Statistical Analysis Of Financial Continuous Fluctuation Intensity Model And Voter Interacting System

The study on nonlinear fluctuation behaviors of financial dynamics has long been the core concern of financial research.Investigations on the volatility dynamics of stock markets are critically important to evaluate investment risks,avoid stock markets crisis,choose to purchase stock portfolio and comprehend some meaningful properties of financial markets.Based on the return volatility series of the real financial market stock indices,a new concept called continuous fluctuation intensity(CFI)is put forward to characterize the fluctuation duration of stock markets and to measure the overall fluctuation intensity of a period in the present paper.The CFI represents the duration for continuous increasing or decreasing return volatilities(or normalized absolute returns)above or below a previous day's value.Distinguished from previous studies on return volatility,the CFI no longer selects a threshold in advance,but chooses a sequence of absolute returns that are continuously growing(or falling).The CFI depicts the overall intensity of absolute returns in a continuously growing(or falling)series,which can be regarded to quantify the fluctuation risk of financial markets during a period,to some extent.To investigate the nonlinear properties of CFI,the probability distribution and p value inspection are applied to inquire tail behaviors and pow-law scaling behaviors of CFI series.Autocorrelation and scatter plot analyses are utilized to study the correlation phenomena of CFI series as well.Further,fractional sample entropy and fuzzy entropy are employed to explore the complexity of CFI series.The complexity measured by these two methods reflects the regularity of CFI series in a certain degree.In order to verify the feasibility of the new statistics,we also use the voter model in the financial physical statistics model to simulate the data and construct the simulation CFI series,and then we use the same methods for statistical analysis.By comparing and analyzing the statistical differences between CFI series,simulation CFI series and return volatil-ity series,the statistical properties and complexity behaviors of the new statistics are revealed.The study manifests that the study of the proposed concept is feasible and valuable.In this paper,the data sets applied for the investigation originate from six global stock market indexes:SSE,SZSE,HSI,DJIA,IXIC and S&P500.