Effect of detrending on multifractal characteristics

Different variants of MFDFA technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending polynomial used within the MFDFA method. The relation between the width of the multifractal spectrum (as well as the Hurst exponent) and the order of the polynomial used in calculation is evident. Furthermore, type of this relation itself depends on the kind of analyzed signal. Therefore, such an analysis can give us some extra information about the correlative structure of the time series being studied.

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

[2]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[3]  José F Fontanari,et al.  Multifractal analysis of DNA walks and trails. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  H. Nakao.  Multi-scaling properties of truncated Lévy flights , 2000, cond-mat/0002027.

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

[6]  Zhiping P. Pang,et al.  Integrative genomic and functional analyses reveal neuronal subtype differentiation bias in human embryonic stem cell lines , 2007, Proceedings of the National Academy of Sciences.

[7]  E. Bacry,et al.  The Multifractal Formalism Revisited with Wavelets , 1994 .

[8]  R. Voss,et al.  ‘1/fnoise’ in music and speech , 1975, Nature.

[9]  Danuta Makowiec,et al.  Multifractal estimates of monofractality in RR-heart series in power spectrum ranges , 2009 .

[10]  J. Kwapień,et al.  Physical approach to complex systems , 2012 .

[11]  M. Ausloos.  Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  H. Stanley,et al.  Multifractal phenomena in physics and chemistry , 1988, Nature.

[13]  P. Poggi,et al.  Uncovering latent singularities from multifractal scaling laws in mixed asymptotic regime. Application to turbulence , 2007, 0711.4862.

[14]  Peter E. Strizhak,et al.  Multifractal Properties of Copper Sulfide Film Formed in Self-Organizing Chemical System , 2002 .

[15]  Jaroslaw Kwapien,et al.  Computational approach to multifractal music , 2011, ArXiv.

[16]  Morten H. Christiansen,et al.  Language as shaped by the brain. , 2008, The Behavioral and brain sciences.

[17]  L. Amaral,et al.  Multifractality in human heartbeat dynamics , 1998, Nature.

[18]  J. Kwapień,et al.  Wavelet versus detrended fluctuation analysis of multifractal structures. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  A. Ludwig,et al.  Boundary criticality and multifractality at the two-dimensional spin quantum Hall transition , 2008, 0803.1343.

[20]  Jaroslaw Kwapien,et al.  The foreign exchange market: return distributions, multifractality, anomalous multifractality and the Epps effect , 2010, 1011.2385.

[21]  A. James.  2010 , 2011, Philo of Alexandria: an Annotated Bibliography 2007-2016.

[22]  Wei-Xing Zhou,et al.  The components of empirical multifractality in financial returns , 2009, 0908.1089.

[23]  Zhi-Yuan Su,et al.  Multifractal analyses of music sequences , 2006 .

[24]  K. Hsü,et al.  Fractal geometry of music. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[25]  J. Kwapień,et al.  Quantitative features of multifractal subtleties in time series , 2009, 0907.2866.