Irreversibility And Permutation Entropy Of Financial Time Series

Financial systems,such as the stock market,are regarded as complex systems with typical characteristics such as non-linearity,multi-component and multi-level.In practice,it is very difficult for us to carry out modeling analysis on complex systems themselves,and instead analyze the time series that reflects the dynamic information of the system to explore the internal mechanism of the complex system.The time series derived from the stock market has non-stationary,multi-scale,nonlinear,and other properties,making it difficult to perform more in-depth research on the traditional methods built on the stationarity and linear assumptions.Therefore,in view of the complexity of financial time series,this paper proposes three methods from different perspectives to explore the intrinsic dynamics of financial time series.Firstly,we have studied the time irreversibility of time series,which is a basic characteristic of the non-equilibrium system.Recently,a novel method has been proposed and has been proved to be effectively used to verify the time irreversibility of time series.However,the disadvantage of this method is that it is based on the single scale analysis,and it is difficult to deal with the time series with multiscale characteristics.Then,we extend this method to multiscale analysis,and combine the phase space reconstruction technique to explore more complex systems.The validity of this new method is proved by the time series such as the Delayed Henon map,and the influence of different parameters on the analysis results is discussed.The new method is also applied to analyze stock index data,which succeed to distinguish the time of financial crisis and the plateau,and classify stock index in different regions.Secondly,we propose the refine composite multiscale weighted-permutation entropy(RCMWPE)to explore the complexity of the financial time series.Previously,the multiscale weighted-permutation entropy(MWPE)has been proposed,which has incorporated amplitude information and been applied to account for the multiple inherent dynamics of time series.However,this method has obvious deficiencies in application,that is,its estimated values show large fluctuation for slight variation of the data locations,and a significant distinction only for the different length of time series.These two shortcomings restrict the wide application of the method.Therefore,we proposed RCMWPE,which shows better characteristics and can overcome MWPE's insufficiency effectively through analyzing the data of simulation and stock index.By analyzing the daily price returns of the stock index,we find that the European stock index and Asian stock index have significantly different volatility properties.In addition,the entropy values of Hang Seng Index(HSI)are close to but higher than those of European markets,reflecting the particularity of the Hong Kong economy,both the European economic management mechanism and the influence of Asian commercial behavior.Finally,we propose the multivariate multiscale weighted fractional order generalized entropy(MMWFOE).Another way to improve the MWPE method is to extend it to the generalized case.In addition,because of the mutual influence between multiple time series of the stock market system,the separate processing of each sequence will ignore the cross information,then we propose MMWFOE.The effectiveness of the new method was verified by noise simulation data,and it was successfully verify the conclusion that the pink noise is more complex than the white noise.The result shows that the proposed method can excavate the intrinsic data more comprehensively.In addition,we analyze the two dimensional data of stock exchange return and volume,not only to explore the complexity differences between stock indexes in different regions,but also to show the evolution of the inherent characteristics of the North American financial market,and to study the relations between the changes of intrinsic characteristics and the financial crisis.