The Complexity And Correlation Analysis Of Time Series Of Complex System

In the real world complex system can be seen everywhere.Analysing time series from these complex systems is one of the important ways to study their internal mechanisms and operational mechanisms.In this paper we focus on the complexity and correlation analysis of time series.Based on some previous researches,several new statistical models are proposed and applied to the analysis of financial time series and traffic signals.First,we study the complexity of time series based on entropy.We propose two new models of modified generalized sample entropy and surrogate data analysis and generalized permutation entropy analysis based on a two-index entropic form.The modified generalized sample entropy and surrogate data analysis,which not only effectively overcomes the limitations of the numerical degradation and the harsh relationship between the length of the time series and the length of the pattern vector from the original method,but also has significant advantages in terms of estimation accuracy,data sensitivity,noise resistance and quantitative analysis,uses the Hausdorff distance to replace the distance of the original method.The generalized permutation entropy analysis based on a two-index entropic form generalizes the permutation entropy into the form with two parameters,which can effectively amplify the subtle changes and the overall trend of the original permutation entropy in continuous sequences.Meanwhile,there is also a power-law relationship between the generalized permutation entropy and the index parameter.We then study the correlation of the time series based on the detrended fluctuation analysis.We propose two methods of cross correlation analysis based on empirical mode decomposition and ensemble empirical mode decomposition and multifractal detrended fluctuation analysis and surrogate data analysis.In the cross-correlation analysis based on empirical mode decomposition and ensemble empirical mode decomposition,we study the long-term cros-correlation between different stock markets from a new perspective by using empirical model decomposition,ensemble empirical mode decomposition and DCCA cross correlation coefficient.Multifractal detrended fluctuation analysis and surrogate data analysis is inspired by generalized sample entropy and surrogate data analysis,which is combined with multifractal detrended fluctuation analysis.The traffic signals of Beijing is studied.We find that the traffic signal and the artificial binary multifractal sequence have high similarity about the shape of curves.They have similar characteristics of multiple fractal and correlation.Finally,we study the multiscale behavior of time series based on the order recurrence plot.We propose a new method of multiscale recurrence quantification analysis based on order recurrence plot.Compared with the conventional recurrence quantification analysis,multiscale recurrence quantification analysis,which is combined with multiscale technology,can discover and identify the potential properties of different systems on different time scales.The results show that the performances of recurrence on the large time scales are different from those of the traditional single time scale,and some systems have more accurate results on the large time scale.Multiscale recurrence quantification analysis has a strong advantage in complex system identification.