Multifractal cross-correlation analysis of traffic time series based on large deviation estimates

Multiscale analysis of cross-correlation between traffic signals is a developing research area, which helps to better understand the characteristics of traffic systems. Multifractal analysis is a multiscale analysis and almost exclusively develops around the concept of Legendre singularity spectrum, but which is structurally blind to subtle features like non-concavity or nonscaling of the distributions in some degree. Large deviations theory overcomes these limitations, and recently, performing estimators were proposed to reliably compute the corresponding large deviations singularity spectrum. In this paper, we apply the large deviations spectrum based on detrend cross-correlation analysis roughness exponent to both artificial and traffic time series and verify that this kind of approach is able to reveal significant information that remains hidden with Legendre spectrum. Meanwhile, we illustrate the presence of non-concavities in the spectra of cross-correlation between traffic series by the presence or absence of accidents and quantify the presence or absence of scale invariance and the generating mechanism of multifractality for cross-correlation between traffic signals.

[1]  J. Barral,et al.  On the Estimation of the Large Deviations Spectrum , 2011 .

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

[3]  Boris Podobnik,et al.  Detrended cross-correlation analysis for non-stationary time series with periodic trends , 2011 .

[4]  Pengjian Shang,et al.  Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis , 2008 .

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

[6]  Boris Podobnik,et al.  Statistical tests for power-law cross-correlated processes. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Borko Stosic,et al.  Correlations and cross-correlations in the Brazilian agrarian commodities and stocks , 2010 .

[8]  Matthew G. Karlaftis,et al.  Spectral and cross-spectral analysis of urban traffic flows , 2001, ITSC 2001. 2001 IEEE Intelligent Transportation Systems. Proceedings (Cat. No.01TH8585).

[9]  Amir Dembo,et al.  Large Deviations Techniques and Applications , 1998 .

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

[11]  Shlomo Havlin,et al.  Delay-induced chaos with multifractal attractor in a traffic flow model , 2002 .

[12]  M. M. Novak,et al.  Fractals and Beyond: Complexities in the Sciences , 1998 .

[13]  Ivo Grosse,et al.  Power-law correlated processes with asymmetric distributions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  R. E. Wilson,et al.  Mechanisms for spatio-temporal pattern formation in highway traffic models , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[15]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[16]  Pengjian Shang,et al.  MULTISCALE ENTROPY ANALYSIS OF TRAFFIC TIME SERIES , 2013 .

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

[18]  Paulo Gonçalves,et al.  Large deviations estimates for the multiscale analysis of heart rate variability , 2012 .

[19]  Schwartz,et al.  Method for generating long-range correlations for large systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Jacques Lévy Véhel,et al.  Signal representation and segmentation based on multifractal stationarity , 2002, Signal Process..

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

[22]  I. Gasser,et al.  Bifurcation analysis of a class of ‘car following’ traffic models , 2004 .

[23]  M. Meyer,et al.  Self-affine fractal variability of human heartbeat interval dynamics in health and disease , 2003, European Journal of Applied Physiology.

[24]  Wilhelm Leutzbach,et al.  Introduction to the Theory of Traffic Flow , 1987 .

[25]  Ivo Grosse,et al.  Fractionally integrated process with power-law correlations in variables and magnitudes. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Jacques Lévy Véhel,et al.  Continuous Large Deviation Multifractal Spectrum: Definition and Estimation , 1998 .

[27]  A. Schadschneider,et al.  Statistical physics of vehicular traffic and some related systems , 2000, cond-mat/0007053.

[28]  H. Stanley,et al.  Cross-correlations between volume change and price change , 2009, Proceedings of the National Academy of Sciences.

[29]  H. Nicholson,et al.  The prediction of traffic flow volumes based on spectral analysis , 1974 .

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

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

[32]  B. Kerner.  THE PHYSICS OF TRAFFIC , 1999 .

[33]  Manying Bai,et al.  Power law and multiscaling properties of the Chinese stock market , 2010 .

[34]  S. Cerutti,et al.  Multifractality and heart rate variability. , 2009, Chaos.

[35]  Yi Yin,et al.  Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets , 2013 .

[36]  Jacques Lévy Véhel,et al.  On Various Multifractal Spectra , 2004 .

[37]  Pengjian Shang,et al.  The cross-correlations of stock markets based on DCCA and time-delay DCCA , 2012 .

[38]  Rudolf H. Riedi,et al.  Multifractal Properties of TCP Traffic: a Numerical Study , 1997 .