Multiscale Irreversibility And Complexity Analysis Of Time Series

Real-world complex systems are composed of various internal components which interact across multiple temporal and spatial scales,showing multiple hierarchies,e-mergence and self-organizing,etc.These make the understanding and characterization of complex systems much more difficult.The main focus of this thesis is applying the irreversibility and complex analysis on time series to explore the inner structure and dynamics of complex systems.Usually,complex system time series has the charac-teristic of nonstationarity and nonlinearity,so the traditional methods which based on stationary and linear hypothesis is no longer proper to apply.In this thesis,we study the irreversibility of nonstationary time series and the dependence of irreversibility on multiple time scale,based on asymmetry of probability distribution.We further study the complexity and its dependence on multi-scale based on entropy analysis from infor-mation theory.This thesis consists of 6 chapters,which is structured as follows:In Chapter 1,we briefly introduce the research background,object,significance and the main works of this thesis.In Chapter 2,we investigate the variations and discuss the dependence of time irre-versibility analysis on different time scales.We focus not only on that time irreversibil-ity index and measurement based on visibility graph(VG),but also that how such prop-erties change with the time scale.Then,we propose the comprehensive multiscale irreversibility analysis based on PG index and based on directed horizontal visibility graph(DHVG),respectively,and firstly analyze six artificial series from white noise,1/f noise,uniform distribution U[0,1],Henon map,logistic map and one-dimensional random walk.Specifically,we study and compare the results of noise added series to verify the validity and robustness of these two models.In addition,we apply the time irreversibility measurements on financial time series and find out that the irreversibility degree of stock series in the same area(like Asian or American)will be closer than others.The results support that we can understand the inner structures and complexity of time series and classify various time series via irreversibility analysis on multiple scales.In Chapter 3,we propose a time irreversibility analysis method which based on se-ries segmentation.In this method,we introduce Jensen-Shannon divergence measure-ment which can detect the change points of sequence,and apply to quantify the char-acteristic of segments from time series,and firstly propose the cross check idea which compare the segments between the series and its subsequence,and identify the common segments which have same boundaries,also measure the irreversibility of these com-mon segments.Then,we employ this method to analyze the oil price series,and figure out the temporal distribution of these common segments is fairly close to the time period of crises,wars or other important events.Besides,we compare the time irreversibility analysis of each segment from daily and weekly price series,and the results show that the significant influence of time scale on the local structure of time series.In Chapter 4,we focus on the multiscale complexity analysis of nonstationarity time series and propose two models.Firstly,we propose the multiscale cross-sample entropy(MCSE)which based on cross-sample entropy(CSE),and apply to measure the complexity between two series,and show the cross relation of them.We employ the MCSE to investigate the similarity and synchronous of financial series.Besides,the complexity of time series has the influence on the synchronous between multiple time series,so we modify the algorithm and set a new measurement ACSE to evaluate the dynamic complexity among multiple series.Secondly,based on permutation entropy,we introduce multiscale weighted-permutation entropy analysis(MSWPE),to quantify the complexity from internal arrangement of time series.The simulated results of bi-nomial multifractal series shows that MSWPE is much stable and reliable in spiky data analyzing.We use MSWPE method to investigate complexities of traffic congestion series,and obtain that the patterns of weekend traffic time series differ from that of the workday time series.In Chapter 5,we discuss the correlation of nonstationary time series on different time scales.First,we propose the multi scale detrended fluctuation analysis to analyze local scale exponents of time series and measure the dependence of dynamic correla-tion on scale range.The estimation of local scale exponent method is different from detrended fluctuation analysis(DFA),and overcomes the limitation of one scale,and shows more details of scale properties,also provides reliable results of the correlation in different scale range.Then,we analyze the heartbeat time series in different patholog-ic states.The results show that the healthy subjects have higher local scale exponents in different scale range,which indicate that the healthy system has higher complexi-ty.While the local scale exponents of patients are fluctuating along with scale range.Furthermore,we also quantify the effects of outliers,length and gender on local scale exponents to show the validity of multiscale detrended fluctuation analysis.In Chapter 6,we summarize this thesis and the future work.