Multiscale Detrended Cross-Correlation Analysis of Traffic Time Series Based on Empirical Mode Decomposition

In this paper, we propose multiscale detrended cross-correlation analysis (MSDCCA) to detect the long-range power-law cross-correlation of considered signals in the presence of nonstationarity. For improving the performance and getting better robustness, we further introduce the empirical mode decomposition (EMD) to eliminate the noise effects and propose MSDCCA method combined with EMD, which is called MS-EDXA method, then systematically investigate the multiscale cross-correlation structure of the real traffic signals. We apply the MSDCCA and MS-EDXA methods to study the cross-correlations in three situations: velocity and volume on one lane, velocities on the present and the next moment and velocities on the adjacent lanes, and further compare their spectrums respectively. When the difference between the spectrums of MSDCCA and MS-EDXA becomes unobvious, there is a crossover which denotes the turning point of difference. The crossover results from the competition between the noise effects in the original signals and the intrinsic fluctuation of traffic signals and divides the plot of spectrums into two regions. In all the three case, MS-EDXA method makes the average of local scaling exponents increased and the standard deviation decreased and provides a relative stable persistent scaling cross-correlated behavior which gets the analysis more precise and more robust and improves the performance after noises being removed. Applying MS-EDXA method avoids the inaccurate characteristics of multiscale cross-correlation structure at the short scale including the spectrum minimum, the range for the spectrum fluctuation and general trend, which are caused by the noise in the original signals. We get the conclusions that the traffic velocity and volume are long-range cross-correlated, which is accordant to their actual evolution, while velocities on the present and the next moment and velocities on adjacent lanes reflect the strong cross-correlations both in temporal and spatial dimensions. We also reveal the similarity and uniqueness in the cross-correlation situations between velocities. Besides, signals on one lane show stronger long-range cross-correlation than that on adjacent lanes. Thus, the multiscale cross-correlation structure acquired by MS-EDXA is more close to the intrinsic mechanism of traffic system and reflects more accurate and more abundant traffic information.