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In this paper, we propose Jensen–Shannon divergence (JSD) based on horizontal visibility graph (HVG) to measure the time series irreversibility for both stationary and non-stationary series efficiently. Numerical simulations are first conducted to show the validity of the proposed method and then empirical applications to the financial time series and traffic time series are investigated. It can be found that JSD shows better robustness than Kullback–Leibler divergence (KLD) on quantifying time series irreversibility and correctly distinguishes the different type of simulated series. For the empirical analysis, JSD based on HVG is able to detect the significant time irreversibility of stock indices and reveal the relationship between different stock indices. JSD results show the time irreversibility of speed time series for different detectors and present better accuracy and robustness than KLD. The hierarchical clustering based on their behavior of time irreversibility obtained by JSD classifies the detectors into four groups. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we employ multiscale cross-sample entropy (MSCE), multiscale detrended cross-correlation analysis (MSDCCA) and DCCA cross-correlation coefficient (σDCCA) measurement to investigate the relationship between time series among different stock markets. We report the results of synchronism and cross-correlation behaviors in US and Chinese stock markets by these three methods. It can be concluded that the MSCE analysis point out the similarity on the cross-correlation among the stock markets while the MSCE makes it difficult to distinguish the indices in the same region and identify the difference and uniqueness of stock markets. However, both the MSDCCA analysis and σDCCA analysis reflect the similarity and uniqueness on the cross-correlation behaviors and reach the consistency. Furthermore, MSDCCA gives detailed multiscale cross-correlation structures and show some new interesting characteristics and conclusions, while the multiscale analysis by σDCCA provides a large amount of information on the cross-correlations and quantifies the level of cross-correlation more clearly and intuitively. MSDCCA and σDCCA methods may be more proper measures for the investigation of the cross-correlation between time series. We believe that such researches are relevant for a better understanding of the stock market mechanisms, and may lead to a better forecasting of the stock indices. [ABSTRACT FROM AUTHOR]