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Scalar time series considered in most studies may be not sufficient to reconstruct the dynamics, while using multivariate time series may demonstrate great advantages over scalar time series if they are available. Multivariate time series are available in the traffic system and we intend to examine the issue for the real data in the traffic system. In this paper, we propose the multivariate predicting method and discuss the prediction performance of multivariate time series by comparison with univariate time series and K-nearest neighbor (KNN) nonparametric regression model. The three kinds of forecast accuracy measure for multivariate predicting method are smaller than those for the other two methods in all cases, which suggest the predicting results for traffic time series by multivariate predicting method are better and more accurate than those based on univariate time series and KNN model. It demonstrates that the proposed multivariate predicting method is more successful in predicting the traffic time series than univariate predicting method and KNN method. The multivariate predicting method has a broad application prospect on prediction because of its advantage on recovering the dynamics of nonlinear system. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the composite multiscale cross-sample entropy (CMCSE) which may induce undefined entropies and then further propose the refined composite multiscale cross-sample entropy (RCMCSE) which modifies CMCSE. First, we apply multiscale cross-sample entropy (MCSE), CMCSE and RCMCSE methods to three types of artificial time series in order to test the validity and accuracy of these methods. Results show that RCMCSE reduces not only standard deviation, but also the probability of inducing undefined entropy effectively, which can provide better robustness and more accurate entropies. Then, these three methods are employed to investigate financial time series including US and Chinese stock indices. For the study between stock indices in the same region, some conclusions which are consistent with previous study are drawn by the RCMCSE results. Meanwhile, it can be found that undefined entropies are induced and the numbers of inducing undefined entropy by three methods for investigation between three US stock indices and two Chinese mainland stock indices are given. Compared with MCSE and CMCSE, RCMCSE method is capable of reducing the number of undefined entropy and providing more accurate entropies. Moreover, the differences on inducing undefined entropy between results for US stock indices & two Chinese mainland stock indices and results for US stock indices & HSI demonstrate a much closer relation between US stock markets and HSI than between US stock markets and two Chinese mainland stock markets. Hence, it can be concluded that RCMCSE is more applicable for the study between US and Chinese stock markets. [ABSTRACT FROM AUTHOR]

We introduce an entropic segmentation algorithm and apply it to decompose the financial sequences into compositionally homogeneous domains. To probe more about the nature of the financial time series, we investigate the statistical properties of the segment from the view of segmentation position and segment length first. We reveal some important and interesting conclusions and information hidden in these time series of stock markets. Then, we focus on the study of the intrinsic properties for each segment in the time series from two aspects: time irreversibility and correlation. The fluctuations on the time irreversibility and the scaling exponent all support that the segments present compositional heterogeneity and verify the segmentation. Meanwhile, we conclude that time irreversibility is inherent in the stock time series and verifies that stock markets are nonequilibrium systems essentially even though segmentation. Moreover, the scaling exponents for each segment point out that the traditional detrended fluctuation analysis is not applicable to measure the correlation for the whole original time series of stock market. [ABSTRACT FROM AUTHOR]