Statistical Analysis Of Nonlinear Potts Financial System Dynamics And Financial Time Series

In this paper,recently introduced permutation entropy and sample entropy are fur-ther developed to the fractional cases,weighted fractional permutation entropy(WFPE)and fractional sample entropy(FSE).The fractional order generalization of information entropy is utilized in the above two complexity approaches,to detect the statistical characteristics of fractional order information in complex systems.The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution,which is useful in describing the dynamics of complex systems.Moreover,the numerical research on nonlinear complexity behaviors is compared be-tween the returns series of Potts financial model and the actual stock markets.And the empirical results confirm the feasibility of the proposed model.And based on the combination of sample entropy and complexity-invariant dis-tance,a new synchrony-measured method,called the composite complexity synchro-nization(CCS),is proposed to measure the degree of synchrony of two time series with same data length.Implementing the multiscale cross-sample entropy and multi-scale composite complexity synchronization(MCCS)analysis for seven representative stock market indexes,multiscale coupling behaviors of logarithmic returns are com-pared.Furthermore,the selective data of different sampling frequency within the same time period are applied to analyze the effect of sampling rate in the data on the MCCS behaviors.And we apply the ensemble empirical mode decomposition to decompose the stock logarithmic returns into the intrinsic mode functions and investigate the extent that they have inherited the coupling behaviors of original returns.Empirical result-s demonstrate the feasibility and effectiveness of the proposed method,and exhibit its superiority in distinguishing the very subtle synchrony behaviors among the time series.