) power-law (yi = (xi + a)b). We find that for both monofractal and multifractal signals, linear filters have no effect on the cross-correlation properties while the influence of polynomial, logarithmic and power-law filters mainly depends on (a) the strength of cross-correlations in the original series; (b) the parameter b of the polynomial filter; (c) the offset δ in the logarithmic filter; and (d) both the parameter a and b of the power-law filter. In addition, the parameter a and b of the exponential filter change the cross-correlation properties of monofractal signal, yet they have little influence on that of multifractal signal.

[1]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[3]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[4]  H. Stanley,et al.  Quantifying cross-correlations using local and global detrending approaches , 2009 .

[5]  Gabjin Oh,et al.  Understanding volatility correlation behavior with a magnitude cross-correlation function. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  H. Stanley,et al.  Detrended cross-correlation analysis: a new method for analyzing two nonstationary time series. , 2007, Physical review letters.

[7]  H. Stanley,et al.  Quantifying signals with power-law correlations: a comparative study of detrended fluctuation analysis and detrended moving average techniques. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Roberto A. Monetti,et al.  Scaling analysis of trends using DFA , 2001 .

[9]  S. Hajian,et al.  Multifractal Detrended Cross-Correlation Analysis of sunspot numbers and river flow fluctuations , 2009, 0908.0132.

[10]  Shlomo Havlin,et al.  A stochastic model of river discharge fluctuations , 2003 .

[11]  S. Havlin,et al.  Nonlinear volatility of river flux fluctuations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  H. Stanley,et al.  Effect of nonlinear filters on detrended fluctuation analysis. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Wei‐Xing Zhou.  Multifractal detrended cross-correlation analysis for two nonstationary signals. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Tom Chau,et al.  An empirical examination of detrended fluctuation analysis for gait data. , 2010, Gait & posture.

[15]  P. Macklem,et al.  Complex systems and the technology of variability analysis , 2004, Critical Care.

[16]  M. Movahed,et al.  Multifractal analysis of light scattering-intensity fluctuations. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Harvard Medical School,et al.  Effect of nonstationarities on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Pengjian Shang,et al.  Modeling traffic flow correlation using DFA and DCCA , 2010 .

[19]  H. Stanley,et al.  Effect of trends on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  S. Havlin,et al.  Detecting long-range correlations with detrended fluctuation analysis , 2001, cond-mat/0102214.

[21]  Heather J. Ruskin,et al.  Cross-Correlation Dynamics in Financial Time Series , 2009, 1002.0321.

[22]  Boris Podobnik,et al.  Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes , 2007, 0709.0838.

[23]  Pengjian Shang,et al.  Minimizing the effect of exponential trends in detrended fluctuation analysis , 2009 .