The Study Of Complexity And Recurrence In Time Series

In recent years,the study of complex systems has received more and more atten-tion.Analyzing the time series of output of complex systems is an important means to understand the behavior characteristics of complex systems.This paper proposes sev-eral new methods to study the complexity and recurrence of time series.The methods are applied to the financial system time series,the sleep physiological time series,and the traffic flow time series respectively.First of all,we studied the higher-order dispersion(HOD)method of the first pass time(FPT)probability and its application in financial market.Based on this method,we study some properties of the transaction data in three Chinese stock markets and the three American stock markets.By using the HOD method to compare the different FPT decay curves,the market was successfully classified.The long-range correlation,the fat tail of the generalized PDF and its coupling with nonlinear correlation are the main factor that causes the multifractal of time series.we take the fluctuation function of multifractal detrended fluctuation analysis(MF-DFA)to distinguish the market and obtains the consist results as the HOD method,whereas the HOD method is capable of fractionizing the stock markets effectively in the same region.Then,this paper also studied the joint cross-recursive map(JCRP)method and its application in sleep physiological signals.The whole night sleep usually contains three main stages:awake(WAKE),rapid eye movement(REM)and non-rapid eye movement(NREM:SWS,N2 and N1).On the one hand,we studied the recurrent characteristics between the cardiac system(ECG signals)and the respiratory system(airflow signals).All the RQA metrics of the proposed JCRP and the partial RQA metrics of the CRP and JRP give valid The classification in three main stages(WAKE,REM and NREM).On the other hand,three different EEG signal channels were used to study the interactions of different subsystems of the brain system during sleep.In this case,the RQA measures of CRP,JRP and JCRP do good in distinguishing the recurrent behaviors of SWS,N2,and {N1,REM,WAKE}.Since the background waves of EEG signals in {N1,REM,WAKE} are more similar,the discrimination between them often need additional signals.Especially,the JCRP and its RQA measures give more significant difference between various sleep stages.In addition,JCRP and its RQA metrics show more significant differences between different sleep stages.Finally,based on permutation entropy,this paper proposes multiscale permuta-tion Fisher information(MPFIM)and weighted multiscale permuted Fisher Informa-tion(WMPFIM)methods.FIM is a method of describing the complexity of dynamic systems.The composition of FIM contains the measure of distribution gradient,so it is also sensitive to tiny local disturbance.We apply the MPFIM and WMPFIM methods to the Beijing Traffic Congestion Index(TCI)time series,and comparing their differ-ences and similarities on weekdays and weekends.The study found that MPFIM and WMPFIM have common fluctuation characteristics for all working days,while week-end MPFIM and WMPFIM also have the same fluctuation characteristics.The MPFIM and WMPFIM methods reveal the differences in the complexity of the TCI series on weekdays and weekends well.However,the WMPFIM method can more significantly demonstrate the difference in the TCI seires complexity between workdays and week-ends,and contains more sequence structure information.