In this paper, we propose a new method of Rényi entropy and surrogate data analysis as a new measure to assess the complexity of a complex dynamical system. Simulations are conducted over artificial sequence and stock market series to provide model test and empirical analysis. The results show that the new method has a strong identification for different series and the [Formula: see text] curves of stock markets are all successfully fitted by exponential functions. These results can be well identified and analyzed in depth.

Sample entropy is a prevailing method used to quantify the complexity of a time series. In this paper a modified method of generalized sample entropy and surrogate data analysis is proposed as a new measure to assess the complexity of a complex dynamical system such as traffic signals. The method based on similarity distance presents a different way of signals patterns match showing distinct behaviors of complexity. Simulations are conducted over synthetic data and traffic signals for providing the comparative study, which is provided to show the power of the new method. Compared with previous sample entropy and surrogate data analysis, the new method has two main advantages. The first one is that it overcomes the limitation about the relationship between the dimension parameter and the length of series. The second one is that the modified sample entropy functions can be used to quantitatively distinguish time series from different complex systems by the similar measure.

In this paper, we propose a new method of multiscale recurrence quantification analysis (MSRQA) to analyze the structure of order recurrence plots. The MSRQA is based on order patterns over a range of time scales. Compared with conventional recurrence quantification analysis (RQA), the MSRQA can show richer and more recognizable information on the local characteristics of diverse systems which successfully describes their recurrence properties. Both synthetic series and stock market indexes exhibit their properties of recurrence at large time scales that quite differ from those at a single time scale. Some systems present more accurate recurrence patterns under large time scales. It demonstrates that the new approach is effective for distinguishing three similar stock market systems and showing some inherent differences.

Empirical mode decomposition (EMD) is a data-driven signal analysis method for nonlinear and nonstationary data. Since it is intuitive, direct, posterior and adaptive, EMD is widely applied to various fields of study. In this paper, EMD and ensemble empirical mode decomposition (EEMD), a modified method of EMD, are applied to financial time series. Through analyzing the intrinsic mode functions (IMFs) of EMD and EEMD, we find EEMD method performs better on the orthogonality of IMFs than EMD. With clustering the ordered frequencies of IMFs, the IMFs obtained from EEMD method are grouped into high-, medium-, and low-frequency components, representing the short-, medium-, and long-term volatilities of the index sequences, respectively. With the cross-correlation analysis of DCCA cross-correlation coefficient, our findings allow us to gain further and detailed insight into the cross-correlations of stock markets.

In this paper a modified method of generalized sample entropy and surrogate data analysis is proposed as a new measure to assess the complexity of a complex dynamical system such as stock market. The method based on Hausdorff distance presents a different way of time series patterns match showing distinct behaviors of complexity. Simulations are conducted over synthetic and real-world data for providing the comparative study. Results show that the modified method is more sensitive to the change of dynamics and has richer information. In addition, exponential functions can be used to successfully fit the curves obtained from the modified method and quantify the changes of complexity for stock market data. (C) 2015 Elsevier B.V. All rights reserved.

Complexity in time series is an intriguing feature of living dynamical systems such as traffic systems, with potential use for identification of system state. Here, we introduce a method for complex system analysis, called generalized sample entropy and surrogate data analysis, to measure the complexity in traffic signals. The behavior of the weekday series is quite different from that of the weekend series. In addition, we propose and discuss a new method of multifractality based on multifractal detrended fluctuation analysis (MF-DFA) and surrogate data MF-DFA is the roost popular method to detect multifractal characteristics of nonstationary time series. This new method is further applied to binomial multifractal series and traffic signals of Beijing, China. Results show that multifractal characteristics of the artificial data are regular and distinguishing the traffic signals of different patterns is significant. Besides, we find that there is a connection of multifractal characteristics between binomial multifractal series and traffic signals. (C) 2015 Elsevier B.V. All rights reserved.

Permutation entropy (PE) is a novel measure to quantify the complexity of nonlinear time series. In this paper, we propose a generalized permutation entropy (PEq,δ) based on the recently postulated entropic form, Sq,δ, which was proposed as an unification of the well-known Sq of nonextensive-statistical mechanics and Sδ, a possibly appropriate candidate for the black-hole entropy. We find that PEq,δ with appropriate parameters can amplify minor changes and trends of complexities in comparison to PE. Experiments with this generalized permutation entropy method are performed with both synthetic and stock data showing its power. Results show that PEq,δ is an exponential function of q and the power (k(δ)) is a constant if δ is determined. Some discussions about k(δ) are provided. Besides, we also find some interesting results about power law.